1
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Hsu CH. Interaction- and phonon-induced topological phase transitions in double helical liquids. NANOSCALE HORIZONS 2024. [PMID: 39049706 DOI: 10.1039/d4nh00254g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/27/2024]
Abstract
Helical liquids, formed by time-reversal pairs of interacting electrons in topological edge channels, provide a platform for stabilizing topological superconductivity upon introducing local and nonlocal pairings through the proximity effect. Here, we investigate the effects of electron-electron interactions and phonons on the topological superconductivity in two parallel channels of such helical liquids. Interactions between electrons in different channels tend to reduce nonlocal pairing, suppressing the topological regime. Additionally, electron-phonon coupling breaks the self duality in the electronic subsystem and renormalizes the pairing strengths. Notably, while earlier perturbative calculations suggested that longitudinal phonons have no effect on helical liquids themselves to the leading order, our nonperturbative analysis shows that phonons can induce transitions between topological and trivial superconductivity, thereby weakening the stability of topological zero modes. Our findings highlight practical limitations in realizing topological zero modes in various systems hosting helical channels, including quantum spin Hall insulators, higher-order topological insulators, and their fractional counterparts recently observed in twisted bilayer systems.
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Affiliation(s)
- Chen-Hsuan Hsu
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan.
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2
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Olshanetsky EB, Gusev GM, Levin AD, Kvon ZD, Mikhailov NN. Multifractal Conductance Fluctuations of Helical Edge States. PHYSICAL REVIEW LETTERS 2023; 131:076301. [PMID: 37656853 DOI: 10.1103/physrevlett.131.076301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 07/23/2023] [Indexed: 09/03/2023]
Abstract
Two-dimensional topological insulators are characterized by the bulk gap and one-dimensional helical states running along the edges. The theory predicts the topological protection of the helical transport from coherent backscattering. However, the unexpected deviations of the conductance from the quantized value and localization of the helical modes are generally observed in long samples. Moreover, at millikelvin temperatures significant mesoscopic fluctuations are developed as a function of the electron energy. Here we report the results of an experimental study of the transport in a HgTe quantum well with an inverted energy spectrum that reveal a multifractality of the conductance fluctuations in the helical edge state dominated transport regime. We attribute observed multifractality to mesoscopic fluctuations of the electron wave function or local density of states at the spin quantum Hall transition. We have shown that the mesoscopic two-dimensional topological insulator provides a highly tunable experimental system in which to explore the physics of the Anderson transition between topological states.
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Affiliation(s)
- E B Olshanetsky
- Institute of Semiconductor Physics, Novosibirsk 630090, Russia
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - G M Gusev
- Instituto de Física da Universidade de São Paulo, 135960-170 São Paulo, SP, Brazil
| | - A D Levin
- Instituto de Física da Universidade de São Paulo, 135960-170 São Paulo, SP, Brazil
| | - Z D Kvon
- Institute of Semiconductor Physics, Novosibirsk 630090, Russia
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - N N Mikhailov
- Institute of Semiconductor Physics, Novosibirsk 630090, Russia
- Novosibirsk State University, Novosibirsk 630090, Russia
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3
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Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator. Symmetry (Basel) 2022. [DOI: 10.3390/sym14081736] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure.
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4
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Deng TS, Pan L, Chen Y, Zhai H. Stability of Time-Reversal Symmetry Protected Topological Phases. PHYSICAL REVIEW LETTERS 2021; 127:086801. [PMID: 34477399 DOI: 10.1103/physrevlett.127.086801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Revised: 03/12/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
In a closed system, it is well known that the time-reversal symmetry can lead to Kramers degeneracy and protect nontrivial topological states such as the quantum spin Hall insulator. In this Letter, we address the issue of whether these effects are stable against coupling to the environment, provided that both the environment and the coupling to the environment also respect time-reversal symmetry. By employing a non-Hermitian Hamiltonian with the Langevin noise term and utilizing the non-Hermitian linear response theory, we show that the spectral functions for Kramers degenerate states can be split by dissipation, and the backscattering between counterpropagating edge states can be induced by dissipation. The latter leads to the absence of accurate quantization of conductance in the case of the quantum spin Hall effect. As an example, we demonstrate this concretely with the Kane-Mele model. Our study can also include interacting topological phases protected by time-reversal symmetry.
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Affiliation(s)
- Tian-Shu Deng
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Lei Pan
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Yu Chen
- Graduate School of China Academy of Engineering Physics, Beijing 100193, China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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5
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Zhang X, Foster MS. Dissipative Hot-Spot-Enabled Shock and Bounce Dynamics via Terahertz Quantum Quenches in Helical Edge States. PHYSICAL REVIEW LETTERS 2021; 127:026801. [PMID: 34296892 DOI: 10.1103/physrevlett.127.026801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Revised: 04/22/2021] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We study quantum quenches of helical liquids with spin-flip inelastic scattering. Counterpropagating charge packets in helical edges can be created by an ultrashort electric pulse applied across a 2D topological insulator. Localized "hot spots" that form due to scattering enable two types of strongly nonlinear wave dynamics. First, propagating packets develop self-focusing shock fronts. Second, colliding packets with opposite charge can exhibit near-perfect retroreflection, despite strong dissipation. This leads to frequency doubling that could be detected experimentally from emitted terahertz radiation.
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Affiliation(s)
- Xinghai Zhang
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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6
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Phong TC, Lam VT, Hoi BD. Tuning electronic phase in noncentrosymmetric quantum spin Hall insulators through physical stimuli. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:325502. [PMID: 34044386 DOI: 10.1088/1361-648x/ac05e4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 05/27/2021] [Indexed: 06/12/2023]
Abstract
In this work, the perturbation-induced phase transitions in noncentrosymmetric quantum spin Hall insulators (QSHIs) are analytically addressed. In particular, the dilute charged impurity, the electric field, and the Zeeman splitting field are considered within the tight-binding Hamiltonian model, Green's function approach, and the Born approximation. Following theC3vsymmetry breaking in the PbBiI compound as a representative QSHI, the band gap becomes larger via the electric field, while the system transits to the semimetallic phase via the dilute charged impurities and Zeeman field, modifying the degenerate states in the electronic density of states. While the coexistence of electric field and impurities demonstrate that the system backs to its initial semiconducting phase, the combined Zeeman field and impurities do not alter the robust semimetallic phase.
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Affiliation(s)
- Tran C Phong
- Center for Theoretical and Computational Physics, University of Education, Hue University, Hue 530000, Viet Nam
| | - Vo T Lam
- Faculty of Natural Sciences Pedagogy, Sai Gon University, 273 An Duong Vuong Str., District 5, Ho Chi Minh City, Vietnam
| | - Bui D Hoi
- Center for Theoretical and Computational Physics, University of Education, Hue University, Hue 530000, Viet Nam
- Department of Physics, University of Education, Hue University, Hue 530000, Vietnam
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7
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Shamim S, Beugeling W, Shekhar P, Bendias K, Lunczer L, Kleinlein J, Buhmann H, Molenkamp LW. Quantized spin Hall conductance in a magnetically doped two dimensional topological insulator. Nat Commun 2021; 12:3193. [PMID: 34045456 PMCID: PMC8160016 DOI: 10.1038/s41467-021-23262-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Accepted: 04/21/2021] [Indexed: 11/22/2022] Open
Abstract
Soon after the discovery of the quantum spin Hall effect, it has been predicted that a magnetic impurity in the presence of strong Coulomb interactions will destroy the quantum spin Hall effect. However, the fate of the quantum spin Hall effect in the presence of magnetic impurities has not yet been experimentally investigated. Here, we report the successful experimental demonstration of a quantized spin Hall resistance in HgTe quantum wells dilutely alloyed with magnetic Mn atoms. These quantum wells exhibit an inverted band structure that is very similar to that of the undoped material. Micron sized devices of (Hg,Mn)Te quantum well (in the topological phase) show a quantized spin Hall resistance of h/2e2 at low temperatures and zero magnetic field. At finite temperatures, we observe signatures of the Kondo effect due to interaction between the helical edge channels and magnetic impurities. Our work lays the foundation for future investigations of magnetically doped quantum spin Hall materials towards the realization of chiral Majorana fermions. The quantum spin Hall effect is expected not to survive the presence of magnetic impurities. Here, authors report full quantization at very low temperatures in HgTe quantum wells alloyed with a few percent of magnetic Mn atoms, due to Kondo screening.
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Affiliation(s)
- Saquib Shamim
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany. .,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany.
| | - Wouter Beugeling
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany.,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Pragya Shekhar
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany.,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Kalle Bendias
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany.,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Lukas Lunczer
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany.,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Johannes Kleinlein
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany.,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Hartmut Buhmann
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany.,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Laurens W Molenkamp
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, Würzburg, Germany. .,Institute for Topological Insulators, Universität Würzburg, Am Hubland, Würzburg, Germany.
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8
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Du T, Li YX, Lu HL, Zhang H, Du S. The competition between the intrinsic and Rashba spin-orbit coupling and effects of correlations on Rashba SOC-driven transitions in the Kane-Mele model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:505601. [PMID: 32990271 DOI: 10.1088/1361-648x/abb517] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 09/03/2020] [Indexed: 06/11/2023]
Abstract
We investigate, firstly, the competition between the Rashba spin-orbit coupling (SOC) and the intrinsic SOC in Kane-Mele model. For the small intrinsic SOC, we investigate the effects of the Rashba SOC on the touching point of the valence and conduction bands when the ratio of the Rashba SOC to the intrinsic SOC is greater than classical value23. For the large intrinsic SOC, we find that the critical ratio of the two SOCs at which the band touching occurs decreases with the increasing intrinsic SOC and the locations of these touching points deviate from pointsKandK' of the Brillouin zone. Furthermore, effects of the Rashba SOC on these touching points are discussed in detail when the ratio is greater than the critical value. The Rashba SOC-driven topologically trivial and non-trivial transitions are also obtained in the first part of the work. Secondly, using the slave-rotor mean field method we investigate the influences of the correlation on the Rashba SOC-driven topologically trivial and non-trivial transitions in both the charge condensate and Mott regions. The topological Mott insulator with gapped or gapless spin excitations which arises from the interplay of the Rashba SOC and correlations is obtained in the work.
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Affiliation(s)
- Tao Du
- Department of Physics, Yunnan Minzu University, Kunming 650504, People's Republic of China
| | - Yue-Xun Li
- Department of Physics, Yunnan Minzu University, Kunming 650504, People's Republic of China
| | - He-Lin Lu
- Department of Physics, Yunnan Minzu University, Kunming 650504, People's Republic of China
| | - Hui Zhang
- Department of Physics, Yunnan Minzu University, Kunming 650504, People's Republic of China
| | - Song Du
- College of Science, Sichuan Agricultural University, Ya'an 625014, People's Republic of China
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9
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Chudzinski P. Contribution of 1D topological states to the extraordinary thermoelectric properties of Bi 2Te 3. Proc Math Phys Eng Sci 2020; 476:20200088. [PMID: 32831608 DOI: 10.1098/rspa.2020.0088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 06/12/2020] [Indexed: 11/12/2022] Open
Abstract
Topological insulators are frequently also one of the best-known thermoelectric materials. It has been recently discovered that in three-dimensional (3D) topological insulators each skew dislocation can host a pair of one-dimensional (1D) topological states-a helical Tomonaga-Luttinger liquid (TLL). We derive exact analytical formulae for thermoelectric Seebeck coefficient in TLL and investigate up to what extent one can ascribe the outstanding thermoelectric properties of Bi2Te3 to these 1D topological states. To this end we take a model of a dense dislocation network and find an analytic formula for an overlap between 1D (the TLL) and 3D electronic states. Our study is applicable to a weakly n-doped Bi2Te3 but also to a broader class of nano-structured materials with artificially created 1D systems. Furthermore, our results can be used at finite frequency settings, e.g. to capture transport activated by photo-excitations.
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Affiliation(s)
- P Chudzinski
- School of Mathematics and Physics, Queen's University Belfast, Belfast, UK
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10
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Sorout AK, Sarkar S, Gangadharaiah S. Dynamics of impurity in the environment of Dirac fermions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:415604. [PMID: 32544895 DOI: 10.1088/1361-648x/ab9d4d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
We study the dynamics of a nonmagnetic impurity interacting with the surface states of a 3D and 2D topological insulator (TI). Employing the linked cluster technique we develop a formalism for obtaining the Green's function of the mobile impurity interacting with the low-energy Dirac fermions. We show that for the non-recoil case in 2D, the Green's function in the long-time limit has a power-law decay in time implying the breakdown of the quasiparticle description of the impurity. The spectral function in turn exhibits a weak power-law singularity. In the recoil case, however, the reduced phase-space for scattering processes implies a non-zero quasiparticle weight and the presence of a coherent part in the spectral function. Performing a weak coupling analysis we find that the mobility of the impurity reveals aT-3/2divergence at low temperatures. In addition, we show that the Green's function of an impurity interacting with the helical edge modes (surface states of 2D TI) exhibit power-law decay in the long-time limit for both the non-recoil and recoil case (with low impurity momentum), indicating the break down of the quasiparticle picture. However, for impurity with high momentum, the quasiparticle picture is restored. The mobility of the heavy impurity interacting with the helical edge modes exhibits unusual behaviour. It has an exponential divergence at low temperatures which can be tuned to a power-law divergence,T-4, by the application of the magnetic field.
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Affiliation(s)
- Ajit Kumar Sorout
- Department of Physics, University of Massachusetts, Amherst, MA 01003, United States of America
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, India
| | - Surajit Sarkar
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, India
| | - Suhas Gangadharaiah
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, India
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11
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Shamim S, Beugeling W, Böttcher J, Shekhar P, Budewitz A, Leubner P, Lunczer L, Hankiewicz EM, Buhmann H, Molenkamp LW. Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator. SCIENCE ADVANCES 2020; 6:eaba4625. [PMID: 32637611 PMCID: PMC7314521 DOI: 10.1126/sciadv.aba4625] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Accepted: 05/08/2020] [Indexed: 06/05/2023]
Abstract
The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.
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Affiliation(s)
- Saquib Shamim
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Wouter Beugeling
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Jan Böttcher
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Pragya Shekhar
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Andreas Budewitz
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Philipp Leubner
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Lukas Lunczer
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Ewelina M. Hankiewicz
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Hartmut Buhmann
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Laurens W. Molenkamp
- Experimentelle Physik III, Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute for Topological Insulators, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
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12
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Poncé S, Li W, Reichardt S, Giustino F. First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:036501. [PMID: 31923906 DOI: 10.1088/1361-6633/ab6a43] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
One of the fundamental properties of semiconductors is their ability to support highly tunable electric currents in the presence of electric fields or carrier concentration gradients. These properties are described by transport coefficients such as electron and hole mobilities. Over the last decades, our understanding of carrier mobilities has largely been shaped by experimental investigations and empirical models. Recently, advances in electronic structure methods for real materials have made it possible to study these properties with predictive accuracy and without resorting to empirical parameters. These new developments are unlocking exciting new opportunities, from exploring carrier transport in quantum matter to in silico designing new semiconductors with tailored transport properties. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. Our aim is threefold: to make this rapidly-growing research area accessible to a broad community of condensed-matter theorists and materials scientists; to identify key challenges that need to be addressed in order to increase the predictive power of these methods; and to identify new opportunities for increasing the impact of these computational methods on the science and technology of advanced materials. The review is organized in three parts. In the first part, we offer a brief historical overview of approaches to the calculation of carrier mobilities, and we establish the conceptual framework underlying modern ab initio approaches. We summarize the Boltzmann theory of carrier transport and we discuss its scope of applicability, merits, and limitations in the broader context of many-body Green's function approaches. We discuss recent implementations of the Boltzmann formalism within the context of density functional theory and many-body perturbation theory calculations, placing an emphasis on the key computational challenges and suggested solutions. In the second part of the article, we review applications of these methods to materials of current interest, from three-dimensional semiconductors to layered and two-dimensional materials. In particular, we discuss in detail recent investigations of classic materials such as silicon, diamond, gallium arsenide, gallium nitride, gallium oxide, and lead halide perovskites as well as low-dimensional semiconductors such as graphene, silicene, phosphorene, molybdenum disulfide, and indium selenide. We also review recent efforts toward high-throughput calculations of carrier transport. In the last part, we identify important classes of materials for which an ab initio study of carrier mobilities is warranted. We discuss the extension of the methodology to study topological quantum matter and materials for spintronics and we comment on the possibility of incorporating Berry-phase effects and many-body correlations beyond the standard Boltzmann formalism.
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Affiliation(s)
- Samuel Poncé
- Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom. Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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13
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Balram AC, Flensberg K, Paaske J, Rudner MS. Current-Induced Gap Opening in Interacting Topological Insulator Surfaces. PHYSICAL REVIEW LETTERS 2019; 123:246803. [PMID: 31922820 DOI: 10.1103/physrevlett.123.246803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Indexed: 06/10/2023]
Abstract
Two-dimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized two-terminal conductance. Quantization is protected by time-reversal symmetry, which forbids elastic backscattering. Paradoxically, the current-carrying state itself breaks the time-reversal symmetry that protects it. Here we show that the combination of electron-electron interactions and momentum-dependent spin polarization in helical edge states gives rise to feedback through which an applied current opens a gap in the edge state dispersion, thereby breaking the protection against elastic backscattering. Current-induced gap opening is manifested via a nonlinear contribution to the system's I-V characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous current-induced gap opening mechanism for the surface states of three-dimensional TIs.
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Affiliation(s)
- Ajit C Balram
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- The Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai 600113, India
| | - Karsten Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jens Paaske
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Mark S Rudner
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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14
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Xu Y, Chen YR, Wang J, Liu JF, Ma Z. Quantized Field-Effect Tunneling between Topological Edge or Interface States. PHYSICAL REVIEW LETTERS 2019; 123:206801. [PMID: 31809113 DOI: 10.1103/physrevlett.123.206801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2019] [Revised: 09/08/2019] [Indexed: 06/10/2023]
Abstract
We study the tunneling through a two-dimensional topological insulator with topologically protected edge states. It is shown that the tunneling probability can be quantized in a broad parameter range, 0 or 1, tuned by an applied transverse electric field. Based on this field-effect tunneling, we propose two types of topological transistors based on helical edge or interface states of quantum spin Hall insulators separately. The quantized tunneling conductance is obtained and shown to be robust against nonmagnetic disorders. Usually, the topological transition is necessary in the operation of topological transistors. These findings provide a new strategy for the design of topological transistors without topological transitions.
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Affiliation(s)
- Yong Xu
- School of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yan-Ru Chen
- School of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jun Wang
- Department of Physics, Southeast University, Nanjing 210096, China
| | - Jun-Feng Liu
- School of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhongshui Ma
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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15
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Kurilovich PD, Kurilovich VD, Burmistrov IS, Gefen Y, Goldstein M. Unrestricted Electron Bunching at the Helical Edge. PHYSICAL REVIEW LETTERS 2019; 123:056803. [PMID: 31491314 DOI: 10.1103/physrevlett.123.056803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2019] [Indexed: 06/10/2023]
Abstract
A quantum magnetic impurity of spin S at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary S. Our full analytical solution reveals that for S>1/2 the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for S=1/2 the Fano factor is bounded between 1 and 2, generalizing earlier studies.
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Affiliation(s)
- Pavel D Kurilovich
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | | | - Igor S Burmistrov
- L. D. Landau Institute for Theoretical Physics, acad. Semenova av. 1-a, 142432 Chernogolovka, Russia
| | - Yuval Gefen
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Moshe Goldstein
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
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16
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Lunczer L, Leubner P, Endres M, Müller VL, Brüne C, Buhmann H, Molenkamp LW. Approaching Quantization in Macroscopic Quantum Spin Hall Devices through Gate Training. PHYSICAL REVIEW LETTERS 2019; 123:047701. [PMID: 31491275 DOI: 10.1103/physrevlett.123.047701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2019] [Revised: 04/24/2019] [Indexed: 06/10/2023]
Abstract
Quantum spin Hall edge channels hold great promise as dissipationless one-dimensional conductors. However, the ideal quantized conductance of 2e^{2}/h is only found in very short channels-in contradiction with the expected protection against backscattering of the topological insulator state. In this Letter we show that enhancing the band gap does not improve quantization. When we instead alter the potential landscape by charging trap states in the gate dielectric using gate training, we approach conductance quantization for macroscopically long channels. Effectively, the scattering length increases to 175 μm, more than 1 order of magnitude longer than in previous works for HgTe-based quantum wells. Our experiments show that the distortion of the potential landscape by impurities, leading to puddle formation in the narrow gap material, is the major obstacle for observing undisturbed quantum spin Hall edge channel transport.
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Affiliation(s)
- Lukas Lunczer
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
- Institute for Topological Insulators, Am Hubland, D-97074 Würzburg, Germany
| | - Philipp Leubner
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - Martin Endres
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - Valentin L Müller
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
- Institute for Topological Insulators, Am Hubland, D-97074 Würzburg, Germany
| | - Christoph Brüne
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - Hartmut Buhmann
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
- Institute for Topological Insulators, Am Hubland, D-97074 Würzburg, Germany
| | - Laurens W Molenkamp
- Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
- Institute for Topological Insulators, Am Hubland, D-97074 Würzburg, Germany
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17
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Electronic thermal conductivity in 2D topological insulator in a HgTe quantum well. Sci Rep 2019; 9:831. [PMID: 30696853 PMCID: PMC6351662 DOI: 10.1038/s41598-018-36705-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Accepted: 10/28/2018] [Indexed: 11/09/2022] Open
Abstract
We have measured the differential resistance in a two-dimensional topological insulator (2DTI) in a HgTe quantum well, as a function of the applied dc current. The transport near the charge neutrality point is characterized by a pair of counter propagating gapless edge modes. In the presence of an electric field, the energy is transported by counter propagating channels in the opposite direction. We test a hot carrier effect model and demonstrate that the energy transfer complies with the Wiedemann Franz law near the charge neutrality point in the edge transport regime.
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18
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Novelli P, Taddei F, Geim AK, Polini M. Failure of Conductance Quantization in Two-Dimensional Topological Insulators due to Nonmagnetic Impurities. PHYSICAL REVIEW LETTERS 2019; 122:016601. [PMID: 31012652 DOI: 10.1103/physrevlett.122.016601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Indexed: 06/09/2023]
Abstract
Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short as 100 nm for atomically thin materials. We show that the combined action of short-range nonmagnetic impurities located near the edges and on site electron-electron interactions effectively creates noncollinear magnetic scatterers, and, hence, results in strong backscattering. The mechanism causes deviations from quantization even at zero temperature and for a modest strength of electron-electron interactions. Our theory provides a straightforward conceptual framework to explain experimental results, especially those in atomically thin crystals, plagued with short-range edge disorder.
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Affiliation(s)
- Pietro Novelli
- Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
- NEST, Scuola Normale Superiore, I-56126 Pisa, Italy
| | - Fabio Taddei
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy
| | - Andre K Geim
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Marco Polini
- Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
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19
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Hsu CH, Stano P, Klinovaja J, Loss D. Majorana Kramers Pairs in Higher-Order Topological Insulators. PHYSICAL REVIEW LETTERS 2018; 121:196801. [PMID: 30468588 DOI: 10.1103/physrevlett.121.196801] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Revised: 08/24/2018] [Indexed: 06/09/2023]
Abstract
We propose a tune-free scheme to realize Kramers pairs of Majorana bound states in recently discovered higher-order topological insulators (HOTIs). We show that, by bringing two hinges of a HOTI into the proximity of an s-wave superconductor, the competition between local and crossed Andreev pairing leads to the formation of Majorana Kramers pairs, when the latter pairing dominates over the former. We demonstrate that such a topological superconductivity is stabilized by moderate electron-electron interactions. The proposed setup avoids the application of a magnetic field or local voltage gates, and requires weaker interactions compared with nonhelical nanowires.
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Affiliation(s)
- Chen-Hsuan Hsu
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Peter Stano
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Applied Physics, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia
| | - Jelena Klinovaja
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Daniel Loss
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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20
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Rachel S. Interacting topological insulators: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:116501. [PMID: 30057370 DOI: 10.1088/1361-6633/aad6a6] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.
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Affiliation(s)
- Stephan Rachel
- School of Physics, University of Melbourne, Parkville, VIC 3010, Australia
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21
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Väyrynen JI, Pikulin DI, Alicea J. Noise-Induced Backscattering in a Quantum Spin Hall Edge. PHYSICAL REVIEW LETTERS 2018; 121:106601. [PMID: 30240259 DOI: 10.1103/physrevlett.121.106601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Indexed: 06/08/2023]
Abstract
Time-reversal symmetry suppresses electron backscattering in a quantum-spin-Hall edge, yielding quantized conductance at zero temperature. Understanding the dominant corrections in finite-temperature experiments remains an unsettled issue. We study a novel mechanism for conductance suppression: backscattering caused by incoherent electromagnetic noise. Specifically, we show that an electric potential fluctuating randomly in time can backscatter electrons inelastically without constraints faced by electron-electron interactions. We quantify noise-induced corrections to the dc conductance in various regimes and propose an experiment to test this scenario.
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Affiliation(s)
- Jukka I Väyrynen
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - Dmitry I Pikulin
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - Jason Alicea
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
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22
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Bendias K, Shamim S, Herrmann O, Budewitz A, Shekhar P, Leubner P, Kleinlein J, Bocquillon E, Buhmann H, Molenkamp LW. High Mobility HgTe Microstructures for Quantum Spin Hall Studies. NANO LETTERS 2018; 18:4831-4836. [PMID: 29975844 DOI: 10.1021/acs.nanolett.8b01405] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The topic of two-dimensional topological insulators has blossomed after the first observation of the quantum spin Hall (QSH) effect in HgTe quantum wells. However, studies have been hindered by the relative fragility of the edge states. Their stability has been a subject of both theoretical and experimental investigation in the past decade. Here, we present a new generation of high quality (Cd,Hg)Te/HgTe-structures based on a new chemical etching method. From magnetotransport measurements on macro- and microscopic Hall bars, we extract electron mobilities μ up to about 400 × 103 cm2/(V s), and the mean free path λmfp becomes comparable to the sample dimensions. The Hall bars show quantized spin Hall conductance, which is remarkably stable up to 15 K. The clean and robust edge states allow us to fabricate high quality side-contacted Josephson junctions, which are significant in the context of topological superconductivity. Our results open up new avenues for fundamental research on QSH effect as well as potential applications in spintronics and topological quantum computation.
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Affiliation(s)
- Kalle Bendias
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Saquib Shamim
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Oliver Herrmann
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Andreas Budewitz
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Pragya Shekhar
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Philipp Leubner
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Johannes Kleinlein
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Erwann Bocquillon
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
- Laboratoire Pierre Aigrain, Ecole Normale Supériere, PSL Research University, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, CNRS , 24 rue Lhomond , 75005 Paris , France
| | - Hartmut Buhmann
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
| | - Laurens W Molenkamp
- Physikalisches Institut (EP3) , Universität Würzburg , Am Hubland, 97074 Würzburg , Germany
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23
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Du L, Li T, Lou W, Wu X, Liu X, Han Z, Zhang C, Sullivan G, Ikhlassi A, Chang K, Du RR. Tuning Edge States in Strained-Layer InAs/GaInSb Quantum Spin Hall Insulators. PHYSICAL REVIEW LETTERS 2017; 119:056803. [PMID: 28949710 DOI: 10.1103/physrevlett.119.056803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2016] [Indexed: 06/07/2023]
Abstract
We report on a class of quantum spin Hall insulators (QSHIs) in strained-layer InAs/GaInSb quantum wells, in which the bulk gaps are enhanced up to fivefold as compared to the binary InAs/GaSb QSHI. Remarkably, with consequently increasing edge velocity, the edge conductance at zero and applied magnetic fields manifests time reversal symmetry-protected properties consistent with the Z_{2} topological insulator. The InAs/GaInSb bilayers offer a much sought-after platform for future studies and applications of the QSHI.
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Affiliation(s)
- Lingjie Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Tingxin Li
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Wenkai Lou
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
| | - Xingjun Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Xiaoxue Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Zhongdong Han
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Chi Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Gerard Sullivan
- Teledyne Scientific and Imaging, Thousand Oaks, California 91603, USA
| | - Amal Ikhlassi
- Teledyne Scientific and Imaging, Thousand Oaks, California 91603, USA
| | - Kai Chang
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
| | - Rui-Rui Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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24
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Väyrynen JI, Glazman LI. Current Noise from a Magnetic Moment in a Helical Edge. PHYSICAL REVIEW LETTERS 2017; 118:106802. [PMID: 28339237 DOI: 10.1103/physrevlett.118.106802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/06/2023]
Abstract
We calculate the two-terminal current noise generated by a magnetic moment coupled to a helical edge of a two-dimensional topological insulator. When the system is symmetric with respect to in-plane spin rotation, the noise is dominated by the Nyquist component even in the presence of a voltage bias V. The corresponding noise spectrum S(V,ω) is determined by a modified fluctuation-dissipation theorem with the differential conductance G(V,ω) in place of the linear one. The differential noise ∂S/∂V, commonly measured in experiments, is strongly dependent on frequency on a small scale τ_{K}^{-1}≪T set by the Korringa relaxation rate of the local moment. This is in stark contrast to the case of conventional mesoscopic conductors where ∂S/∂V is frequency independent and defined by the shot noise. In a helical edge, a violation of the spin-rotation symmetry leads to the shot noise, which becomes important only at a high bias. Uncharacteristically for a fermion system, this noise in the backscattered current is super-Poissonian.
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Affiliation(s)
- Jukka I Väyrynen
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Leonid I Glazman
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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25
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Rachel S. Quantum phase transitions of topological insulators without gap closing. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:405502. [PMID: 27530509 DOI: 10.1088/0953-8984/28/40/405502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the [Formula: see text] topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators.
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Affiliation(s)
- Stephan Rachel
- Institute for Theoretical Physics, TU Dresden, 01062 Dresden, Germany
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26
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Xie HY, Li H, Chou YZ, Foster MS. Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid. PHYSICAL REVIEW LETTERS 2016; 116:086603. [PMID: 26967434 DOI: 10.1103/physrevlett.116.086603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Indexed: 06/05/2023]
Abstract
The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.
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Affiliation(s)
- Hong-Yi Xie
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Heqiu Li
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Yang-Zhi Chou
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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27
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Tsvelik AM, Yevtushenko OM. Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain. PHYSICAL REVIEW LETTERS 2015; 115:216402. [PMID: 26636861 DOI: 10.1103/physrevlett.115.216402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2015] [Indexed: 06/05/2023]
Abstract
We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z_{2} symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localization.
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Affiliation(s)
- A M Tsvelik
- Brookhaven National Laboratory, Upton, New York 11973-5000, USA
| | - O M Yevtushenko
- Ludwig Maximilians University, Arnold Sommerfeld Center and Center for Nano-Science, Munich DE-80333, Germany
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28
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Traverso Ziani N, Crépin F, Trauzettel B. Fractional Wigner Crystal in the Helical Luttinger Liquid. PHYSICAL REVIEW LETTERS 2015; 115:206402. [PMID: 26613457 DOI: 10.1103/physrevlett.115.206402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2015] [Indexed: 06/05/2023]
Abstract
The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two-particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they, instead, represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we demonstrate that the state characterized by such fractional oscillations still bears the signatures of spin-momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a nontrivial spin texture.
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Affiliation(s)
- N Traverso Ziani
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - F Crépin
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - B Trauzettel
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
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29
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Chou YZ, Levchenko A, Foster MS. Helical Quantum Edge Gears in 2D Topological Insulators. PHYSICAL REVIEW LETTERS 2015; 115:186404. [PMID: 26565481 DOI: 10.1103/physrevlett.115.186404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2015] [Indexed: 06/05/2023]
Abstract
We show that two-terminal transport can measure the Luttinger liquid (LL) parameter K, in helical LLs at the edges of two-dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip interedge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature (T→0) perfect drag regime, the conductance is (e^{2}/h)(2K+1)/(K+1). At higher T, we predict a conductivity ~T^{-4K+3}. The conductivity for a single edge is also computed.
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Affiliation(s)
- Yang-Zhi Chou
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Alex Levchenko
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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30
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Li T, Wang P, Fu H, Du L, Schreiber KA, Mu X, Liu X, Sullivan G, Csáthy GA, Lin X, Du RR. Observation of a Helical Luttinger Liquid in InAs/GaSb Quantum Spin Hall Edges. PHYSICAL REVIEW LETTERS 2015; 115:136804. [PMID: 26451576 DOI: 10.1103/physrevlett.115.136804] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Indexed: 06/05/2023]
Abstract
We report on the observation of a helical Luttinger liquid in the edge of an InAs/GaSb quantum spin Hall insulator, which shows characteristic suppression of conductance at low temperature and low bias voltage. Moreover, the conductance shows power-law behavior as a function of temperature and bias voltage. The results underscore the strong electron-electron interaction effect in transport of InAs/GaSb edge states. Because of the fact that the Fermi velocity of the edge modes is controlled by gates, the Luttinger parameter can be fine tuned. Realization of a tunable Luttinger liquid offers a one-dimensional model system for future studies of predicted correlation effects.
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Affiliation(s)
- Tingxin Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Pengjie Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hailong Fu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Lingjie Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Kate A Schreiber
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Xiaoyang Mu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xiaoxue Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Gerard Sullivan
- Teledyne Scientific and Imaging, Thousand Oaks, California 91603, USA
| | - Gábor A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Xi Lin
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Rui-Rui Du
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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31
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Liu H, Jiang H, Sun QF, Xie XC. Dephasing effect on backscattering of helical surface states in 3D topological insulators. PHYSICAL REVIEW LETTERS 2014; 113:046805. [PMID: 25105645 DOI: 10.1103/physrevlett.113.046805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2013] [Indexed: 06/03/2023]
Abstract
We analyze the dephasing effect on the backscattering behavior of the helical surface states in 3D topological insulators. We show that the combination of dephasing and impurity scattering can cause backscattering in the helical states. Especially for the charge impurity case, the backscattering cross section becomes extremely large around the Dirac point. This large backscattering behavior can lead to the anomalous "gaplike" features found in recent experiments [T. Sato et al., Nat. Phys. 7, 840 (2011)].
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Affiliation(s)
- Haiwen Liu
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hua Jiang
- College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Qing-Feng Sun
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - X C Xie
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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32
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Spanton EM, Nowack KC, Du L, Sullivan G, Du RR, Moler KA. Images of edge current in InAs/GaSb quantum wells. PHYSICAL REVIEW LETTERS 2014; 113:026804. [PMID: 25062220 DOI: 10.1103/physrevlett.113.026804] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2014] [Indexed: 06/03/2023]
Abstract
Quantum spin Hall devices with edges much longer than several microns do not display ballistic transport; that is, their measured conductances are much less than e(2)/h per edge. We imaged edge currents in InAs/GaSb quantum wells with long edges and determined an effective edge resistance. Surprisingly, although the effective edge resistance is much greater than h/e(2), it is independent of temperature up to 30 K within experimental resolution. Known candidate scattering mechanisms do not explain our observation of an effective edge resistance that is large yet temperature independent.
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Affiliation(s)
- Eric M Spanton
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA and Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Katja C Nowack
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA and Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Lingjie Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Gerard Sullivan
- Teledyne Scientific and Imaging, Thousand Oaks, California 91630, USA
| | - Rui-Rui Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Kathryn A Moler
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA and Department of Physics, Stanford University, Stanford, California 94305, USA and Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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33
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Pikulin DI, Hyart T. Interplay of exciton condensation and the quantum spin hall effect in InAs/GaSb bilayers. PHYSICAL REVIEW LETTERS 2014; 112:176403. [PMID: 24836261 DOI: 10.1103/physrevlett.112.176403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Indexed: 06/03/2023]
Abstract
We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For a small tunneling amplitude between the layers, we find that the system is prone to the formation of an s-wave exciton condensate phase, where the spin structure of the order parameter is uniquely determined by the small spin-orbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and does not support edge transport. On the contrary, for a large tunneling amplitude, we obtain a topologically nontrivial quantum spin Hall insulator phase with a p-wave exciton order parameter, which enhances the hybridization gap. These topologically distinct insulators are separated by an insulating phase with spontaneously broken time-reversal symmetry. Close to the phase transition between the quantum spin Hall and time-reversal broken phases, the edge transport shows quantized conductance in small samples, whereas in long samples the mean free path associated with the backscattering at the edge is temperature independent, in agreement with recent experiments.
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Affiliation(s)
- D I Pikulin
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - T Hyart
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
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34
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Knez I, Rettner CT, Yang SH, Parkin SSP, Du L, Du RR, Sullivan G. Observation of edge transport in the disordered regime of topologically insulating InAs/GaSb quantum wells. PHYSICAL REVIEW LETTERS 2014; 112:026602. [PMID: 24484034 DOI: 10.1103/physrevlett.112.026602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2013] [Indexed: 06/03/2023]
Abstract
We observe edge transport in the topologically insulating InAs/GaSb system in the disordered regime. Using asymmetric current paths we show that conduction occurs exclusively along the device edge, exhibiting a large Hall signal at zero magnetic fields, while for symmetric current paths, the conductance between the two mesoscopicly separated probes is quantized to 2e2/h. Both quantized and self-averaged transport show resilience to magnetic fields, and are temperature independent for temperatures between 20 mK and 1 K.
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Affiliation(s)
- Ivan Knez
- IBM Research-Almaden, San Jose, California 95120, USA
| | | | - See-Hun Yang
- IBM Research-Almaden, San Jose, California 95120, USA
| | | | - Lingjie Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Rui-Rui Du
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Gerard Sullivan
- Teledyne Scientific and Imaging, Thousand Oaks, California 91630, USA
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35
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Nowack KC, Spanton EM, Baenninger M, König M, Kirtley JR, Kalisky B, Ames C, Leubner P, Brüne C, Buhmann H, Molenkamp LW, Goldhaber-Gordon D, Moler KA. Imaging currents in HgTe quantum wells in the quantum spin Hall regime. NATURE MATERIALS 2013; 12:787-791. [PMID: 23770727 DOI: 10.1038/nmat3682] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2013] [Accepted: 05/07/2013] [Indexed: 06/02/2023]
Abstract
The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.
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Affiliation(s)
- Katja C Nowack
- 1] Department of Applied Physics, Stanford University, Stanford, California 94305, USA [2] Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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36
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Väyrynen JI, Goldstein M, Glazman LI. Helical edge resistance introduced by charge puddles. PHYSICAL REVIEW LETTERS 2013; 110:216402. [PMID: 23745899 DOI: 10.1103/physrevlett.110.216402] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2013] [Indexed: 06/02/2023]
Abstract
We study the influence of electron puddles created by doping of a 2D topological insulator on its helical edge conductance. A single puddle is modeled by a quantum dot tunnel coupled to the helical edge. It may lead to significant inelastic backscattering within the edge because of the long electron dwelling time in the dot. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on the temperature and doping level and compare it with recent experimental data.
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Affiliation(s)
- Jukka I Väyrynen
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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37
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Cheianov V, Glazman LI. Mesoscopic fluctuations of conductance of a helical edge contaminated by magnetic impurities. PHYSICAL REVIEW LETTERS 2013; 110:206803. [PMID: 25167438 DOI: 10.1103/physrevlett.110.206803] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2013] [Indexed: 06/03/2023]
Abstract
Elastic backscattering of electrons moving along the helical edge is prohibited by time-reversal symmetry. We demonstrate, however, that an ensemble of magnetic impurities may cause time-reversal symmetry-preserving quasielastic backscattering, resulting in interference effects in the conductance. The characteristic energy transferred in a backscattering event is suppressed due to the Ruderman-Kittel-Kasuya-Yosida interaction of localized spins (the suppression is exponential in the total number of magnetic impurities). We predict the statistics of conductance fluctuations to differ from those in the conventional case of a one-dimensional system with quenched disorder.
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Affiliation(s)
- Vadim Cheianov
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Leonid I Glazman
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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38
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Bardarson JH, Moore JE. Quantum interference and Aharonov-Bohm oscillations in topological insulators. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:056501. [PMID: 23552181 DOI: 10.1088/0034-4885/76/5/056501] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Topological insulators (TIs) have an insulating bulk but a metallic surface. In the simplest case, the surface electronic structure of a three-dimensional (3D) TI is described by a single two-dimensional (2D) Dirac cone. A single 2D Dirac fermion cannot be realized in an isolated 2D system with time-reversal symmetry, but rather owes its existence to the topological properties of the 3D bulk wavefunctions. The transport properties of such a surface state are of considerable current interest; they have some similarities with graphene, which also realizes Dirac fermions, but have several unique features in their response to magnetic fields. In this review we give an overview of some of the main quantum transport properties of TI surfaces. We focus on the efforts to use quantum interference phenomena, such as weak anti-localization and the Aharonov-Bohm effect, to verify in a transport experiment the Dirac nature of the surface state and its defining properties. In addition to explaining the basic ideas and predictions of the theory, we provide a survey of recent experimental work.
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Affiliation(s)
- Jens H Bardarson
- Department of Physics, University of California, Berkeley, CA 94720, USA
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39
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Hohenadler M, Assaad FF. Correlation effects in two-dimensional topological insulators. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:143201. [PMID: 23470861 DOI: 10.1088/0953-8984/25/14/143201] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.
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Affiliation(s)
- M Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany.
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