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Jeong Y, Park H, Kim T, Watanabe K, Taniguchi T, Jung J, Jang J. Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene. Nat Commun 2024; 15:6351. [PMID: 39069539 DOI: 10.1038/s41467-024-50475-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Accepted: 07/12/2024] [Indexed: 07/30/2024] Open
Abstract
In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moiré superlattice potential enriches the BBG physics with the formation of topological minibands - potentially leading to tunable exotic quantum transport. Here, we present magnetotransport measurements of a high-quality bilayer graphene-hexagonal boron nitride (hBN) heterostructure. The zero-degree alignment generates a strong moiré superlattice potential for the electrons in BBG and the resulting Landau fan diagram of longitudinal and Hall resistance displays a Hofstadter butterfly pattern with a high level of detail. We demonstrate that the intricate relationship between valley and layer degrees of freedom controls the topology of moiré-induced bands, significantly influencing the energetics of interacting quantum phases in the BBG superlattice. We further observe signatures of field-induced correlated insulators, helical edge states and clear quantizations of interaction-driven topological quantum phases, such as symmetry broken Chern insulators.
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Affiliation(s)
- Yungi Jeong
- Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea
| | - Hangyeol Park
- Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea
| | - Taeho Kim
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul, Korea
- Department of Smart Cities, University of Seoul, Seoul, Korea
| | - Joonho Jang
- Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea.
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.
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2
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Krishna Kumar R, Chen X, Auton GH, Mishchenko A, Bandurin DA, Morozov SV, Cao Y, Khestanova E, Ben Shalom M, Kretinin AV, Novoselov KS, Eaves L, Grigorieva IV, Ponomarenko LA, Fal'ko VI, Geim AK. High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices. Science 2018; 357:181-184. [PMID: 28706067 DOI: 10.1126/science.aal3357] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Accepted: 06/09/2017] [Indexed: 11/03/2022]
Abstract
Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that graphene superlattices support a different type of quantum oscillation that does not rely on Landau quantization. The oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few tesla. We attribute this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the flux quantum per superlattice unit cell. Our work hints at unexplored physics in Hofstadter butterfly systems at high temperatures.
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Affiliation(s)
- R Krishna Kumar
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.,Department of Physics, University of Lancaster, Lancaster LA1 4YW, UK
| | - X Chen
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - G H Auton
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - A Mishchenko
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - D A Bandurin
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - S V Morozov
- Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, Chernogolovka 142432, Russia.,National University of Science and Technology (MISiS), Moscow 119049, Russia
| | - Y Cao
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - E Khestanova
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - M Ben Shalom
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - A V Kretinin
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.,School of Materials, University of Manchester, Manchester M13 9PL, UK
| | - K S Novoselov
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - L Eaves
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.,School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - I V Grigorieva
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - L A Ponomarenko
- Department of Physics, University of Lancaster, Lancaster LA1 4YW, UK
| | - V I Fal'ko
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. .,National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - A K Geim
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. .,National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
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3
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Wang S, Scarabelli D, Du L, Kuznetsova YY, Pfeiffer LN, West KW, Gardner GC, Manfra MJ, Pellegrini V, Wind SJ, Pinczuk A. Observation of Dirac bands in artificial graphene in small-period nanopatterned GaAs quantum wells. NATURE NANOTECHNOLOGY 2018; 13:29-33. [PMID: 29180741 DOI: 10.1038/s41565-017-0006-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2015] [Accepted: 09/21/2017] [Indexed: 05/16/2023]
Abstract
Charge carriers in graphene behave like massless Dirac fermions (MDFs) with linear energy-momentum dispersion 1, 2 , providing a condensed-matter platform for studying quasiparticles with relativistic-like features. Artificial graphene (AG)-a structure with an artificial honeycomb lattice-exhibits novel phenomena due to the tunable interplay between topology and quasiparticle interactions 3-6 . So far, the emergence of a Dirac band structure supporting MDFs has been observed in AG using molecular 5 , atomic 6, 7 and photonic systems 8-10 , including those with semiconductor microcavities 11 . Here, we report the realization of an AG that has a band structure with vanishing density of states consistent with the presence of MDFs. This observation is enabled by a very small lattice constant (a = 50 nm) of the nanofabricated AG patterns superimposed on a two-dimensional electron gas hosted by a high-quality GaAs quantum well. Resonant inelastic light-scattering spectra reveal low-lying transitions that are not present in the unpatterned GaAs quantum well. These excitations reveal the energy dependence of the joint density of states for AG band transitions. Fermi level tuning through the Dirac point results in a collapse of the density of states at low transition energy, suggesting the emergence of the MDF linear dispersion in the AG.
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Affiliation(s)
- Sheng Wang
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
| | - Diego Scarabelli
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
- Rigetti Quantum Computing, Berkeley, CA, USA
| | - Lingjie Du
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA.
| | | | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Ken W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Geoff C Gardner
- Department of Physics and Astronomy, and School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, and School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
| | | | - Shalom J Wind
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
| | - Aron Pinczuk
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
- Department of Physics, Columbia University, New York, NY, USA
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5
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Pradhan S. Hofstadter butterfly in the Falicov-Kimball model on some finite 2D lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:505502. [PMID: 27768603 DOI: 10.1088/0953-8984/28/50/505502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied in comparison to a square lattice. Using a Falicov-Kimball model, the effects of Coulomb correlation, magnetic field and finite system size on their energy spectrum are observed. Exact diagonalization and Monte Carlo simulation methods (based on a modified Metropolis algorithm) have been employed to examine the recursive structure of the Hofstadter spectrum in the presence of several electronic correlation strengths for different system sizes. It is possible to introduce a gap in the density of states even in the absence of electron correlation, which is anticipated as a metal to insulator transition driven by an orbital magnetic field. With further inclusion of the interaction, the gap in the spectrum is modified and in some cases the correlation is found to suppress extra states manifested by the finite size effects. At a certain flux, the opened gap due to magnetic field is reduced by the Coulomb interaction. An orbital current is calculated for both the square and the triangular lattice with and without electron correlation. In the non-interacting limit, the bulk current shows several patterns, while the edge current shows oscillations with magnetic flux. The oscillations persist in the interacting limit for the square lattice, but not for the triangular lattice.
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Affiliation(s)
- Subhasree Pradhan
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. Department of Physics, Jhargram Raj College, Jhargram, West Bengal 721507, India
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6
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Deng H, Liu Y, Jo I, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal. PHYSICAL REVIEW LETTERS 2016; 117:096601. [PMID: 27610870 DOI: 10.1103/physrevlett.117.096601] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2016] [Indexed: 06/06/2023]
Abstract
When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings (ν≪1), its direct observation has been elusive. Here we present a new technique and experimental results directly probing the magnetic-field-induced WC. We measure the magnetoresistance of a bilayer electron system where one layer has a very low density and is in the WC regime (ν≪1), while the other ("probe") layer is near ν=1/2 and hosts a sea of composite fermions (CFs). The data exhibit commensurability oscillations in the magnetoresistance of the CF layer, induced by the periodic potential of WC electrons in the other layer, and provide a unique, direct glimpse at the symmetry of the WC, its lattice constant, and melting. They also demonstrate a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasiparticles of another many-body state.
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Affiliation(s)
- H Deng
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - Y Liu
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - I Jo
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, USA
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7
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Wang L, Gao Y, Wen B, Han Z, Taniguchi T, Watanabe K, Koshino M, Hone J, Dean CR. Evidence for a fractional fractal quantum Hall effect in graphene superlattices. Science 2015; 350:1231-4. [DOI: 10.1126/science.aad2102] [Citation(s) in RCA: 128] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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8
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Artoni M, La Rocca GC, Ferrari G. Quasi-periodic Wannier–Stark ladders from driven atomic Bloch oscillations. Proc Math Phys Eng Sci 2014. [DOI: 10.1098/rspa.2014.0421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Periodic Wannier–Stark ladder structures of the energy resonances associated with Bloch oscillations can be readily modified into quasi-periodic ones that exhibit peculiar self-similar effects. A compact theoretical description of the dynamics of driven Bloch oscillations is developed here within the quasi-momentum representation. We identify a rather viable scheme based on ultracold atomic wavepackets subject to gravity in a driven optical lattice potential where a self-similar scaling could be observed. Its feasibility in terms of realistic experimental parameters is also discussed.
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Affiliation(s)
- M. Artoni
- Department of Engineering and Information Technology, Brescia University, Brescia, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS) and Istituto Nazionale di Ottica (INO), Firenze, Italy
| | | | - G. Ferrari
- European Laboratory for Nonlinear Spectroscopy (LENS) and Istituto Nazionale di Ottica (INO), Firenze, Italy
- INO-CNR BEC Center and Dipartimento di Fisica, Trento University, 38123 Povo, Italy
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10
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Polini M, Guinea F, Lewenstein M, Manoharan HC, Pellegrini V. Artificial honeycomb lattices for electrons, atoms and photons. NATURE NANOTECHNOLOGY 2013; 8:625-633. [PMID: 24002076 DOI: 10.1038/nnano.2013.161] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2013] [Accepted: 07/17/2013] [Indexed: 06/02/2023]
Abstract
Artificial honeycomb lattices offer a tunable platform for studying massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band-structure engineering and cooperative effects leads to spectacular manifestations in tunnelling and optical spectroscopies.
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Affiliation(s)
- Marco Polini
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy.
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11
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Dean CR, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard KL, Hone J, Kim P. Hofstadter's butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 2013; 497:598-602. [PMID: 23676673 DOI: 10.1038/nature12186] [Citation(s) in RCA: 569] [Impact Index Per Article: 51.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2012] [Accepted: 04/03/2013] [Indexed: 11/09/2022]
Abstract
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. When subject to both a magnetic field and a periodic electrostatic potential, two-dimensional systems of electrons exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from an interplay between the characteristic lengths associated with the two quantizing fields, and is one of the first quantum fractals discovered in physics. In the decades since its prediction, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical atomic lattices (with periodicities of less than one nanometre) require unfeasibly large magnetic fields to reach the commensurability condition, and in artificially engineered structures (with periodicities greater than about 100 nanometres) the corresponding fields are too small to overcome disorder completely. Here we demonstrate that moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic modulation with ideal length scales of the order of ten nanometres, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of a Hofstadter spectrum in bilayer graphene means that it is possible to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.
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Affiliation(s)
- C R Dean
- Department of Physics, The City College of New York, New York, New York 10031, USA
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13
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Singha A, Gibertini M, Karmakar B, Yuan S, Polini M, Vignale G, Katsnelson MI, Pinczuk A, Pfeiffer LN, West KW, Pellegrini V. Two-Dimensional Mott-Hubbard Electrons in an Artificial Honeycomb Lattice. Science 2011; 332:1176-9. [DOI: 10.1126/science.1204333] [Citation(s) in RCA: 162] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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Kapit E, Mueller E. Exact parent Hamiltonian for the quantum Hall states in a lattice. PHYSICAL REVIEW LETTERS 2010; 105:215303. [PMID: 21231318 DOI: 10.1103/physrevlett.105.215303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2010] [Revised: 07/13/2010] [Indexed: 05/30/2023]
Abstract
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.
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Affiliation(s)
- Eliot Kapit
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, USA
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Berciu M, Rappoport TG, Jankó B. Manipulating spin and charge in magnetic semiconductors using superconducting vortices. Nature 2005; 435:71-5. [PMID: 15875016 DOI: 10.1038/nature03559] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2004] [Accepted: 03/10/2005] [Indexed: 11/08/2022]
Abstract
The continuous need for miniaturization and increase in device speed drives the electronics industry to explore new avenues of information processing. One possibility is to use electron spin to store, manipulate and carry information. All such 'spintronics' applications are faced with formidable challenges in finding fast and efficient ways to create, transport, detect, control and manipulate spin textures and currents. Here we show how most of these operations can be performed in a relatively simple manner in a hybrid system consisting of a superconducting film and a paramagnetic diluted magnetic semiconductor (DMS) quantum well. Our proposal is based on the observation that the inhomogeneous magnetic fields of the superconducting film create local spin and charge textures in the DMS quantum well, leading to a variety of effects such as Bloch oscillations and an unusual quantum Hall effect. We exploit recent progress in manipulating magnetic flux bundles (vortices) in superconductors and show how these can create, manipulate and control the spin textures in DMSs.
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Affiliation(s)
- Mona Berciu
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
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