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Yoo HM, Korkusinski M, Miravet D, Baldwin KW, West K, Pfeiffer L, Hawrylak P, Ashoori RC. Time, momentum, and energy resolved pump-probe tunneling spectroscopy of two-dimensional electron systems. Nat Commun 2023; 14:7440. [PMID: 37978193 PMCID: PMC10656415 DOI: 10.1038/s41467-023-43268-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 11/06/2023] [Indexed: 11/19/2023] Open
Abstract
Real-time probing of electrons can uncover intricate relaxation mechanisms and many-body interactions in strongly correlated materials. Here, we introduce time, momentum, and energy resolved pump-probe tunneling spectroscopy (Tr-MERTS). The method allows the injection of electrons at a particular energy and observation of their subsequent decay in energy-momentum space. Using Tr-MERTS, we visualize electronic decay processes, with lifetimes from tens of nanoseconds to tens of microseconds, in Landau levels formed in a GaAs quantum well. Although most observed features agree with simple energy-relaxation, we discovered a splitting in the nonequilibrium energy spectrum in the vicinity of a ferromagnetic state. An exact diagonalization study suggests that the splitting arises from a maximally spin-polarized state with higher energy than a conventional equilibrium skyrmion. Furthermore, we observe time-dependent relaxation of the splitting, which we attribute to single-flipped spins forming skyrmions. These results establish Tr-MERTS as a powerful tool for studying the properties of a 2DES beyond equilibrium.
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Affiliation(s)
- H M Yoo
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - M Korkusinski
- Emerging Technologies Division, National Research Council of Canada, Ottawa, ON, K1A 0R6, Canada
| | - D Miravet
- Department of Physics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - L Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - P Hawrylak
- Department of Physics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada
| | - R C Ashoori
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
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2
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Liu X, Farahi G, Chiu CL, Papic Z, Watanabe K, Taniguchi T, Zaletel MP, Yazdani A. Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet. Science 2022; 375:321-326. [PMID: 34855512 DOI: 10.1126/science.abm3770] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.
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Affiliation(s)
- Xiaomeng Liu
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Gelareh Farahi
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Cheng-Li Chiu
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Zlatko Papic
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, CA 94720, USA
| | - Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
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3
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Patlatiuk T, Scheller CP, Hill D, Tserkovnyak Y, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Evolution of the quantum Hall bulk spectrum into chiral edge states. Nat Commun 2018; 9:3692. [PMID: 30209251 PMCID: PMC6135798 DOI: 10.1038/s41467-018-06025-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2018] [Accepted: 08/13/2018] [Indexed: 11/30/2022] Open
Abstract
One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment-thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction.
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Affiliation(s)
- T Patlatiuk
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - C P Scheller
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - D Hill
- Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA
| | - Y Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA
| | - G Barak
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - A Yacoby
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - D M Zumbühl
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland.
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4
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Liu D, Chen S, Zhang S, Ma N. Intrinsic plasmarons in warm graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:425601. [PMID: 28737502 DOI: 10.1088/1361-648x/aa81ad] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Based on a self-consistent method, we predict theoretically that there exist intrinsic plasmarons in graphene at nonzero temperature, with a well defined mode, as shown by the result of Landau damping. We find that there are sharp differences between the discussed system and the QCD/QED system. Firstly, the thermal mass is proportional to [Formula: see text] but not [Formula: see text]. Secondly, at [Formula: see text], the fermion channel and plasmaron channel are nearly degenerate, and furthermore the energy difference between fermion and plasmaron becomes larger and larger with increasing q in the region [Formula: see text]. Thirdly, the fermion behaves as a 'relativistic particle' with nonzero mass, and the plasmaron exhibits an abnormal dispersion at moderate momentum.
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Affiliation(s)
- Daqing Liu
- School of Mathematics and Physics, Changzhou University, Changzhou 213164, People's Republic of China
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5
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Mukherjee S, Mandal SS. Anomalously low magnetoroton energies of the unconventional fractional quantum Hall States of composite fermions. PHYSICAL REVIEW LETTERS 2015; 114:156802. [PMID: 25933328 DOI: 10.1103/physrevlett.114.156802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Indexed: 06/04/2023]
Abstract
We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8 at very low wave vectors with anomalously low energies which do not have any analog to the conventional fractional quantum Hall states. Rather slow decay of the oscillations of the pair-correlation functions in these states is responsible for the low-energy magnetorotons. This is a manifestation of the distinct topology predicted previously for these fractional quantum Hall effect states. Experimental consequences of our theory are also discussed.
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Affiliation(s)
- Sutirtha Mukherjee
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | - Sudhansu S Mandal
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700032, India
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6
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Krishtopenko SS. Electron spin resonance and cyclotron resonance for fractional quantum Hall states in narrow-gap QW heterostructures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:105601. [PMID: 23406894 DOI: 10.1088/0953-8984/25/10/105601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We report a theoretical study of the energies of cyclotron resonance (CR) and electron spin resonance (ESR) for fractional quantum Hall states (FQHS) in n-type narrow-gap quantum well (QW) heterostructures. Using the generalized single-mode approximation (GSMA) based on the 8-band k·p Hamiltonian, we calculate the many-body corrections to the CR and ESR energies for FQHS, providing theoretical evidence of the Kohn and Larmor theorem violation in narrow-gap QWs. We predict the correlation-induced reduction of CR energies and the correlation-induced enhancement of ESR energies as compared with the values obtained within the Hartree-Fock approximation. We demonstrate a nonlinear dependence of the CR and ESR energies on a Landau level filling factor.
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Affiliation(s)
- S S Krishtopenko
- Institute for Physics of Microstructures RAS, GSP-105, 603950, Nizhny Novgorod, Russia. ds
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Abanin DA, Pesin DA. Interaction-induced topological insulator states in strained graphene. PHYSICAL REVIEW LETTERS 2012; 109:066802. [PMID: 23006292 DOI: 10.1103/physrevlett.109.066802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2012] [Indexed: 06/01/2023]
Abstract
The electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for both studying the Dirac fermions in new regimes and for new device applications. Certain natural configurations of strain generate large nearly uniform pseudomagnetic fields, which have opposite signs in the two valleys, and give rise to flat spin- and valley-degenerate pseudo-Landau levels (PLLs). Here we consider the effect of the Coulomb interactions in strained graphene with a uniform pseudomagnetic field. We show that the spin or valley degeneracies of the PLLs get lifted by the interactions, giving rise to topological insulator states. In particular, when a nonzero PLL is quarter or three-quarter filled, an anomalous quantum Hall state spontaneously breaking time-reversal symmetry emerges. At half-filled PLLs, a weak spin-orbital interaction stabilizes the time-reversal-symmetric quantum spin-Hall state. These many-body states are characterized by the quantized conductance and persist to a high temperature scale set by the Coulomb interactions, which we estimate to be a few hundreds Kelvin at moderate strain values. At fractional fillings, fractional quantum Hall states breaking valley symmetry emerge. These results suggest a new route to realizing robust topological states in mesoscopic graphene.
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Affiliation(s)
- D A Abanin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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8
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Papić Z, Thomale R, Abanin DA. Tunable electron interactions and fractional quantum Hall States in graphene. PHYSICAL REVIEW LETTERS 2011; 107:176602. [PMID: 22107550 DOI: 10.1103/physrevlett.107.176602] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2011] [Indexed: 05/31/2023]
Abstract
The recent discovery of fractional quantum Hall (FQH) states in graphene raises the question of whether the physics of graphene offers any advantages over GaAs-based materials in exploring strongly correlated states of two-dimensional electrons. Here we propose a method to continuously tune the effective electron interactions in graphene and its bilayer by the dielectric environment of the sample. Using this method, the charge gaps of prominent FQH states, including ν=1/3 or ν=5/2 states, can be increased several times, or reduced to zero. The tunability of the interactions can be used to realize and stabilize various strongly correlated phases and explore the transitions between them.
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Affiliation(s)
- Z Papić
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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9
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Rhone TD, Majumder D, Dennis BS, Hirjibehedin C, Dujovne I, Groshaus JG, Gallais Y, Jain JK, Mandal SS, Pinczuk A, Pfeiffer L, West K. Higher-energy composite fermion levels in the fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2011; 106:096803. [PMID: 21405644 DOI: 10.1103/physrevlett.106.096803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2010] [Indexed: 05/30/2023]
Abstract
Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect.
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Affiliation(s)
- Trevor D Rhone
- Department of Physics, Columbia University, New York, New York 10027, USA
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10
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MacDonald AH. Theory of high-energy features in the tunneling spectra of quantum-Hall systems. PHYSICAL REVIEW LETTERS 2010; 105:206801. [PMID: 21231254 DOI: 10.1103/physrevlett.105.206801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2010] [Indexed: 05/30/2023]
Abstract
We show that the low-temperature sash features in lowest Landau-level (LLL) tunneling spectra recently discovered by Dial and Ashoori are intimately related to the discrete Haldane-pseudopotential interaction energy scales that govern fractional quantum-Hall physics. Our analysis is based on expressions for the tunneling density of states which become exact at filling factors close to ν=0 and ν=1, where the sash structure is most prominent. We comment on other aspects of LLL correlation physics that can be revealed by accurate temperature-dependent tunneling data.
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Affiliation(s)
- A H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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11
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Song YJ, Otte AF, Kuk Y, Hu Y, Torrance DB, First PN, de Heer WA, Min H, Adam S, Stiles MD, MacDonald AH, Stroscio JA. High-resolution tunnelling spectroscopy of a graphene quartet. Nature 2010; 467:185-9. [DOI: 10.1038/nature09330] [Citation(s) in RCA: 159] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2010] [Accepted: 07/07/2010] [Indexed: 11/09/2022]
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