Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene

Hunt, B. M.; Li, J. I.  A.; Zibrov, A. A.; Wang, L.; Taniguchi, T.; Watanabe, K.; Hone, J.; Dean, C. R.; Zaletel, M.; Ashoori, R. C.; Young, A. F.

doi:10.1038/s41467-017-00824-w

Title: Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene

Abstract

The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.

Authors:

Hunt, B. M. ^[1];

^[2]; Zibrov, A. A. ^[3]; Wang, L. ^[4]; Taniguchi, T. ^[5];

^[5]; Hone, J. ^[4]; Dean, C. R. ^[4]; Zaletel, M. ^[6]; Ashoori, R. C. ^[7]; Young, A. F. ^[8]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics; Columbia Univ., New York, NY (United States). Dept. of Physics; Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics
Columbia Univ., New York, NY (United States). Dept. of Physics
Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
Columbia Univ., New York, NY (United States)
National Inst. for Materials Science (NIMS), Tsukuba (Japan)
Microsoft Research, Santa Barbara, CA (United States). Station Q
Massachusetts Inst. of Tech., Cambridge, MA (United States)
Massachusetts Inst. of Tech., Cambridge, MA (United States); Univ. of California, Santa Barbara, CA (United States)

Publication Date:: Mon Oct 16 00:00:00 EDT 2017

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1529936

Alternate Identifier(s):: OSTI ID: 1545718

Grant/Contract Number:: FG02-08ER46514

Resource Type:: Accepted Manuscript

Journal Name:: Nature Communications

Additional Journal Information:: Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2041-1723

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Hunt, B. M., Li, J. I.  A., Zibrov, A. A., Wang, L., Taniguchi, T., Watanabe, K., Hone, J., Dean, C. R., Zaletel, M., Ashoori, R. C., and Young, A. F. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene.  United States: N. p., 2017. 
Web.  doi:10.1038/s41467-017-00824-w.

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                    Hunt, B. M., Li, J. I.  A., Zibrov, A. A., Wang, L., Taniguchi, T., Watanabe, K., Hone, J., Dean, C. R., Zaletel, M., Ashoori, R. C., & Young, A. F. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene.  United States.  https://doi.org/10.1038/s41467-017-00824-w

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                    Hunt, B. M., Li, J. I.  A., Zibrov, A. A., Wang, L., Taniguchi, T., Watanabe, K., Hone, J., Dean, C. R., Zaletel, M., Ashoori, R. C., and Young, A. F. Mon .  
"Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene".  United States.  https://doi.org/10.1038/s41467-017-00824-w.  https://www.osti.gov/servlets/purl/1529936.

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@article{osti_1529936,

  title        = {Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene},

  author       = {Hunt, B. M. and Li, J. I.  A. and Zibrov, A. A. and Wang, L. and Taniguchi, T. and Watanabe, K. and Hone, J. and Dean, C. R. and Zaletel, M. and Ashoori, R. C. and Young, A. F.},

  abstractNote = {The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.},

  doi          = {10.1038/s41467-017-00824-w},

  journal      = {Nature Communications},

  number       = 1,

  volume       = 8,

  place        = {United States},

  year         = {Mon Oct 16 00:00:00 EDT 2017},

  month        = {Mon Oct 16 00:00:00 EDT 2017}

}

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Figures / Tables:

Fig. 1: Layer polarization of bilayer graphene at zero magnetic field. a Measurement schematic showing geometric gate capacitances c_t and c_b and interlayer capacitance c₀. Capacitance is measured using a cryogenic bridge circuit by comparison with a standard capacitor C_std, measured to be 404± 20 fF (see “Methods”). b Devicemore »

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Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
journal, July 2019

Chong, Su Kong; Han, Kyu Bum; Sparks, Taylor D.
Physical Review Letters, Vol. 123, Issue 3
DOI: 10.1103/physrevlett.123.036804

Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
text, January 2019

Lane, Thomas L. M.; Knothe, Angelika; Fal'ko, Vladimir I.
arXiv
DOI: 10.48550/arxiv.1904.00918

Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
text, January 2018

Lee, Jong Yeon; Wang, Chong; Zaletel, Michael P.
arXiv
DOI: 10.48550/arxiv.1802.09538

Parallel transport and layer-resolved thermodynamic measurements in twisted bilayer graphene
journal, December 2021

Piccinini, G.; Mišeikis, V.; Watanabe, K.
Physical Review B, Vol. 104, Issue 24
DOI: 10.1103/physrevb.104.l241410

Large Landau-level splitting in a tunable one-dimensional graphene superlattice probed by magnetocapacitance measurements
journal, July 2018

Kuiri, Manabendra; Gupta, Gaurav Kumar; Ronen, Yuval
Physical Review B, Vol. 98, Issue 3
DOI: 10.1103/physrevb.98.035418

Thirty Years of Composite Fermions and Beyond
text, January 2020

Jain, J. K.
arXiv
DOI: 10.48550/arxiv.2011.13488

Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect
journal, June 2019

Island, J. O.; Cui, X.; Lewandowski, C.
Nature, Vol. 571, Issue 7763
DOI: 10.1038/s41586-019-1304-2

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Correlated Hofstadter spectrum and flavour phase diagram in magic-angle twisted bilayer graphene

Journal Article Yu, Jiachen ; Foutty, Benjamin A. ; Han, Zhaoyu ; ... - Nature Physics

In magic-angle twisted bilayer graphene, the moiré superlattice potential gives rise to narrow electronic bands that support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here we simultaneously unveil sequences of broken-symmetry Chern insulators and resolve sharp phase transitions between competing states with different topological quantum numbersmore »« less
https://doi.org/10.1038/s41567-022-01589-w

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Carrier dynamics and spin–valley–layer effects in bilayer transition metal dichalcogenides

Journal Article Ciccarino, Christopher J. ; Chakraborty, Chitraleema ; Englund, Dirk R. ; ... - Faraday Discussions

Transition metal dichalcogenides are an interesting class of low dimensional materials in mono- and few-layer form with diverse applications in valleytronic, optoelectronic and quantum devices. Therefore, the general nature of the band-edges and the interplay with valley dynamics is important from a fundamental and technological standpoint. Bilayers introduce interlayer coupling effects which can have a significant impact on the valley polarization. The combined effect of spin–orbit and interlayer coupling can strongly modify the band structure, phonon interactions and overall carrier dynamics in the material. In this paper we use first-principles calculations of electron–electron and electron–phonon interactions to investigate bilayer MoS₂more »« less
https://doi.org/10.1039/c8fd00159f

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Valley-Coherent Quantum Anomalous Hall State in AB-Stacked ${MoTe}_{2} / {W S e}_{2}$ Bilayers

Journal Article Tao, Zui ; Shen, Bowen ; Jiang, Shengwei ; ... - Physical Review. X

Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands. Here, we show that the newly discovered QAH state in AB-stacked MoTe2/WSe2 moiré bilayers is not valleymore »« less
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Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund’s coupling determines the spin-structure of the IVCmore »« less
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We have fabricated a high-quality monolayer WSe{sub 2} film on bilayer graphene by epitaxial growth and revealed the electronic states by spin- and angle-resolved photoemission spectroscopy. We observed a direct energy gap at the Brillouin-zone corner in contrast to the indirect nature of gap in bulk WSe{sub 2}, which is attributed to the lack of interlayer interaction and the breaking of space-inversion symmetry in monolayer film. A giant spin splitting of ∼0.5 eV, which is the largest among known monolayer transition-metal dichalcogenides, is observed in the energy band around the zone corner. The present results suggest a high potential applicability ofmore »« less
https://doi.org/10.1063/1.4928658

Similar Records

Title: Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene

Abstract

Citation Formats

Figures / Tables:

Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene text, January 2012

Observation of Helical Edge States and Fractional Quantum Hall Effect in a Graphene Electron-hole Bilayer text, January 2016

Broken-symmetry states and divergent resistance in suspended bilayer graphene journal, September 2009

Spin and pseudospins in layered transition metal dichalcogenides journal, April 2014

Capacitance measurements of a quantized two-dimensional electron gas in the regime of the quantum Hall effect journal, May 1985

Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer journal, October 2016

Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene journal, October 2010

Topological Phases in the Zeroth Landau Level of Bilayer Graphene text, January 2013

Tunable fractional quantum Hall phases in bilayer graphene journal, July 2014

Nonabelions in the fractional quantum hall effect journal, August 1991

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene journal, September 2012

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene text, January 2012

Competing ordered states with filling factor two in bilayer graphene journal, July 2014

Quantum spin-valley Hall effect in AB-stacked bilayer silicene journal, December 2019

Charge 2 e Skyrmions in Bilayer Graphene journal, August 2009

Optically Pumped NMR Evidence for Finite-Size Skyrmions in GaAs Quantum Wells near Landau Level Filling ν = 1 journal, June 1995

Canted Antiferromagnetic Phase of the ν = 0 Quantum Hall State in Bilayer Graphene journal, July 2012

Charge 2e skyrmions in bilayer graphene text, January 2009

Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene journal, August 2008

Observation of Quantum Hall Valley Skyrmions text, January 2005

Spin and valley quantum Hall ferromagnetism in graphene journal, May 2012

Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene text, January 2013

Tunable fractional quantum Hall phases in bilayer graphene journal, July 2014

Energy gaps and layer polarization of integer and fractional quantum Hall states in bilayer graphene text, January 2016

Quantum Hall ferromagnetic phases in the Landau level N = 0 of a graphene bilayer journal, March 2013

Chemical Potential and Quantum Hall Ferromagnetism in Bilayer Graphene text, January 2014

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene text, January 2012

Measurement of the electronic compressibility of bilayer graphene journal, July 2010

The electronic properties of bilayer graphene journal, April 2013

Evidence for a spin phase transition at charge neutrality in bilayer graphene journal, January 2013

Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene journal, October 2010

Observation of Quantum Hall “Valley Skyrmions” journal, August 2005

Tunable Fractional Quantum Hall Phases in Bilayer Graphene text, January 2014

Symmetry Breaking in the Zero-Energy Landau Level in Bilayer Graphene journal, February 2010

Single-electron capacitance spectroscopy of discrete quantum levels journal, May 1992

Capacitance of graphene bilayer as a probe of layer-specific properties journal, August 2011

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene text, January 2012

Topological Phases in the Zeroth Landau Level of Bilayer Graphene journal, January 2014

Broken symmetry states and divergent resistance in suspended bilayer graphene text, January 2009

Infinite density matrix renormalization group for multicomponent quantum Hall systems text, January 2014

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene journal, July 2012

Spin and valley quantum Hall ferromagnetism in graphene text, January 2012

A Stable Pfaffian State in Bilayer Graphene text, January 2011

Breaking of Particle-Hole Symmetry by Landau Level Mixing in the ν = 5 / 2 Quantized Hall State journal, March 2011

The electronic properties of bilayer graphene text, January 2012

Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene journal, May 2014

Chemical potential and quantum Hall ferromagnetism in bilayer graphene journal, July 2014

Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene journal, February 2016

Spin and pseudospins in layered transition metal dichalcogenides journal, April 2014

Stable Pfaffian State in Bilayer Graphene journal, October 2011

Evidence for a spontaneous gapped state in ultraclean bilayer graphene journal, June 2012

Orbital and interlayer skyrmion crystals in bilayer graphene journal, December 2010

Lattice theory of pseudospin ferromagnetism in bilayer graphene: Competing interaction-induced quantum Hall states journal, March 2011

One-Dimensional Electrical Contact to a Two-Dimensional Material journal, October 2013

Accurate tight-binding models for the π bands of bilayer graphene journal, January 2014

Infinite density matrix renormalization group for multicomponent quantum Hall systems journal, January 2015

Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene journal, October 2018

Evidence for a topological “exciton Fermi sea” in bilayer graphene journal, July 2018

Integer quantum Hall transition in a fraction of a Landau level journal, January 2018

Quantum Hall ferroelectric helix in bilayer graphene journal, March 2019

Imaging Anyons with Scanning Tunneling Microscopy journal, March 2018

Quantum Effects in the Capacitance of Field-Effect Transistors with a Double Quantum Well journal, September 2019

Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene text, January 2018

Unconventional anisotropic even-denominator fractional quantum Hall state in a system with mass anisotropy text, January 2018

Scattering of Magnons at Graphene Quantum-Hall-Magnet Junctions journal, March 2021

Disorder in twisted bilayer graphene journal, June 2020

Equilibration of Quantum hall edges in symmetry broken bilayer graphene text, January 2018

Tuning superconductivity in twisted bilayer graphene journal, January 2019

Observation of terahertz-induced magnetooscillations in graphene text, January 2020

Evidence for a topological "exciton Fermi sea" in bilayer graphene text, January 2018

Odd- and even-denominator fractional quantum Hall states in monolayer WSe2 journal, July 2020

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands journal, June 2019

Evidence for a topological “exciton Fermi sea” in bilayer graphene journal, July 2018

Valley-polarized magnetic state in hole-doped monolayers of transition-metal dichalcogenides journal, October 2018

Landau levels of bilayer graphene in a WSe2 /bilayer graphene van der Waals heterostructure journal, November 2019

Energy levels of graphene magnetic circular quantum dot journal, January 2020

Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
text, January 2012

Observation of Helical Edge States and Fractional Quantum Hall Effect in a Graphene Electron-hole Bilayer
text, January 2016

Broken-symmetry states and divergent resistance in suspended bilayer graphene
journal, September 2009

Spin and pseudospins in layered transition metal dichalcogenides
journal, April 2014

Capacitance measurements of a quantized two-dimensional electron gas in the regime of the quantum Hall effect
journal, May 1985

Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer
journal, October 2016

Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene
journal, October 2010

Topological Phases in the Zeroth Landau Level of Bilayer Graphene
text, January 2013

Tunable fractional quantum Hall phases in bilayer graphene
journal, July 2014

Nonabelions in the fractional quantum hall effect
journal, August 1991

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
journal, September 2012

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
text, January 2012

Competing ordered states with filling factor two in bilayer graphene
journal, July 2014

Quantum spin-valley Hall effect in AB-stacked bilayer silicene
journal, December 2019

Charge $2 e$ Skyrmions in Bilayer Graphene
journal, August 2009

Optically Pumped NMR Evidence for Finite-Size Skyrmions in GaAs Quantum Wells near Landau Level Filling $ν = 1$
journal, June 1995

Canted Antiferromagnetic Phase of the $ν = 0$ Quantum Hall State in Bilayer Graphene
journal, July 2012

Charge 2e skyrmions in bilayer graphene
text, January 2009

Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene
journal, August 2008

Observation of Quantum Hall Valley Skyrmions
text, January 2005

Spin and valley quantum Hall ferromagnetism in graphene
journal, May 2012

Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
text, January 2013

Tunable fractional quantum Hall phases in bilayer graphene
journal, July 2014

Energy gaps and layer polarization of integer and fractional quantum Hall states in bilayer graphene
text, January 2016

Quantum Hall ferromagnetic phases in the Landau level $N = 0$ of a graphene bilayer
journal, March 2013

Chemical Potential and Quantum Hall Ferromagnetism in Bilayer Graphene
text, January 2014

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
text, January 2012

Measurement of the electronic compressibility of bilayer graphene
journal, July 2010

The electronic properties of bilayer graphene
journal, April 2013

Evidence for a spin phase transition at charge neutrality in bilayer graphene
journal, January 2013

Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene
journal, October 2010

Observation of Quantum Hall “Valley Skyrmions”
journal, August 2005

Tunable Fractional Quantum Hall Phases in Bilayer Graphene
text, January 2014

Symmetry Breaking in the Zero-Energy Landau Level in Bilayer Graphene
journal, February 2010

Single-electron capacitance spectroscopy of discrete quantum levels
journal, May 1992

Capacitance of graphene bilayer as a probe of layer-specific properties
journal, August 2011

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
text, January 2012

Topological Phases in the Zeroth Landau Level of Bilayer Graphene
journal, January 2014

Broken symmetry states and divergent resistance in suspended bilayer graphene
text, January 2009

Infinite density matrix renormalization group for multicomponent quantum Hall systems
text, January 2014

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
journal, July 2012

Spin and valley quantum Hall ferromagnetism in graphene
text, January 2012

A Stable Pfaffian State in Bilayer Graphene
text, January 2011

Breaking of Particle-Hole Symmetry by Landau Level Mixing in the $ν = 5 / 2$ Quantized Hall State
journal, March 2011

The electronic properties of bilayer graphene
text, January 2012

Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene
journal, May 2014

Chemical potential and quantum Hall ferromagnetism in bilayer graphene
journal, July 2014

Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene
journal, February 2016

Spin and pseudospins in layered transition metal dichalcogenides
journal, April 2014

Stable Pfaffian State in Bilayer Graphene
journal, October 2011

Evidence for a spontaneous gapped state in ultraclean bilayer graphene
journal, June 2012

Orbital and interlayer skyrmion crystals in bilayer graphene
journal, December 2010

Lattice theory of pseudospin ferromagnetism in bilayer graphene: Competing interaction-induced quantum Hall states
journal, March 2011

One-Dimensional Electrical Contact to a Two-Dimensional Material
journal, October 2013

Accurate tight-binding models for the $π$ bands of bilayer graphene
journal, January 2014

Infinite density matrix renormalization group for multicomponent quantum Hall systems
journal, January 2015

Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene
journal, October 2018

Evidence for a topological “exciton Fermi sea” in bilayer graphene
journal, July 2018

Integer quantum Hall transition in a fraction of a Landau level
journal, January 2018

Quantum Hall ferroelectric helix in bilayer graphene
journal, March 2019

Imaging Anyons with Scanning Tunneling Microscopy
journal, March 2018

Quantum Effects in the Capacitance of Field-Effect Transistors with a Double Quantum Well
journal, September 2019

Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene
text, January 2018

Unconventional anisotropic even-denominator fractional quantum Hall state in a system with mass anisotropy
text, January 2018

Scattering of Magnons at Graphene Quantum-Hall-Magnet Junctions
journal, March 2021

Disorder in twisted bilayer graphene
journal, June 2020

Equilibration of Quantum hall edges in symmetry broken bilayer graphene
text, January 2018

Tuning superconductivity in twisted bilayer graphene
journal, January 2019

Observation of terahertz-induced magnetooscillations in graphene
text, January 2020

Evidence for a topological "exciton Fermi sea" in bilayer graphene
text, January 2018

Odd- and even-denominator fractional quantum Hall states in monolayer WSe2
journal, July 2020

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands
journal, June 2019

Evidence for a topological “exciton Fermi sea” in bilayer graphene
journal, July 2018

Valley-polarized magnetic state in hole-doped monolayers of transition-metal dichalcogenides
journal, October 2018

Landau levels of bilayer graphene in a WSe2 /bilayer graphene van der Waals heterostructure
journal, November 2019

Energy levels of graphene magnetic circular quantum dot
journal, January 2020

A review of the quantum Hall effects in MgZnO/ZnO heterostructures
journal, March 2018

Coupled Quantum Dots in Bilayer Graphene
journal, July 2018

Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
journal, September 2019

Optical control of the layer degree of freedom through Wannier–Stark states in polar 3R MoS ₂
journal, May 2019