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

Journal Article · 16 October 2017 · Nature Communications

DOI: https://doi.org/10.1038/s41467-017-00824-w · OSTI ID:1529936

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)

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.

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

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

Grant/Contract Number:: FG02-08ER46514

OSTI ID:: 1529936

Alternate ID(s):: OSTI ID: 1545718

Journal Information:: Nature Communications, Vol. 8, Issue 1; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (56)

Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene Bao, Wenzhong; Velasco, Jairo; Zhang, Fan arXiv https://doi.org/10.48550/arxiv.1202.3212	text	January 2012
Observation of Helical Edge States and Fractional Quantum Hall Effect in a Graphene Electron-hole Bilayer Sanchez-Yamagishi, J. D.; Luo, J. Y.; Young, A. F. arXiv https://doi.org/10.48550/arxiv.1602.06815	text	January 2016
Broken-symmetry states and divergent resistance in suspended bilayer graphene Feldman, Benjamin E.; Martin, Jens; Yacoby, Amir Nature Physics, Vol. 5, Issue 12 https://doi.org/10.1038/nphys1406	journal	September 2009
Spin and pseudospins in layered transition metal dichalcogenides Xu, Xiaodong; Yao, Wang; Xiao, Di Nature Physics, Vol. 10, Issue 5 https://doi.org/10.1038/nphys2942	journal	April 2014
Capacitance measurements of a quantized two-dimensional electron gas in the regime of the quantum Hall effect Goodall, R. K.; Higgins, R. J.; Harrang, J. P. Physical Review B, Vol. 31, Issue 10 https://doi.org/10.1103/physrevb.31.6597	journal	May 1985
Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer Sanchez-Yamagishi, Javier D.; Luo, Jason Y.; Young, Andrea F. Nature Nanotechnology, Vol. 12, Issue 2 https://doi.org/10.1038/nnano.2016.214	journal	October 2016
Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene Weitz, R. T.; Allen, M. T.; Feldman, B. E. Science, Vol. 330, Issue 6005 https://doi.org/10.1126/science.1194988	journal	October 2010
Topological Phases in the Zeroth Landau Level of Bilayer Graphene Papić, Z.; Abanin, D. A. arXiv https://doi.org/10.48550/arxiv.1307.2909	text	January 2013
Tunable fractional quantum Hall phases in bilayer graphene Maher, Patrick; Wang, Lei; Gao, Yuanda Science, Vol. 345, Issue 6192 https://doi.org/10.1126/science.1252875	journal	July 2014
Observation of Quantum Hall “Valley Skyrmions” Shkolnikov, Y. P.; Misra, S.; Bishop, N. C. Physical Review Letters, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevLett.95.066809	journal	August 2005
Nonabelions in the fractional quantum hall effect Moore, Gregory; Read, Nicholas Nuclear Physics B, Vol. 360, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90407-O	journal	August 1991
Charge 2 e Skyrmions in Bilayer Graphene Abanin, D. A.; Parameswaran, S. A.; Sondhi, S. L. Physical Review Letters, Vol. 103, Issue 7 https://doi.org/10.1103/PhysRevLett.103.076802	journal	August 2009
Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene Feldman, B. E.; Krauss, B.; Smet, J. H. Science, Vol. 337, Issue 6099 https://doi.org/10.1126/science.1224784	journal	September 2012
Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene Feldman, Benjamin E.; Krauss, Benjamin; Smet, Jurgen H. arXiv https://doi.org/10.48550/arxiv.1201.5128	text	January 2012
Competing ordered states with filling factor two in bilayer graphene Velasco Jr, J.; Lee, Y.; Zhang, F. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5550	journal	July 2014
Quantum spin-valley Hall effect in AB-stacked bilayer silicene Lee, Kyu Won; Lee, Cheol Eui Scientific Reports, Vol. 9, Issue 1 https://doi.org/10.1038/s41598-019-55927-9	journal	December 2019
Optically Pumped NMR Evidence for Finite-Size Skyrmions in GaAs Quantum Wells near Landau Level Filling ν = 1 Barrett, S. E.; Dabbagh, G.; Pfeiffer, L. N. Physical Review Letters, Vol. 74, Issue 25 https://doi.org/10.1103/PhysRevLett.74.5112	journal	June 1995
Canted Antiferromagnetic Phase of the ν = 0 Quantum Hall State in Bilayer Graphene Kharitonov, Maxim Physical Review Letters, Vol. 109, Issue 4 https://doi.org/10.1103/PhysRevLett.109.046803	journal	July 2012
Charge 2e skyrmions in bilayer graphene Abanin, D. A.; Parameswaran, S. A.; Sondhi, S. L. arXiv https://doi.org/10.48550/arxiv.0904.0040	text	January 2009
Observation of Quantum Hall Valley Skyrmions Shkolnikov, Y. P.; Misra, S.; Bishop, N. C. arXiv https://doi.org/10.48550/arxiv.cond-mat/0505118	text	January 2005
Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene Barlas, Yafis; Côté, R.; Nomura, K. Physical Review Letters, Vol. 101, Issue 9 https://doi.org/10.1103/PhysRevLett.101.097601	journal	August 2008
Spin and valley quantum Hall ferromagnetism in graphene Young, A. F.; Dean, C. R.; Wang, L. Nature Physics, Vol. 8, Issue 7 https://doi.org/10.1038/nphys2307	journal	May 2012
Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene Kou, Angela; Feldman, Benjamin E.; Levin, Andrei J. arXiv https://doi.org/10.48550/arxiv.1312.7033	text	January 2013
Single-electron capacitance spectroscopy of discrete quantum levels Ashoori, R. C.; Stormer, H. L.; Weiner, J. S. Physical Review Letters, Vol. 68, Issue 20 https://doi.org/10.1103/physrevlett.68.3088	journal	May 1992
Tunable fractional quantum Hall phases in bilayer graphene Maher, Patrick; Wang, Lei; Gao, Yuanda Science, Vol. 345, Issue 6192 https://doi.org/10.1126/science.1252875	journal	July 2014
Energy gaps and layer polarization of integer and fractional quantum Hall states in bilayer graphene Shi, Yanmeng; Lee, Yongjin; Che, Shi arXiv https://doi.org/10.48550/arxiv.1601.04116	text	January 2016
Quantum Hall ferromagnetic phases in the Landau level N = 0 of a graphene bilayer Lambert, J.; Côté, R. Physical Review B, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevB.87.115415	journal	March 2013
Chemical Potential and Quantum Hall Ferromagnetism in Bilayer Graphene Lee, Kayoung; Fallahazad, Babak; Xue, Jiamin arXiv https://doi.org/10.48550/arxiv.1401.0659	text	January 2014
Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene Shizuya, K. arXiv https://doi.org/10.48550/arxiv.1205.6330	text	January 2012
Measurement of the electronic compressibility of bilayer graphene Henriksen, E. A.; Eisenstein, J. P. Physical Review B, Vol. 82, Issue 4 https://doi.org/10.1103/PhysRevB.82.041412	journal	July 2010
The electronic properties of bilayer graphene McCann, Edward; Koshino, Mikito Reports on Progress in Physics, Vol. 76, Issue 5 https://doi.org/10.1088/0034-4885/76/5/056503	journal	April 2013
Evidence for a spin phase transition at charge neutrality in bilayer graphene Maher, P.; Dean, C. R.; Young, A. F. Nature Physics, Vol. 9, Issue 3 https://doi.org/10.1038/nphys2528	journal	January 2013
Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene Weitz, R. T.; Allen, M. T.; Feldman, B. E. Science, Vol. 330, Issue 6005 https://doi.org/10.1126/science.1194988	journal	October 2010
Tunable Fractional Quantum Hall Phases in Bilayer Graphene Maher, Patrick; Wang, Lei; Gao, Yuanda arXiv https://doi.org/10.48550/arxiv.1403.2112	text	January 2014
Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene Shizuya, K. arXiv https://doi.org/10.48550/arxiv.1205.6330	text	January 2012
Topological Phases in the Zeroth Landau Level of Bilayer Graphene Papić, Z.; Abanin, D. A. Physical Review Letters, Vol. 112, Issue 4 https://doi.org/10.1103/PhysRevLett.112.046602	journal	January 2014
Broken symmetry states and divergent resistance in suspended bilayer graphene Feldman, Benjamin E.; Martin, Jens; Yacoby, Amir arXiv https://doi.org/10.48550/arxiv.0909.2883	text	January 2009
Infinite density matrix renormalization group for multicomponent quantum Hall systems Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank arXiv https://doi.org/10.48550/arxiv.1410.3861	text	January 2014
Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene Shizuya, K. Physical Review B, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevB.86.045431	journal	July 2012
Spin and valley quantum Hall ferromagnetism in graphene Young, Andrea F.; Dean, Cory R.; Wang, Lei arXiv https://doi.org/10.48550/arxiv.1201.4167	text	January 2012
A Stable Pfaffian State in Bilayer Graphene Apalkov, Vadim M.; Chakraborty, Tapash arXiv https://doi.org/10.48550/arxiv.1104.2020	text	January 2011
Breaking of Particle-Hole Symmetry by Landau Level Mixing in the ν = 5 / 2 Quantized Hall State Rezayi, Edward H.; Simon, Steven H. Physical Review Letters, Vol. 106, Issue 11 https://doi.org/10.1103/PhysRevLett.106.116801	journal	March 2011
The electronic properties of bilayer graphene McCann, Edward; Koshino, Mikito arXiv https://doi.org/10.48550/arxiv.1205.6953	text	January 2012
Symmetry Breaking in the Zero-Energy Landau Level in Bilayer Graphene Zhao, Y.; Cadden-Zimansky, P.; Jiang, Z. Physical Review Letters, Vol. 104, Issue 6 https://doi.org/10.1103/PhysRevLett.104.066801	journal	February 2010
Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene Kou, A.; Feldman, B. E.; Levin, A. J. Science, Vol. 345, Issue 6192 https://doi.org/10.1126/science.1250270	journal	May 2014
Chemical potential and quantum Hall ferromagnetism in bilayer graphene Lee, Kayoung; Fallahazad, Babak; Xue, Jiamin Science, Vol. 345, Issue 6192 https://doi.org/10.1126/science.1251003	journal	July 2014
Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene Shi, Yanmeng; Lee, Yongjin; Che, Shi Physical Review Letters, Vol. 116, Issue 5 https://doi.org/10.1103/PhysRevLett.116.056601	journal	February 2016
Spin and pseudospins in layered transition metal dichalcogenides Xu, Xiaodong; Yao, Wang; Xiao, Di Nature Physics, Vol. 10, Issue 5 https://doi.org/10.1038/nphys2942	journal	April 2014
Stable Pfaffian State in Bilayer Graphene Apalkov, Vadim M.; Chakraborty, Tapash Physical Review Letters, Vol. 107, Issue 18 https://doi.org/10.1103/PhysRevLett.107.186803	journal	October 2011
Evidence for a spontaneous gapped state in ultraclean bilayer graphene Bao, W.; Velasco, J.; Zhang, F. Proceedings of the National Academy of Sciences, Vol. 109, Issue 27 https://doi.org/10.1073/pnas.1205978109	journal	June 2012
Orbital and interlayer skyrmion crystals in bilayer graphene Côté, R.; Luo, Wenchen; Petrov, Branko Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.245307	journal	December 2010
Lattice theory of pseudospin ferromagnetism in bilayer graphene: Competing interaction-induced quantum Hall states Jung, Jeil; Zhang, Fan; MacDonald, Allan H. Physical Review B, Vol. 83, Issue 11 https://doi.org/10.1103/PhysRevB.83.115408	journal	March 2011
One-Dimensional Electrical Contact to a Two-Dimensional Material Wang, L.; Meric, I.; Huang, P. Y. Science, Vol. 342, Issue 6158 https://doi.org/10.1126/science.1244358	journal	October 2013
Capacitance of graphene bilayer as a probe of layer-specific properties Young, Andrea F.; Levitov, Leonid S. Physical Review B, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevB.84.085441	journal	August 2011
Accurate tight-binding models for the π bands of bilayer graphene Jung, Jeil; MacDonald, Allan H. Physical Review B, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevB.89.035405	journal	January 2014
Infinite density matrix renormalization group for multicomponent quantum Hall systems Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.045115	journal	January 2015

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