Odd- and even-denominator fractional quantum Hall states in monolayer WSe2

Shi, Qianhui; Shih, En-Min; Gustafsson, Martin V.; Rhodes, Daniel A.; Kim, Bumho; Watanabe, Kenji; Taniguchi, Takashi; Papić, Zlatko; Hone, James; Dean, Cory R.

doi:10.1038/s41565-020-0685-6

Odd- and even-denominator fractional quantum Hall states in monolayer WSe₂

Journal Article · Mon Jul 06 00:00:00 EDT 2020 · Nature Nanotechnology

DOI:https://doi.org/10.1038/s41565-020-0685-6· OSTI ID:1803082

Shi, Qianhui ^[1]; ^[2]; Gustafsson, Martin V. ^[3]; Rhodes, Daniel A. ^[2]; Kim, Bumho ^[2]; ^[4]; Taniguchi, Takashi ^[4]; Papić, Zlatko ^[5]; ^[2]; ^[2]

Columbia Univ., New York, NY (United States); OSTI
Columbia Univ., New York, NY (United States)
Columbia Univ., New York, NY (United States); Raytheon BBN Technologies Corp., Cambridge, MA (United States)
National Institute for Materials Science (NIMS), Tsukuba (Japan)
University of Leeds (United Kingdom)

Monolayer semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure facilitates gate tunability just like graphene does, but unlike graphene, TMDs have the advantage of a sizable band gap and strong spin–orbit coupling. Measurements under large magnetic fields have revealed an unusual Landau level (LL) structure, distinct from other 2D electron systems. However, owing to the limited sample quality and poor electrical contact, probing the lowest LLs has been challenging, and observation of electron correlations within the fractionally filled LL regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of monolayer WSe₂ in the extreme quantum limit, and observe fractional quantum Hall states in the lowest three LLs. The odd-denominator fractional quantum Hall sequences demonstrate a systematic evolution with the LL orbital index, consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Finally, our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime.

View Accepted Manuscript (DOE)

Research Organization:: Columbia Univ., New York, NY (United States)

Sponsoring Organization:: EPSRC; National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: SC0016703

OSTI ID:: 1803082

Journal Information:: Nature Nanotechnology, Journal Name: Nature Nanotechnology Journal Issue: 7 Vol. 15; ISSN 1748-3387

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (37)

Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene Hunt, B. M.; Li, J. I. A.; Zibrov, A. A. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00824-w	journal	October 2017
Emergent Dirac Gullies and Gully-Symmetry-Breaking Quantum Hall States in A B A Trilayer Graphene Zibrov, A. A.; Rao, P.; Kometter, C. Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/physrevlett.121.167601	journal	October 2018
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
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Approaching the Intrinsic Limit in Transition Metal Diselenides via Point Defect Control Edelberg, Drew; Rhodes, Daniel; Kerelsky, Alexander Nano Letters, Vol. 19, Issue 7 https://doi.org/10.1021/acs.nanolett.9b00985	journal	June 2019
Observation of Even Denominator Fractional Quantum Hall Effect in Suspended Bilayer Graphene Ki, Dong-Keun; Fal’ko, Vladimir I.; Abanin, Dmitry A. Nano Letters, Vol. 14, Issue 4 https://doi.org/10.1021/nl5003922	journal	March 2014
Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level Zibrov, A. A.; Kometter, C.; Zhou, H. Nature, Vol. 549, Issue 7672 https://doi.org/10.1038/nature23893	journal	September 2017
Multicomponent fractional quantum Hall effect in graphene Dean, C. R.; Young, A. F.; Cadden-Zimansky, P. Nature Physics, Vol. 7, Issue 9 https://doi.org/10.1038/nphys2007	journal	May 2011
Even-denominator fractional quantum Hall physics in ZnO Falson, J.; Maryenko, D.; Friess, B. Nature Physics, Vol. 11, Issue 4 https://doi.org/10.1038/nphys3259	journal	March 2015
Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2 Gustafsson, Martin V.; Yankowitz, Matthew; Forsythe, Carlos Nature Materials, Vol. 17, Issue 5 https://doi.org/10.1038/s41563-018-0036-2	journal	March 2018
Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene Zibrov, A. A.; Spanton, E. M.; Zhou, H. Nature Physics, Vol. 14, Issue 9 https://doi.org/10.1038/s41567-018-0190-0	journal	July 2018
Compressibility of the two-dimensional electron gas: Measurements of the zero-field exchange energy and fractional quantum Hall gap Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W. Physical Review B, Vol. 50, Issue 3 https://doi.org/10.1103/PhysRevB.50.1760	journal	July 1994
Two point-contact interferometer for quantum Hall systems de C. Chamon, C.; Freed, D. E.; Kivelson, S. A. Physical Review B, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevB.55.2331	journal	January 1997
Competition between quantum-liquid and electron-solid phases in intermediate Landau levels Goerbig, M. O.; Lederer, P.; Smith, C. Morais Physical Review B, Vol. 69, Issue 11 https://doi.org/10.1103/PhysRevB.69.115327	journal	March 2004
Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two-dimensional electron layers: Finite-thickness effects Peterson, Michael R.; Jolicoeur, Th.; Das Sarma, S. Physical Review B, Vol. 78, Issue 15 https://doi.org/10.1103/PhysRevB.78.155308	journal	October 2008
Tunable interactions and phase transitions in Dirac materials in a magnetic field Papić, Z.; Abanin, D. A.; Barlas, Y. Physical Review B, Vol. 84, Issue 24 https://doi.org/10.1103/PhysRevB.84.241306	journal	December 2011
Spin- and valley-dependent magneto-optical properties of MoS 2 Rose, Félix; Goerbig, M. O.; Piéchon, Frédéric Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.125438	journal	September 2013
Surprising robustness of particle-hole symmetry for composite-fermion liquids Sreejith, G. J.; Zhang, Yuhe; Jain, J. K. Physical Review B, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevB.96.125149	journal	September 2017
Large effective mass and interaction-enhanced Zeeman splitting of K -valley electrons in MoSe 2 Larentis, Stefano; Movva, Hema C. P.; Fallahazad, Babak Physical Review B, Vol. 97, Issue 20 https://doi.org/10.1103/PhysRevB.97.201407	journal	May 2018
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
Coupled Spin and Valley Physics in Monolayers of MoS 2 and Other Group-VI Dichalcogenides Xiao, Di; Liu, Gui-Bin; Feng, Wanxiang Physical Review Letters, Vol. 108, Issue 19 https://doi.org/10.1103/PhysRevLett.108.196802	journal	May 2012
Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in Dirac Materials: Application to an Isolated MoS 2 Trilayer Li, Xiao; Zhang, Fan; Niu, Qian Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRevLett.110.066803	journal	February 2013
Gap Reversal at Filling Factors 3 + 1 / 3 and 3 + 1 / 5 : Towards Novel Topological Order in the Fractional Quantum Hall Regime Kleinbaum, Ethan; Kumar, Ashwani; Pfeiffer, L. N. Physical Review Letters, Vol. 114, Issue 7 https://doi.org/10.1103/PhysRevLett.114.076801	journal	February 2015
Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe 2 Movva, Hema C. P.; Fallahazad, Babak; Kim, Kyounghwan Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/PhysRevLett.118.247701	journal	June 2017
Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer MoS 2 Pisoni, Riccardo; Kormányos, Andor; Brooks, Matthew Physical Review Letters, Vol. 121, Issue 24 https://doi.org/10.1103/PhysRevLett.121.247701	journal	December 2018
High-Quality Magnetotransport in Graphene Using the Edge-Free Corbino Geometry Zeng, Y.; Li, J. I. A.; Dietrich, S. A. Physical Review Letters, Vol. 122, Issue 13 https://doi.org/10.1103/PhysRevLett.122.137701	journal	April 2019
Two-Dimensional Magnetotransport in the Extreme Quantum Limit Tsui, D. C.; Stormer, H. L.; Gossard, A. C. Physical Review Letters, Vol. 48, Issue 22 https://doi.org/10.1103/PhysRevLett.48.1559	journal	May 1982
Observation of an even-denominator quantum number in the fractional quantum Hall effect Willett, R.; Eisenstein, J. P.; Störmer, H. L. Physical Review Letters, Vol. 59, Issue 15 https://doi.org/10.1103/PhysRevLett.59.1776	journal	October 1987
Exact Quantization of the Even-Denominator Fractional Quantum Hall State at ν = 5 / 2 Landau Level Filling Factor Pan, W.; Xia, J. -S.; Shvarts, V. Physical Review Letters, Vol. 83, Issue 17 https://doi.org/10.1103/PhysRevLett.83.3530	journal	October 1999
Competition between a Fractional Quantum Hall Liquid and Bubble and Wigner Crystal Phases in the Third Landau Level Gervais, G.; Engel, L. W.; Stormer, H. L. Physical Review Letters, Vol. 93, Issue 26 https://doi.org/10.1103/PhysRevLett.93.266804	journal	December 2004
Particle-Hole Symmetry and the Pfaffian State Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236806	journal	December 2007
Particle-Hole Symmetry and the ν = 5 2 Quantum Hall State Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236807	journal	December 2007
Electronic properties of graphene in a strong magnetic field Goerbig, M. O. Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1193	journal	November 2011
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
Even-denominator fractional quantum Hall states in bilayer graphene Li, J. I. A.; Tan, C.; Chen, S. Science, Vol. 358, Issue 6363 https://doi.org/10.1126/science.aao2521	journal	October 2017
Scaling approach to the phase diagram of quantum Hall systems Goerbig, M. O.; Smith, C. Morais Europhysics Letters (EPL), Vol. 63, Issue 5 https://doi.org/10.1209/epl/i2003-00585-0	journal	September 2003
Supporting Data for Fractional Quantum Hall Effect in Monolayer WSe2 Papic, Zlatko; Shi, Qianhui University of Leeds https://doi.org/10.5518/807	dataset	January 2020

Similar Records

Even-denominator fractional quantum Hall effect at a Landau level crossing

Journal Article · Tue Apr 01 00:00:00 EDT 2014 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:1352837

Quantum Transport in 2D Semiconductors

Technical Report · Thu Dec 14 23:00:00 EST 2023 · OSTI ID:2204858

Even denominator fractional quantum Hall states in higher Landau levels of graphene

Journal Article · Sun Nov 25 19:00:00 EST 2018 · Nature Physics · OSTI ID:1489119

Related Subjects

36 MATERIALS SCIENCE
materials science
quantum hall
science & technology
two-dimensional materials

Odd- and even-denominator fractional quantum Hall states in monolayer WSe2

Citation Formats

References (37)

Similar Records

Related Subjects

Odd- and even-denominator fractional quantum Hall states in monolayer WSe₂