Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing

Zhao, Jianyun; Zhang, Yuhe; Jain, J. K.

doi:10.1103/PhysRevLett.121.116802

Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing

Journal Article · Tue Sep 11 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.121.116802· OSTI ID:1489112

Zhao, Jianyun ^[1]; Zhang, Yuhe ^[2]; Jain, J. K. ^[2]

The Pennsylvania State Univ., University Park, PA (United States); Penn State University
The Pennsylvania State Univ., University Park, PA (United States)

Here, the interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the non-perturbative fixed phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the ν – κ plane, where ν is the filling factor and κ is the strength of Landau level mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν = n/(2pn + 1) being much more susceptible to crystallization due to Landau level mixing than those at ν = n/(2pn + 1). Our results explain the qualitative difference between the experimental behaviors observed in n-doped and p-doped GaAs quantum wells, and, in particular, the existence of an insulating state for ν < 1/3 and also for 1/3 < ν < 2/5 in low density p-doped systems. We predict that in the vicinity of ν = 1/5 and ν = 2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal but rather into a strongly correlated crystal of composite fermions carrying two vortices.

View Accepted Manuscript (DOE)

Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0005042

OSTI ID:: 1489112

Alternate ID(s):: OSTI ID: 1469437

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 11 Vol. 121; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (62)

Microwave resonances in low-filling insulating phases of two-dimensional electron and hole systems Engel, L. W.; Li, C. -C; Shahar, D. Physica E: Low-dimensional Systems and Nanostructures, Vol. 1, Issue 1-4 https://doi.org/10.1016/S1386-9477(97)00025-8	journal	January 1997
Pinning mode resonances of new phases of 2D electron systems in high magnetic fields Sambandamurthy, G.; Wang, Zhihai; Lewis, R. M. Solid State Communications, Vol. 140, Issue 2 https://doi.org/10.1016/j.ssc.2006.05.053	journal	October 2006
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Melting of a 2D quantum electron solid in high magnetic field Chen, Yong P.; Sambandamurthy, G.; Wang, Z. H. Nature Physics, Vol. 2, Issue 7 https://doi.org/10.1038/nphys322	journal	June 2006
Sharp tunnelling resonance from the vibrations of an electronic Wigner crystal Jang, Joonho; Hunt, Benjamin M.; Pfeiffer, Loren N. Nature Physics, Vol. 13, Issue 4 https://doi.org/10.1038/nphys3979	journal	December 2016
Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy Kim, Sungmin; Schwenk, Johannes; Walkup, Daniel Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-22886-7	journal	May 2021
Fixed‐node quantum Monte Carlo for molecules ^a) b) Reynolds, Peter J.; Ceperley, David M.; Alder, Berni J. The Journal of Chemical Physics, Vol. 77, Issue 11 https://doi.org/10.1063/1.443766	journal	December 1982
XXIV. On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure Thomson, J. J. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 7, Issue 39 https://doi.org/10.1080/14786440409463107	journal	March 1904
On the Interaction of Electrons in Metals Hubbard, J. Proceedings of the Physical Society. Section A, Vol. 68, Issue 5 https://doi.org/10.1088/0370-1298/68/5/413	journal	May 1955
On the Interaction of Electrons in Metals Wigner, E. Physical Review, Vol. 46, Issue 11 https://doi.org/10.1103/PhysRev.46.1002	journal	December 1934
Static and dynamic properties of a two-dimensional Wigner crystal in a strong magnetic field Maki, Kazumi; Zotos, Xenophon Physical Review B, Vol. 28, Issue 8 https://doi.org/10.1103/PhysRevB.28.4349	journal	October 1983
Crystallization of the incompressible quantum-fluid state of a two-dimensional electron gas in a strong magnetic field Levesque, D.; Weis, J. J.; MacDonald, A. H. Physical Review B, Vol. 30, Issue 2 https://doi.org/10.1103/PhysRevB.30.1056	journal	July 1984
Liquid-solid transition and the fractional quantum-Hall effect Lam, Pui K.; Girvin, S. M. Physical Review B, Vol. 30, Issue 1 https://doi.org/10.1103/PhysRevB.30.473	journal	July 1984
Fractional quantum Hall effect and Chern-Simons gauge theories Lopez, Ana; Fradkin, Eduardo Physical Review B, Vol. 44, Issue 10 https://doi.org/10.1103/PhysRevB.44.5246	journal	September 1991
Electrical conductivity and Wigner crystallization Paalanen, M. A.; Willett, R. L.; Ruel, R. R. Physical Review B, Vol. 45, Issue 23 https://doi.org/10.1103/PhysRevB.45.13784	journal	June 1992
Effect of Landau-level mixing on quantum-liquid and solid states of two-dimensional hole systems Santos, M. B.; Jo, J.; Suen, Y. W. Physical Review B, Vol. 46, Issue 20 https://doi.org/10.1103/PhysRevB.46.13639	journal	November 1992
Theory of the half-filled Landau level Halperin, B. I.; Lee, Patrick A.; Read, Nicholas Physical Review B, Vol. 47, Issue 12 https://doi.org/10.1103/PhysRevB.47.7312	journal	March 1993
Wigner crystal versus Hall insulator Manoharan, H. C.; Shayegan, M. Physical Review B, Vol. 50, Issue 23 https://doi.org/10.1103/PhysRevB.50.17662	journal	December 1994
Quantitative study of large composite-fermion systems Jain, J. K.; Kamilla, R. K. Physical Review B, Vol. 55, Issue 8 https://doi.org/10.1103/PhysRevB.55.R4895	journal	February 1997
Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field Yi, Hangmo; Fertig, H. A. Physical Review B, Vol. 58, Issue 7 https://doi.org/10.1103/PhysRevB.58.4019	journal	August 1998
Microwave resonance and weak pinning in two-dimensional hole systems at high magnetic fields Li, C. -C.; Yoon, J.; Engel, L. W. Physical Review B, Vol. 61, Issue 16 https://doi.org/10.1103/PhysRevB.61.10905	journal	April 2000
Hamiltonian theory of the composite-fermion Wigner crystal Narevich, R.; Murthy, Ganpathy; Fertig, H. A. Physical Review B, Vol. 64, Issue 24 https://doi.org/10.1103/PhysRevB.64.245326	journal	December 2001
Transition from a fractional quantum Hall liquid to an electron solid at Landau level filling ν = 1 3 in tilted magnetic fields Pan, W.; Csáthy, G. A.; Tsui, D. C. Physical Review B, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevB.71.035302	journal	January 2005
Maximum-density droplet to lower-density droplet transition in quantum dots Güçlü, A. D.; Umrigar, C. J. Physical Review B, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevB.72.045309	journal	July 2005
Phase boundary between the fractional quantum Hall liquid and the Wigner crystal at low filling factors and low temperatures: A path integral Monte Carlo study He, W. J.; Cui, T.; Ma, Y. M. Physical Review B, Vol. 72, Issue 19 https://doi.org/10.1103/PhysRevB.72.195306	journal	November 2005
Structure and dynamics of spherical crystals characterized for the Thomson problem Wales, David J.; Ulker, Sidika Physical Review B, Vol. 74, Issue 21 https://doi.org/10.1103/PhysRevB.74.212101	journal	December 2006
Defect motifs for spherical topologies Wales, David J.; McKay, Hayley; Altschuler, Eric L. Physical Review B, Vol. 79, Issue 22 https://doi.org/10.1103/PhysRevB.79.224115	journal	June 2009
Landau level mixing and the fractional quantum Hall effect Sodemann, I.; MacDonald, A. H. Physical Review B, Vol. 87, Issue 24 https://doi.org/10.1103/PhysRevB.87.245425	journal	June 2013
Transport of a sliding Wigner crystal in the four flux composite fermion regime Zhang, Chi; Du, Rui-Rui; Manfra, M. J. Physical Review B, Vol. 92, Issue 7 https://doi.org/10.1103/PhysRevB.92.075434	journal	August 2015
Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems Zhang, Yuhe; Jain, J. K.; Eisenstein, J. P. Physical Review B, Vol. 95, Issue 19 https://doi.org/10.1103/PhysRevB.95.195105	journal	May 2017
Quantum Monte Carlo with variable spins: Fixed-phase and fixed-node approximations Melton, Cody A.; Mitas, Lubos Physical Review E, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevE.96.043305	journal	October 2017
Competing Crystal Phases in the Lowest Landau Level Archer, Alexander C.; Park, Kwon; Jain, Jainendra K. Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.146804	journal	October 2013
Fractional Quantum Hall Effect and Wigner Crystal of Interacting Composite Fermions Liu, Yang; Kamburov, D.; Hasdemir, S. Physical Review Letters, Vol. 113, Issue 24 https://doi.org/10.1103/PhysRevLett.113.246803	journal	December 2014
Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal Deng, H.; Liu, Y.; Jo, I. Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.096601	journal	August 2016
Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect Zhang, Yuhe; Wójs, A.; Jain, J. K. Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.116803	journal	September 2016
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
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevLett.50.1395	journal	May 1983
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States Haldane, F. D. M. Physical Review Letters, Vol. 51, Issue 7 https://doi.org/10.1103/PhysRevLett.51.605	journal	August 1983
Composite-fermion approach for the fractional quantum Hall effect Jain, J. K. Physical Review Letters, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevLett.63.199	journal	July 1989
Evidence for two-dimentional quantum Wigner crystal Goldman, V. J.; Santos, M.; Shayegan, M. Physical Review Letters, Vol. 65, Issue 17 https://doi.org/10.1103/PhysRevLett.65.2189	journal	October 1990
Quantum liquid versus electron solid around ν=1/5 Landau-level filling Jiang, H. W.; Willett, R. L.; Stormer, H. L. Physical Review Letters, Vol. 65, Issue 5 https://doi.org/10.1103/PhysRevLett.65.633	journal	July 1990
Observation of a reentrant insulating phase near the 1/3 fractional quantum Hall liquid in a two-dimensional hole system Santos, M. B.; Suen, Y. W.; Shayegan, M. Physical Review Letters, Vol. 68, Issue 8 https://doi.org/10.1103/PhysRevLett.68.1188	journal	February 1992
Wigner crystallization in the fractional quantum Hall regime: A variational quantum Monte Carlo study Zhu, Xuejun; Louie, Steven G. Physical Review Letters, Vol. 70, Issue 3 https://doi.org/10.1103/PhysRevLett.70.335	journal	January 1993
Fractional quantum Hall liquid, Wigner solid phase boundary at finite density and magnetic field Price, Rodney; Platzman, P. M.; He, Song Physical Review Letters, Vol. 70, Issue 3 https://doi.org/10.1103/PhysRevLett.70.339	journal	January 1993
Quantum freezing of the fractional quantum Hall liquid Platzman, P. M.; Price, Rodney Physical Review Letters, Vol. 70, Issue 22 https://doi.org/10.1103/PhysRevLett.70.3487	journal	May 1993
New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field Ortiz, G.; Ceperley, D. M.; Martin, R. M. Physical Review Letters, Vol. 71, Issue 17 https://doi.org/10.1103/PhysRevLett.71.2777	journal	October 1993
Evidence for a Bilayer Quantum Wigner Solid Manoharan, H. C.; Suen, Y. W.; Santos, M. B. Physical Review Letters, Vol. 77, Issue 9 https://doi.org/10.1103/PhysRevLett.77.1813	journal	August 1996
Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study Melik-Alaverdian, V.; Bonesteel, N. E.; Ortiz, G. Physical Review Letters, Vol. 79, Issue 26 https://doi.org/10.1103/PhysRevLett.79.5286	journal	December 1997
Transition from an Electron Solid to the Sequence of Fractional Quantum Hall States at Very Low Landau Level Filling Factor Pan, W.; Stormer, H. L.; Tsui, D. C. Physical Review Letters, Vol. 88, Issue 17 https://doi.org/10.1103/PhysRevLett.88.176802	journal	April 2002
Correlation Lengths of the Wigner-Crystal Order in a Two-Dimensional Electron System at High Magnetic Fields Ye, P. D.; Engel, L. W.; Tsui, D. C. Physical Review Letters, Vol. 89, Issue 17 https://doi.org/10.1103/PhysRevLett.89.176802	journal	October 2002
Evidence for Two Different Solid Phases of Two-Dimensional Electrons in High Magnetic Fields Chen, Yong P.; Lewis, R. M.; Engel, L. W. Physical Review Letters, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevLett.93.206805	journal	November 2004
Microscopic Verification of Topological Electron-Vortex Binding in the Lowest Landau-Level Crystal State Chang, Chia-Chen; Jeon, Gun Sang; Jain, Jainendra K. Physical Review Letters, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevLett.94.016809	journal	January 2005
Magnetic-Field-Induced Insulating Phases at Large r s Csáthy, G. A.; Noh, Hwayong; Tsui, D. C. Physical Review Letters, Vol. 94, Issue 22 https://doi.org/10.1103/PhysRevLett.94.226802	journal	June 2005
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001
Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level Jain, J. K.; Kamilla, R. K. International Journal of Modern Physics B, Vol. 11, Issue 22 https://doi.org/10.1142/S0217979297001301	journal	September 1997
Landau Level Mixing and the Fractional Quantum Hall Effect Sodemann, Inti; MacDonald, A. H. arXiv https://doi.org/10.48550/arxiv.1302.3896	text	January 2013
Sharp Tunneling Resonance from the Vibrations of an Electronic Wigner Crystal Jang, Joonho; Hunt, Benjamin; Pfeiffer, Loren N. arXiv https://doi.org/10.48550/arxiv.1604.06220	text	January 2016
Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems Zhang, Yuhe; Jain, J. K.; Eisenstein, J. P. arXiv https://doi.org/10.48550/arxiv.1702.08595	text	January 2017
Quantum Monte Carlo with variable spins: fixed-phase and fixed-node approximations Melton, Cody A.; Mitas, Lubos arXiv https://doi.org/10.48550/arxiv.1703.03481	text	January 2017
Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor Pan, W.; Stormer, H. L.; Tsui, D. C. arXiv https://doi.org/10.48550/arxiv.cond-mat/0303428	text	January 2003
Evidence for a Bilayer Quantum Wigner Solid Manoharan, H. C.; Suen, Y. W.; Santos, M. B. arXiv https://doi.org/10.48550/arxiv.cond-mat/9603008	text	January 1996
Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level Jain, J. K.; Kamilla, R. K. arXiv https://doi.org/10.48550/arxiv.cond-mat/9704031	text	January 1997

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