Zero-field magnetic response functions in Landau levels

Gao, Yang; Niu, Qian

doi:10.1073/pnas.1702595114

Title: Zero-field magnetic response functions in Landau levels

Journal Article · Tue Jun 27 00:00:00 EDT 2017 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.1702595114· OSTI ID:1366767

Gao, Yang; Niu, Qian

Here, we present a fresh perspective on the Landau level quantization rule; that is, by successively including zero-field magnetic response functions at zero temperature, such as zero-field magnetization and susceptibility, the Onsager’s rule can be corrected order by order. Such a perspective is further reinterpreted as a quantization of the semiclassical electron density in solids. Our theory not only reproduces Onsager’s rule at zeroth order and the Berry phase and magnetic moment correction at first order but also explains the nature of higher-order corrections in a universal way. In applications, those higher-order corrections are expected to curve the linear relation between the level index and the inverse of the magnetic field, as already observed in experiments. Our theory then provides a way to extract the correct value of Berry phase as well as the magnetic susceptibility at zero temperature from Landau level fan diagrams in experiments. Moreover, it can be used theoretically to calculate Landau levels up to second-order accuracy for realistic models.

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF); National Basic Research Program of China (NBRPC); Welch Foundation

Grant/Contract Number:: FG03-02ER45958; 2013CB921900; EFMA-1641101; F-1255

OSTI ID:: 1366767

Alternate ID(s):: OSTI ID: 1418601

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 114 Journal Issue: 28; ISSN 0027-8424

Publisher:: National Academy of Sciences, Washington, DC (United States)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 22 works

Citation information provided by
Web of Science

References (40)

Quantum Theory of Orbital Magnetization and Its Generalization to Interacting Systems Shi, Junren; Vignale, G.; Xiao, Di Physical Review Letters, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevLett.99.197202	journal	November 2007
Experimental observation of the quantum Hall effect and Berry's phase in graphene Zhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L. Nature, Vol. 438, Issue 7065, p. 201-204 https://doi.org/10.1038/nature04235	journal	November 2005
Walk inside Hofstadter's butterfly Guillement, J. P.; Helffer, B.; Treton, P. Journal de Physique, Vol. 50, Issue 15 https://doi.org/10.1051/jphys:0198900500150201900	journal	January 1989
Landau-level subband structure of electrons on a square lattice MacDonald, A. H. Physical Review B, Vol. 28, Issue 12 https://doi.org/10.1103/PhysRevB.28.6713	journal	December 1983
Landau level spectrum of Bloch electrons in a honeycomb lattice Rammal, R. Journal de Physique, Vol. 46, Issue 8 https://doi.org/10.1051/jphys:019850046080134500	journal	January 1985
Periodic Orbits and Classical Quantization Conditions Gutzwiller, Martin C. Journal of Mathematical Physics, Vol. 12, Issue 3 https://doi.org/10.1063/1.1665596	journal	March 1971
Oscillatory angular dependence of the magnetoresistance in a topological insulator ${Bi}_{1 - x} {Sb}_{x}$ Taskin, A. A.; Segawa, Kouji; Ando, Yoichi Physical Review B, Vol. 82, Issue 12 https://doi.org/10.1103/PhysRevB.82.121302	journal	September 2010
Orbital diamagnetism in multilayer graphenes: Systematic study with the effective mass approximation Koshino, Mikito; Ando, Tsuneya Physical Review B, Vol. 76, Issue 8 https://doi.org/10.1103/PhysRevB.76.085425	journal	August 2007
Orbital magnetism in coupled-bands models Raoux, Arnaud; Piéchon, Frédéric; Fuchs, Jean-Noël Physical Review B, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevB.91.085120	journal	February 2015
Berry phase in graphene: Semiclassical perspective Carmier, Pierre; Ullmo, Denis Physical Review B, Vol. 77, Issue 24 https://doi.org/10.1103/PhysRevB.77.245413	journal	June 2008
Topological Phase Diagram of a Two-Subband Electron System Lee, X. Y.; Jiang, H. W.; Schaff, W. J. Physical Review Letters, Vol. 83, Issue 18 https://doi.org/10.1103/PhysRevLett.83.3701	journal	November 1999
Floating of critical states and the QH to insulator transition Potempa, H.; Schweitzer, L. Physica B: Condensed Matter, Vol. 298, Issue 1-4 https://doi.org/10.1016/S0921-4526(01)00254-X	journal	April 2001
An example of phase holonomy in WKB theory Wilkinson, M. Journal of Physics A: Mathematical and General, Vol. 17, Issue 18 https://doi.org/10.1088/0305-4470/17/18/016	journal	December 1984
Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands Chang, Ming-Che; Niu, Qian Physical Review B, Vol. 53, Issue 11 https://doi.org/10.1103/PhysRevB.53.7010	journal	March 1996
Quantum Oscillations and Hall Anomaly of Surface States in the Topological Insulator Bi₂Te₃ Qu, D.-X.; Hor, Y. S.; Xiong, J. Science, Vol. 329, Issue 5993, p. 821-824 https://doi.org/10.1126/science.1189792	journal	July 2010
Large bulk resistivity and surface quantum oscillations in the topological insulator ${Bi}_{2} {Te}_{2} Se$ Ren, Zhi; Taskin, A. A.; Sasaki, Satoshi Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.241306	journal	December 2010
Interpretation of the de Haas-van Alphen effect Onsager, L. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 43, Issue 344 https://doi.org/10.1080/14786440908521019	journal	September 1952
Geometrical effects in orbital magnetic susceptibility Gao, Yang; Yang, Shengyuan A.; Niu, Qian Physical Review B, Vol. 91, Issue 21 https://doi.org/10.1103/PhysRevB.91.214405	journal	June 2015
Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models Fuchs, J. N.; Piéchon, F.; Goerbig, M. O. The European Physical Journal B, Vol. 77, Issue 3 https://doi.org/10.1140/epjb/e2010-00259-2	journal	September 2010
Semiclassical theory of potential scattering for massless Dirac fermions Reijnders, K. J. A.; Tudorovskiy, T.; Katsnelson, M. I. Annals of Physics, Vol. 333 https://doi.org/10.1016/j.aop.2013.03.001	journal	June 2013
Manipulating surface states in topological insulator nanoribbons Xiu, Faxian; He, Liang; Wang, Yong Nature Nanotechnology, Vol. 6, Issue 4 https://doi.org/10.1038/nnano.2011.19	journal	February 2011
Berry Phase Correction to Electron Density of States in Solids Xiao, Di; Shi, Junren; Niu, Qian Physical Review Letters, Vol. 95, Issue 13 https://doi.org/10.1103/PhysRevLett.95.137204	journal	September 2005
Manifestation of Berry's Phase in Metal Physics Mikitik, G. P.; Sharlai, Yu. V. Physical Review Letters, Vol. 82, Issue 10, p. 2147-2150 https://doi.org/10.1103/PhysRevLett.82.2147	journal	March 1999
Lectures on Morse theory, old and new Bott, Raoul Bulletin of the American Mathematical Society, Vol. 7, Issue 2 https://doi.org/10.1090/S0273-0979-1982-15038-8	journal	April 1982
Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer McCann, Edward; Fal’ko, Vladimir I. Physical Review Letters, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevLett.96.086805	journal	March 2006
Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder Koschny, Th.; Schweitzer, L. Physical Review B, Vol. 67, Issue 19 https://doi.org/10.1103/PhysRevB.67.195307	journal	May 2003
Two-dimensional surface state in the quantum limit of a topological insulator Analytis, James G.; McDonald, Ross D.; Riggs, Scott C. Nature Physics, Vol. 6, Issue 12 https://doi.org/10.1038/nphys1861	journal	November 2010
Gate-tuned normal and superconducting transport at the surface of a topological insulator Sacépé, Benjamin; Oostinga, Jeroen B.; Li, Jian Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1586	journal	September 2011
Observation of topological transition of Fermi surface from a spindle torus to a torus in bulk Rashba spin-split BiTeCl Xiang, Fei-Xiang; Wang, Xiao-Lin; Veldhorst, Menno Physical Review B, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevB.92.035123	journal	July 2015
Levitation of Extended-State Bands in a Strong Magnetic Field Laughlin, R. B. Physical Review Letters, Vol. 52, Issue 25 https://doi.org/10.1103/PhysRevLett.52.2304	journal	June 1984
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields Hofstadter, Douglas R. Physical Review B, Vol. 14, Issue 6 https://doi.org/10.1103/PhysRevB.14.2239	journal	September 1976
Semiclassical Theory of Magnetic Energy Levels and Magnetic Susceptibility of Bloch Electrons Roth, Laura M. Physical Review, Vol. 145, Issue 2 https://doi.org/10.1103/PhysRev.145.434	journal	May 1966
Berry phase of nonideal Dirac fermions in topological insulators Taskin, A. A.; Ando, Yoichi Physical Review B, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevB.84.035301	journal	July 2011
Quantum oscillations in a topological insulator Bi2Te2Se with large bulk resistivity () Xiong, Jun; Petersen, A. C.; Qu, Dongxia Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, Issue 5 https://doi.org/10.1016/j.physe.2011.09.011	journal	February 2012
Berry phase effects on electronic properties Xiao, Di; Chang, Ming-Che; Niu, Qian Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.1959	journal	July 2010
Landau-level crossing in two-subband systems in a tilted magnetic field Duarte, C. A.; Gusev, G. M.; Quivy, A. A. Physical Review B, Vol. 76, Issue 7 https://doi.org/10.1103/PhysRevB.76.075346	journal	August 2007
Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe Brüne, C.; Liu, C. X.; Novik, E. G. Physical Review Letters, Vol. 106, Issue 12 https://doi.org/10.1103/PhysRevLett.106.126803	journal	March 2011
Weak Field Phase Diagram for an Integer Quantum Hall Liquid Liu, D. Z.; Xie, X. C.; Niu, Q. Physical Review Letters, Vol. 76, Issue 6 https://doi.org/10.1103/PhysRevLett.76.975	journal	February 1996
Two-dimensional gas of massless Dirac fermions in graphene Novoselov, K. S.; Geim, A. K.; Morozov, S. V. Nature, Vol. 438, Issue 7065, p. 197-200 https://doi.org/10.1038/nature04233	journal	November 2005
Theory of Bloch Electrons in a Magnetic Field Kohn, W. Proceedings of the Physical Society, Vol. 72, Issue 6 https://doi.org/10.1088/0370-1328/72/6/426	journal	December 1958

Similar Records

Intrinsic relative magnetoconductivity of nonmagnetic metals

Journal Article · Mon Apr 24 00:00:00 EDT 2017 · Physical Review B · OSTI ID:1366767

Gao, Yang; Yang, Shengyuan A.; Niu, Qian

Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle

Journal Article · Fri Jul 23 00:00:00 EDT 2021 · Proceedings of the National Academy of Sciences of the United States of America · OSTI ID:1366767

Lu, Xiaobo; Lian, Biao; Chaudhary, Gaurav; +8 more

Unusual interlayer quantum transport behavior caused by the zeroth Landau level in YbMnBi₂

Journal Article · Thu Sep 21 00:00:00 EDT 2017 · Nature Communications · OSTI ID:1366767

Liu, J. Y.; Hu, J.; Graf, D.; +10 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Landau level
magnetic susceptibility
Berry phase
Hofstadter butterfly
topological insulator

Title: Zero-field magnetic response functions in Landau levels

Citation Formats

References (40)

Similar Records

Related Subjects