TY - JOUR

T1 - Zero-field magnetic response functions in Landau levels

AU - Gao, Yang

AU - Niu, Qian

AU - Vanderbilt, David

N1 - Funding Information:
We acknowledge useful discussions with H. Chen and L. Zhang. Y.G. and Q.N. are supported by National Basic Research Program of China (NBRPC) Grant 2013CB921900, Department of Energy (DOE) Grant DE-FG03-02ER45958 (Division of Materials Science and Engineering), National Science Foundation Grant EFMA-1641101, and Welch Foundation Grant F-1255. The calculation of the Landau level in the tight-binding graphene model is supported by the DOE grant.

PY - 2017/7/11

Y1 - 2017/7/11

N2 - 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.

AB - 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.

KW - Berry phase

KW - Hofstadter butterfly

KW - Landau level

KW - Magnetic susceptibility

KW - Topological insulator

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U2 - 10.1073/pnas.1702595114

DO - 10.1073/pnas.1702595114

M3 - Article

C2 - 28655849

AN - SCOPUS:85023168518

SN - 0027-8424

VL - 114

SP - 7295

EP - 7300

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 28

ER -