Zero-field magnetic response functions in Landau levels

Yang Gao, Qian Niu, David Vanderbilt

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)7295-7300
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number28
StatePublished - Jul 11 2017

All Science Journal Classification (ASJC) codes

  • General


  • Berry phase
  • Hofstadter butterfly
  • Landau level
  • Magnetic susceptibility
  • Topological insulator


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