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Cited by 297Quantum and electron transport phenomenaTopological Materials and PhenomenaSpectral Theory in Mathematical Physics

Berry Phase, Hyperorbits, and the Hofstadter Spectrum

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Chang, Ming-Che, Niu, Qian·1995·Physical Review Letters
DOI 10.1103/physrevlett.75.1348
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Abstract

We develop a semiclassical theory for the dynamics of electrons in a magnetic Bloch band, where the Berry phase plays an important role. This theory, together with the Boltzmann equation, provides a framework for studying transport problems in high magnetic fields. We also derive an Onsager-like formula for the quantization of cyclotron orbits, and we find a connection between the number of orbits and Hall conductivity. This connection is employed to explain the clustering structure of the Hofstadter spectrum. The advantage of this theory is its generality and conceptual simplicity.

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  • A semi-classical wavepacket moves as a coherent object with an additional anomalous Hall velocity due to Berry curvature at its centre-of-mass when an external force is applied or control parameter pumped.

    “In the simplest case, a semi-classical wavepacket moves as a coherent object governed by classical equations of motion with an additional 'anomalous' Hall velocity due to the geometrical Berry curvature at its centre-ofmass, as an external force is applied or as the control parameter is pumped 1,4 .”

    From Experimental measurement of the Berry curvature from anomalous transport (2017) · cites this paper as [4]

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Research works printed but not linked: 4

  1. [1][1] N. W. Ashcroft and N. D. Mermin, Solid State Physics , (W. B. Saunders Co., Philadelphia, 1976) Chapter 12. -
  2. [8][8] M. V. Berry, Proc. Roy. Soc. London A392 , 45 (1984); B. Simon, Phys. Rev. Lett. 51 , 2167 (1983). -
  3. [13][13] A factor of 1 / 2 has been inserted to the right hand side for the following reason: The orbit acuqires a phase shift of -π/ 2 whenever it passes a caustic turning point. In this case, there are two caustics for a cyclotron orbit. Therefore there is an additional phase lag of -π contributes to the nondynamical phase. For more detail, see L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th ed. (Pergmon, Oxford, 1987). Van Houten's paper in Ref. 12 also has a nice discussion on the additional phase shift. -
  4. [18][18] M. Wilkinson, Proc. R. Soc. Lond. A391 , 305 (1984); J. Phys. A20 , 4337 (1987); 27 , 8123 (1994) and references therein. -

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Authors
Chang, M.-C., & Niu, Q.
Affiliations
The University of Texas at Austin (US)
ORCID
Niu, Qian
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
1995-08-14
Volume
75
Issue
7
Pages
1348-1351
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.75.1348
OpenAlex
W2170455764
Cited by
297
References
24
Citations by year
2026: 17 · 2025: 23 · 2024: 20 · 2023: 23 · 2022: 25 · 2021: 19 · 2020: 15 · 2019: 16 · 2018: 22 · 2017: 11 · 2016: 12 · 2015: 15 · 2014: 8 · 2013: 6 · 2012: 7
FWCI
0.49
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
Keywords
Berry phase, Hofstadter spectrum, semiclassical theory, Boltzmann equation, high magnetic fields, Onsager reciprocal relations, Hall conductivity, electron transport

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