中国物理B ›› 2022, Vol. 31 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/ac2f2c

• •    下一篇

Revealing Chern number from quantum metric

Anwei Zhang(张安伟)1,2,†   

  1. 1 Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China;
    2 Department of Physics, Ajou University, Suwon 16499, Korea
  • 收稿日期:2021-09-01 修回日期:2021-10-04 接受日期:2021-10-13 出版日期:2022-03-16 发布日期:2022-03-10
  • 通讯作者: Anwei Zhang E-mail:zawcuhk@gmail.com
  • 基金资助:
    We would like to thank R. B. Liu for useful discussion and N. Goldman for helpful comment.

Revealing Chern number from quantum metric

Anwei Zhang(张安伟)1,2,†   

  1. 1 Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China;
    2 Department of Physics, Ajou University, Suwon 16499, Korea
  • Received:2021-09-01 Revised:2021-10-04 Accepted:2021-10-13 Online:2022-03-16 Published:2022-03-10
  • Contact: Anwei Zhang E-mail:zawcuhk@gmail.com
  • Supported by:
    We would like to thank R. B. Liu for useful discussion and N. Goldman for helpful comment.

摘要: Chern number is usually characterized by Berry curvature. Here, by investigating the Dirac model of even-dimensional Chern insulator, we give the general relation between Berry curvature and quantum metric, which indicates that the Chern number can be encoded in quantum metric as well as the surface area of the Brillouin zone on the hypersphere embedded in Euclidean parameter space. We find that there is a corresponding relationship between the quantum metric and the metric on such a hypersphere. We give the geometrical property of quantum metric. Besides, we give a protocol to measure the quantum metric in the degenerate system.

关键词: quantum metric, Chern insulator, topological physics

Abstract: Chern number is usually characterized by Berry curvature. Here, by investigating the Dirac model of even-dimensional Chern insulator, we give the general relation between Berry curvature and quantum metric, which indicates that the Chern number can be encoded in quantum metric as well as the surface area of the Brillouin zone on the hypersphere embedded in Euclidean parameter space. We find that there is a corresponding relationship between the quantum metric and the metric on such a hypersphere. We give the geometrical property of quantum metric. Besides, we give a protocol to measure the quantum metric in the degenerate system.

Key words: quantum metric, Chern insulator, topological physics

中图分类号:  (Geometry, differential geometry, and topology)

  • 02.40.-k
03.65.Vf (Phases: geometric; dynamic or topological) 61.82.Ms (Insulators)