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
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.
Anwei Zhang(张安伟) Revealing Chern number from quantum metric 2022 Chin. Phys. B 31 040201
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