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Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
by Paolo Molignini, Bastien Lapierre, R. Chitra, Wei Chen
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Submission summary
| Authors (as registered SciPost users): | Wei Chen · Bastien Lapierre · Paolo Molignini |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2207.00016v4 (pdf) |
| Date accepted: | 2023-07-20 |
| Date submitted: | 2023-07-12 01:08 |
| Submitted by: | Chen, Wei |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials to circularly polarized light over a wide range of frequencies, measured in units of the fine structure constant, can be used to extract a spectral function that frequency-integrates to the Chern number, offering a simple optical experiment to measure it. This method is subsequently generalized to finite temperature and locally on every lattice site by a linear response theory, which helps to extract the Chern marker that maps the Chern number to lattice sites. The long range response in our theory corresponds to a Chern correlator that acts like the internal fluctuation of the Chern marker, and is found to be enhanced in the topologically nontrivial phase. Finally, from the Fourier transform of the valence band Berry curvature, a nonlocal Chern marker is further introduced, whose decay length diverges at topological phase transitions and therefore serves as a faithful indicator of the transitions, and moreover can be interpreted as a Wannier state correlation function. The concepts discussed in this work explore multi-faceted aspects of topology and should help address the impact of system inhomogeneities.
List of changes
(1) In the beginning of Sec 2.2, we have mentioned that our formalism is analogous to that derives the Faraday effect in solids.
(2) At the end of Sec 2.2, we have elaborated explicitly that our finite temperature formalism that describes the optical absorption process is different from the finite temperature formalism that describes the DC Hall conductance.
(3) In page 10, we have mentioned the experimental measurement of the Chern number spectral function in cold atoms.
(4) In page 10 and 11, we demonstrate a simple way to perceive the topologically nontrivial phase of a 2D time-reversal breaking material by human eyes from the transparency of the material in macroscopic scale.
Published as SciPost Phys. Core 6, 059 (2023)