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Speaker: Takahiro Misawa (ISSP, UTokyo)
Time & Date: 13:00 – 14:00, May 15, 2023 (JST)
Place: Online (Zoom meeting)
keio-univ.zoom.us/j/81109733929?pwd=SWtUM2xIVG9xdVpGMG1KZUdhcnk2QT09
(Meeting ID: 811 0973 3929, Passcode: 260740)
Title: Zeros of Green functions in topological insulators –
A tool for visualizing topological phases
Abstract:
Recently, we have found that the zeros of the diagonal components of
the Green functions are useful quantities for detecting a wide range
of topological insulators [1]. In particular, we have shown that the
zeros of the Green functions traverse the band gap due to band
inversions in the topological phases. Utilizing this feature, we can
distinguish topological phases by seeing whether the zeros traverse
the band gap. For microscopic models of the conventional six classes
of topological insulators, we show that the traverses of the zeros
universally occur in the topological phases. We also show that
higher-order topological insulators, which have recently attracted
much attention, can also be detected by the zeros of the Green
functions.
Interestingly, the recently rediscovered eigenvector-eigenvalue
identity [2], which is a simple but long-time-overlooked mathematical
formula in linear algebra, plays an important role in the analysis of
the zeros of the Green functions. Furthermore, by using the zeros of
the Green function, we find that a conventional antiferromagnetic Mott
insulator in κ-(BEDT-TTF)2Cu[N(CN)2]Cl can be regarded as a correlated
topological insulator [3].
[1] T. Misawa and Y. Yamaji, Phys. Rev. Research 4, 023177 (2022).
[2] P. Denton, S. Parke, T. Tao, and X. Zhang, Bull. Am. Math. Soc. 59, 31
(2022). The story on the finding of the eigenvector-eigenvalue
identity is available at
www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/
[3] T. Misawa and M. Naka, arXiv:2301.04490.
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—
Satoshi Morita (森田 悟史)
Graduate School of Science and Technology, Keio University
smorita.github.io/
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