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Microscopic investigation of chiral crystals

Date : Friday, July 1st, 2022 16:00 - 17:00 Place : On Zoom and Main Lecture Room (A632) at ISSP Lecturer : Hiroaki KUSUNOSE Affiliation : Meiji University and ISSP Committee Chair : Hirokazu TSUNETSUGU (ex. 63597)
e-mail: tsune@issp.u-tokyo.ac.jp

Chirality is a three-dimensional geometric property which is characterized by the absence of any mirror and inversion symmetry operations. Ten of the thirty-two crystallographic point groups belong to this category, and they must have a time-reversal (T) even pseudoscalar representation [1]. A concrete microscopic representation of the chirality is an electric-toroidal (ET) monopole, G0, which becomes active under proper rotations only [2].
Although a monopole seems to be featureless, the pseudoscalar nature cannot be described by a point-like degree of freedom, implying that it has internal degrees of freedom. Indeed, from symmetry point of view, we can decompose G0 as (R1 x R2)・R3 or (M1 x M2)・R3 and so on, where Ri and Mi are independent electric and magnetic dipoles. In these expressions, the vector products are axial vector which suggests that chiral crystal is able to convert between axial and polar quantities through such internal degrees of freedom.
In order to elucidate such a parity conversion property in chiral crystals, we construct the tight-binding model for the typical chiral system of elemental Te and investigated the microscopic expressions of G0 and possible parity conversion responses, namely, electric-field induced rotation and its inverse responses based on the model [3]. We found that the nearestneighbor spin-dependent imaginary hopping is essential ingredient of chirality and is responsible for the electric-field induced lattice rotation and its inverse process.
The conjugate field of G0 (the spin-dependent imaginary hopping) is the combined fields such as the electric current and magnetic field which must be parallel with each other. Along this line, we discuss that the sign of the product of these quantities can control the preferred handedness of chiral crystals, i.e., absolute enantioselection.
We would like to thank J. Kishine, H. Yamamoto, Y. Togawa, Y. Kato, J. Kishine, A. Kato for fruitful discussions.

[1] L.D. Barron, “Molecular Light Scattering and Optical Activity”, 2nd ed. (Cambridge University Press, 2004).
[2] S. Hayami, M. Yatsushiro, Y. Yanagi, and H. Kusunose, Phys. Rev. B, 98, 165110 (2018).
[3] R. Oiwa and H. Kusunose, arXiv:2203.15192.

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(Published on: Thursday June 23rd, 2022)