Resonant Second-Harmonic Generation as a Probe of Quantum Geometry

Pankaj Bhalla, Kamal Das, Dimitrie Culcer, and Amit Agarwal

Phys. Rev. Lett. 129, 227401 – Published 23 November 2022

Abstract

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higher-order pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal ${WTe}_{2}$ and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

Received 16 August 2021
Revised 6 March 2022
Accepted 14 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.227401

Physics Subject Headings (PhySH)

Electrical conductivity Photoconductivity Photoinduced effect Symmetry protected topological states

2-dimensional systems 3-dimensional systems Semimetals

Boltzmann theory Optical second-harmonic generation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Pankaj Bhalla^1,2,3,*,∥, Kamal Das ^4,†,∥, Dimitrie Culcer^3,5,‡, and Amit Agarwal ^4,§

¹Department of Physics, School of Engineering and Sciences, SRM University AP, Amaravati, 522240, India
²Beijing Computational Science Research Center, Beijing 100193, China
³ARC Centre of Excellence in Future Low-Energy Electronics Technologies, The University of New South Wales, Sydney 2052, Australia
⁴Department of Physics, Indian Institute of Technology Kanpur, Kanpur-208016, India
⁵School of Physics, The University of New South Wales, Sydney 2052, Australia

^*pankaj.b@srmap.edu.in
^†kamaldas@iitk.ac.in
^‡d.culcer@unsw.edu.au
^§amitag@iitk.ac.in
^∥These authors contributed equally to this work.

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Issue

Vol. 129, Iss. 22 — 23 November 2022

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