In solid materials, electrons are usually described by the non-relativistic Schrodinger equation since electron velocity is much slower than the speed of light. However, the relativistic Dirac/Weyl equation can emerge as a low-energy effective theory for electrons in certain materials. These systems are dubbed “Dirac/Weyl materials” and provide a tunable platform to test quantum relativistic phenomena in table-top experiments. Owing to the linear-in-momentum form, a variety of physical fields, including magnetization, phonon and strain, can couple to Dirac/Weyl quasi-particles in a similar form as the minimal gauge coupling. These physical fields thus are dubbed the “pseudo-gauge field”, which provides a useful theoretical concept to understand or predict a variety of physical phenomena beyond the electromagnetic response in Dirac/Weyl materials. In this talk, I will focus on the physical phenomena related to the pseudo-gauge field created by strain and phonons. I will first discuss the Berry curvature contribution to the piezo-electric response, which can be understood as the Hall current response driven by strain-induced pseudo-electric field . Our theory predicts a jump of piezo-electric coefficients across a topological phase transition in 2D Dirac materials. Then I will discuss the influence of electron Berry curvature on phonon dynamics through the pseudo-gauge coupling form of electron-phonon interaction . This leads to a “helical texture” of phonon angular momentum in the momentum space. Finally, I will show phonons can also induce a gravitational torsion field for Weyl fermions in chiral crystals and discuss the possibility of probing Nieh-Yan anomaly through thermal transport measurement .
 Piezoelectricity and topological quantum phase transitions in two-dimensional spin-orbit coupled crystals with time-reversal symmetry, Jiabin Yu, Chao-Xing Liu, Nature Communications 11, 2290 (2020).
 Phonon Helicity Induced by Electronic Berry Curvature in Dirac Materials, Lun-Hui Hu, Jiabin Yu, Ion Garate, Chao-Xing Liu, Phys. Rev. Lett. 127, 125901, 2021
 Probing Nieh-Yan Anomaly through phonon dynamics in the Kramers-Weyl semimetals of Chiral Crystals, Chao-Xing Liu, arXiv:2104.04859, 2021.
Chao-Xing Liu's Recording: