Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals

Abstract

We study the low-frequency properties of the bulk photovoltaic effect in topological semimetals. The bulk photovoltaic effect is a nonlinear optical effect that generates DC photocurrents under uniform irradiation, allowed by noncentrosymmetry. It is a promising mechanism for a terahertz photodetection based on topological semimetals. Here, we systematically investigate the low-frequency behavior of the second-order optical conductivity in point-node semimetals. Through symmetry and power-counting analysis, we show that Dirac and Weyl points with tilted cones show the leading low-frequency divergence. In particular, we find new divergent behaviors of the conductivity of Dirac and Weyl points under circularly polarized light, where the conductivity scales as ${\omega }^{-2}$ and ${\omega }^{-1}$ near the gap-closing point in two and three dimensions, respectively. We provide a further perspective on the low-frequency bulk photovoltaic effect by revealing the complete quantum geometric meaning of the second-order optical conductivity tensor. The bulk photovoltaic effect has two origins, which are the transition of electron position and the transition of electron velocity during the optical excitation, and the resulting photocurrents are respectively called the shift current and the injection current. Based on an analysis of two-band models, we show that the injection current is controlled by the quantum metric and Berry curvature, whereas the shift current is governed by the Christoffel symbols near the gap-closing points in semimetals. Finally, for further demonstrations of our theory beyond simple two-band models, we perform first-principles calculations on magnetic Dirac semimetal MnGeO${}_3$and Weyl semimetal PrGeAl. Our work brings out new insights into the structure of nonlinear optical responses as well as for the design of semimetal-based terahertz photodetectors.

27 pages, 10 figures, first-principles calculations added

References in corpus (14)

• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet
• Photocurrents in Weyl semimetals
• Semimetals for high performance photodetection
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Abelian and Non-Abelian Quantum Geometric Tensor
• Photogalvanic effect in Weyl semimetals
• Nonlinear Optical Properties of Transition Metal Dichalcogenide MX${}_2$ (M = Mo, W; X = S, Se) Monolayers and Trilayers from First-principles Calculations
• The study of magnetic topological semimetals by first principles calculations
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Observation of Weyl fermions in a magnetic non-centrosymmetric crystal
• Shift charge and spin photocurrents in Dirac surface states of topological insulator
• Resonant photovoltaic effect in doped magnetic semiconductors
• Noncentrosymmetric compensated half-metal hosting pure spin Weyl nodes, triple nodal points, nodal loops, and nexus fermions

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