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, which is 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 ω−2 and ω−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 the shift and injection photocurrent conductivities as well as geometric quantities of antiferromagnetic MnGeO3 and ferromagnetic PrGeAl, respectively, as representatives of real magnetic Dirac and Weyl semimetals. Our calculations reveal gigantic peaks in many nonvanishing elements of photoconductivity tensors below a photon energy of about 0.2 eV in both MnGeO3 and PrGeAl. In particular, we show the ω−1 enhancement of the shift conductivity tensors due to the divergent behavior of the geometric quantities near the Dirac and Weyl points as well as slightly gapped topological nodes. Moreover, the low-frequency bulk photovoltaic effect is tunable by carrier doping and magnetization orientation rotation. Our work brings new insights into the structure of nonlinear optical responses as well as the design of semimetal-based terahertz photodetectors.3 MoreReceived 14 June 2020Revised 14 September 2020Accepted 8 October 2020DOI:https://doi.org/10.1103/PhysRevX.10.041041Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasPhotovoltaic effectPhysical SystemsDirac semimetalMagnetic systemsWeyl semimetalTechniquesBloch wave theorySymmetries in condensed matterCondensed Matter & Materials Physics

Highlights

  • Topological semimetals are emerging as efficient infrared and terahertz photodetectors [1]

  • We show that tilted Dirac point (DP) and Weyl points (WPs) can generate the leading divergence

  • The divergence of the responses in our model should not be interpreted as a physical divergence, and it is cut off at ω ∼ Γ

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Summary

INTRODUCTION

Topological semimetals are emerging as efficient infrared and terahertz photodetectors [1]. The calculated quantum metric and Christoffel symbol of the first kind exhibit divergent behaviors near both the gapless and gapped Dirac points, leading to the geometric enhancement in linear injection and circular shift currents, respectively. Both T and PT symmetries are broken in FM PrGeAl [43], and all four types of the bulk photovoltaic effect may emerge in FM PrGeAl, as our theory predicts (Table I).

SHIFT AND INJECTION CURRENTS
SYMMETRY AND POWER-COUNTING ANALYSIS
Symmetry of the shift and injection conductivities
Power-counting analysis of the low-energy divergence
QUANTUM GEOMETRIC ASPECTS
Shift and injection conductivity for Dirac Hamiltonians
Geometry on the generalized Bloch sphere
More on the geometric aspect of the shift current
Generalization to multibands
MODEL CALCULATIONS
Tilted Weyl and Dirac semimetals: k-linear order
Dirac surface state
FIRST-PRINCIPLES CALCULATIONS FOR REAL TOPOLOGICAL SEMIMETALS
Antiferromagnetic Dirac semimetal MnGeO3
Ferromagnetic Weyl semimetal PrGeAl
DISCUSSION
Quantum geometric tensor
Dirac Hamiltonian
Metric connection
Symplectic connection

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