Quantized Integrated Shift Effect in Multigap Topological Phases

Abstract

We show that certain three-dimensional multigap topological insulators can host quantized integrated shift photoconductivities due to bulk invariants that are defined under reality conditions imposed by additional symmetries. We recast the quantization in terms of the integrated torsion tensor and the non-Abelian Berry connection constituting Chern-Simons forms. Physically, we recognize that the topological quantization emerges purely from virtual transitions contributing to the optical response. Our findings provide another quantized electromagnetic dc response due to the nontrivial band topology, beyond the quantum anomalous Hall effect of Chern insulators and quantized circular photogalvanic effect found in Weyl semimetals.

8+13 pages; 3+4 figures

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• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Optical signatures of Euler superconductors
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• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Quantization of spin circular photogalvanic effect in altermagnetic Weyl semimetals
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
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• Orbital magnetization reveals multiband topology
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Unified theory of the photovoltaic Hall effect by field- and light-induced Berry curvatures
• Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Quantum geometry and low-frequency optical conductivity of nodal planes
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Nonlinear Odd Viscoelastic Effect