Quantum geometry-driven photogalvanic responses in semi-Dirac systems

TL;DR

This paper explores how the photogalvanic effect in semi-Dirac systems reveals underlying quantum geometric properties, with distinct signatures in different phases, offering a new way to probe quantum geometry in anisotropic materials.

Contribution

It provides a comprehensive theoretical analysis linking photogalvanic responses to quantum geometric quantities in semi-Dirac systems, highlighting phase-dependent signatures and potential applications.

Findings

Optical conductivities are significantly enhanced in type-II semi-Dirac systems.

The $xxx$ component of shift conductivity reverses sign at the Lifshitz transition in type-II phase.

Combined CPGE and LPGE signatures distinguish between type-I and type-II semi-Dirac phases.

Abstract

The photogalvanic effect (PGE), a fundamental nonlinear optical phenomenon in non-centrosymmetric materials, generates direct photocurrent under polarized light. Using quantum kinetic theory within the relaxation-time approximation, we theoretically investigate the PGE as a probe of quantum geometry in anisotropic type-I and type-II semi-Dirac (SD) systems, characterized by distinct electronic structures. We systematically analyse various microscopic contributions to the PGE conductivity, including injection, shift, resonance, higher-order pole, and anomalous terms, and emphasize their connections to different quantum geometric quantities, namely, Berry curvature, quantum metric, and metric connection. By studying the frequency and chemical-potential dependence of the PGE conductivity in SD systems, we find that the optical conductivities in the type-II case are significantly enhanced relative to those in type-I. For the circular PGE (CPGE), Berry-curvature-driven contributions remain qualitatively similar in both phases, whereas the linear PGE (LPGE) displays clear qualitative differences. In particular, the $xxx$ component of the shift conductivity in the type-II phase reverses sign upon tuning the perturbation parameter $\delta$, providing a direct signature of the Lifshitz transition. In contrast, other components remain sign-invariant, as in type-I SD systems. These combined CPGE and LPGE signatures provide an unambiguous distinction between the two SD phases. The predicted effects, realizable in TiO$_2$/VO$_2$ heterostructures, establish PGE as a sensitive probe of quantum geometry with potential applications in polarization-selective photodetection, optical rectification, and next-generation optoelectronic devices.