Probing quantum geometric capacitance via photonic spin Hall effect

TL;DR

This paper explores how the photonic spin Hall effect at terahertz frequencies can be used to measure the quantum geometric capacitance of two-dimensional insulators, providing a new optical probing method.

Contribution

It introduces a method to extract quantum geometric capacitance from beam shifts in the photonic spin Hall effect near the Brewster angle.

Findings

Beam shifts are detectable and comparable to wavelength near the Brewster angle.

Linear and quadratic approximations enable extraction of geometric capacitance from measurements.

THz PSHE can serve as a probe for quantum geometric properties of 2D insulators.

Abstract

The non-dissipative quasistatic longitudinal optical response of insulators is characterized by an intrinsic geometric capacitance, determined by the ratio of the quantum metric to the energy gap, as recently stablished. We study the photonic spin Hall effect (PSHE) in this low-frequency regime, induced by reflection from an atomically thin material serving as the interface between two dielectrics. As a function of the magnitude of this geometric capacitance, covering values typical of graphene-family systems and for incidence close to the Brewster angle, the calculated in-plane and transverse beam shifts become comparable to the wavelength and thus detectable. At sufficiently low frequencies, we derive linear and quadratic approximations that allow the geometric capacitance to be extracted from measurements of the beam displacements. We provide an upper bound for the beam shifts. The results suggest that THz PSHE might be a useful probe of the quantum geometric capacitance of two-dimensional insulators.