Optical conductivity of topological surface states with emergent supersymmetry

TL;DR

This paper derives exact optical conductivity results for topological surface states at a quantum critical point with emergent supersymmetry, revealing deep connections between conductivity, viscosity, and entanglement entropy.

Contribution

It provides the first exact calculations of optical conductivity at a supersymmetric quantum critical point in topological insulator surface states, highlighting novel symmetry relations.

Findings

Exact optical conductivity at the QCP with supersymmetry

Relations between conductivity, shear viscosity, and entanglement entropy

Implications for experimental detection in topological insulators

Abstract

Topological states of electrons present new avenues to explore the rich phenomenology of correlated quantum matter. Topological insulators (TIs) in particular offer an experimental setting to study novel quantum critical points (QCPs) of massless Dirac fermions, which exist on the sample's surface. Here, we obtain exact results for the zero- and finite-temperature optical conductivity at the semimetal-superconductor QCP for these topological surface states. This strongly interacting QCP is described by a scale invariant theory with emergent supersymmetry, which is a unique symmetry mixing bosons and fermions. We show that supersymmetry implies exact relations between the optical conductivity and two otherwise unrelated properties: the shear viscosity and the entanglement entropy. We discuss experimental considerations for the observation of these signatures in TIs.