Sum rule for the optical Hall angle

TL;DR

This paper establishes a new sum rule for the optical Hall angle in electronic media, providing insights into the transverse response of electronic fluids to electric fields, analogous to the f-sum rule.

Contribution

It introduces a novel sum rule for the optical Hall angle applicable to general electronic media, expanding understanding of their optical response properties.

Findings

Derivation of the sum rule for the optical Hall angle

Application examples to various electronic media

Physical interpretation of the sum rule

Abstract

We consider the optical Hall conductivity of a general electronic medium and prove that the optical Hall angle obeys a new sum rule. This sum rule governs the response of an electronic fluid to a Lorentz electric field and can thought of as the transverse counterpart to the f-sum rule in optical conductivity. The physical meaning of this sum rule is discussed, giving a number of examples of its application to a variety of of electronic media.