Thermal Hall Effect and Geometry with Torsion

Andrey Gromov and Alexander G. Abanov

Phys. Rev. Lett. 114, 016802 – Published 6 January 2015

Abstract

We formulate a geometric framework that allows us to study momentum and energy transport in nonrelativistic systems. It amounts to a coupling of the nonrelativistic system to the Newton-Cartan (NC) geometry with torsion. The approach generalizes the classic Luttinger’s formulation of thermal transport. In particular, we clarify the geometric meaning of the fields conjugated to energy and energy current. These fields describe the geometric background with nonvanishing temporal torsion. We use the developed formalism to construct the equilibrium partition function of a nonrelativistic system coupled to the NC geometry in $2 + 1$ dimensions and to derive various thermodynamic relations.

Received 30 July 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.016802

Authors & Affiliations

Andrey Gromov¹ and Alexander G. Abanov²

¹Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
²Department of Physics and Astronomy and Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York 11794, USA