Theory of Orbital Magnetic Quadrupole Moment and Nonlinear Anomalous Thermoelectric Transport

TL;DR

This paper develops a microscopic, gauge-invariant theory of the magnetic quadrupole moment in crystals with specific symmetries and links it to nonlinear thermoelectric effects, with applications to cuprate superconductors.

Contribution

It introduces a new gauge-invariant expression for the magnetic quadrupole moment and connects it to nonlinear thermoelectric transport phenomena in materials.

Findings

Derived a gauge-invariant formula for $ ext{Q}_{ij}$ in crystals.

Showed $ ext{Q}_{ij}$ causes intrinsic nonlinear thermoelectric currents.

Predicted unique behaviors of nonlinear Nernst and Hall effects in cuprates.

Abstract

We present a microscopic theory of the magnetic quadrupole moment density $\mathcal{Q}_{ij}$ in periodic crystals with combined time reversal ($\mathcal{T}$) and inversion ($\mathcal{I}$) symmetry. We obtain a gauge-invariant expression with clear physical interpretation and demonstrate the typical behaviour of $\mathcal{Q}_{ij}$ in a minimal two-band model that hosts a tilted Dirac cone. We then show that $\mathcal{Q}_{ij}$ leads to an intrinsic nonlinear anomalous thermoelectric current. As an example, we calculate the nonlinear Nernst and Hall current in the loop-current model for cuprate superconductors, and demonstrate their unique behaviour and capability of indicating $\mathcal{TI}$-invariance.