Thermodynamic Multipoles and Dissipative Conductivities in Metallic Systems

TL;DR

This paper extends the concept of thermodynamic multipoles to metallic systems, revealing their direct relation to dissipative conductivities and identifying extrema at specific chemical potentials.

Contribution

It introduces a heuristic framework linking Fermi-surface thermodynamic multipoles to dissipative transport responses in metals, beyond previous equilibrium insulating system focus.

Findings

Conductivities show maxima where Fermi-surface multipoles vanish.

Electric quadrupole relates to charge conductivity extrema.

Magnetic octupole relates to spin conductivity extrema.

Abstract

Multipoles provide a systematic framework for describing the electronic structures of quantum materials from a symmetry perspective. Thermodynamic multipole moments in crystalline solids exhibit direct microscopic connections to certain allowed physical responses beyond symmetry; however, such relations have thus far been limited to dissipationless responses in equilibrium insulating systems. Here, this framework is extended at a heuristic level by focusing on the Fermi-surface contributions to thermodynamic multipole moments. These contributions establish direct relations to dissipative transport responses characteristic of metals, including charge and spin conductivities. A key consequence is that the conductivities exhibit extrema, typically maxima, at chemical potentials where the corresponding Fermi-surface contributions to the multipoles vanish, specifically, the electric quadrupole for charge conductivity and the magnetic octupole for spin conductivity. These findings uncover a previously overlooked aspect of thermodynamic multipole moments, opening a new perspective on dissipative transport in metallic systems.