Transverse Thermoelectric Response as a Probe for Existence of Quasiparticles

TL;DR

This paper investigates how the transverse thermoelectric response can serve as a probe for the existence of quasiparticles, revealing that quasiparticle emergence enforces antisymmetry in thermoelectric coefficients, unlike in non-quasiparticle systems.

Contribution

It demonstrates that the antisymmetry relation for thermoelectric coefficients indicates quasiparticle presence, providing a new diagnostic tool for non-Fermi liquid states.

Findings

Antisymmetry of thermoelectric coefficients holds for noninteracting particles.

Approximate antisymmetry in Boltzmann theory for elastic scattering dominates.

Strong breakdown of antisymmetry observed in weakly-coupled spin-gapped Luttinger liquids.

Abstract

The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey sigma_{xy} = - sigma_{yx}. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, alpha_{xy}= - alpha_{yx}, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces alpha_{xy} = - alpha_{yx}. This suggests that quasiparticle-free groundstates (so-called non-Fermi liquids) may be detected by examining the relationship between alpha_{xy} and alpha_{yx} in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results: (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles; (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid the latter lead to deviations that vanish as T^3. (iii) We calculate the thermoelectric response in a model of weakly-coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of alpha. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.