# Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions

## TL;DR

This paper investigates how thermal and electrical conductivities in metals and superconductors change near quantum phase transitions involving antiferromagnetic and topological order loss, revealing doping-dependent behaviors and proposing models to explain experimental data.

## Contribution

It extends universal conductivity results to include antiferromagnetic and topological quantum transitions, and introduces a doping-dependent scattering rate model to reconcile theory with experiments.

## Key findings

- Heat conductivity varies with doping near quantum critical points.
- Conductivities are similar in clean and dirty regimes for metals and superconductors.
- Proposed a doping-dependent scattering rate to match Hall and longitudinal conductivity data.

## Abstract

We study thermal and electrical transport in metals and superconductors near a quantum phase transition where antiferromagnetic order disappears. The same theory can also be applied to quantum phase transitions involving the loss of certain classes of intrinsic topological order. For a clean superconductor, we recover and extend the well-known universal results. The heat conductivity for commensurate and incommensurate antiferromagnetism coexisting with superconductivity shows a markedly different doping dependence near the quantum critical point, thus allowing to distinguish the states. In the dirty limit, the results for the conductivities are qualitatively similar for the metal and the superconductor. In this regime, the geometric properties of the Fermi surface allow for a very good phenomenological understanding of the numerical results on the conductivities. In the simplest model, we find that the conductivities do not track the doping evolution of the Hall coefficient, in contrast to recent experimental findings. We propose a doping dependent scattering rate, possibly due to quenched short-range charge fluctuations below optimal doping, to consistently describe both the Hall data and the longitudinal conductivities.