Transport in a One-Dimensional Hyperconductor

TL;DR

This paper investigates the transport properties of a one-dimensional hyperconductor, revealing conditions for finite conductivities, violations of the Wiedemann-Franz law, and complex temperature-dependent scaling behaviors influenced by disorder and electron interactions.

Contribution

It provides the first detailed analysis of electrical and thermal conductivities in a 1D hyperconductor with disorder and umklapp scattering, identifying regimes of finite and divergent conductivities and exploring law violations.

Findings

Electrical conductivity follows a power-law temperature dependence.

Thermal conductivity diverges at low temperatures.

Violations of the Wiedemann-Franz law are demonstrated.

Abstract

We define a `hyperconductor' to be a material whose electrical and thermal DC conductivities are infinite at zero temperature and finite at any non-zero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially-gap-generating interactions and potentially-localizing disorder. In this paper, we compute the low-temperature DC and AC electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter $\Delta_X$, is a power law, $\sigma \propto 1/T^{1 - 2(2-\Delta_X)}$ when $\Delta_X \geq 2$, down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which $\Delta_X = 2$ and $\Delta_X \approx 2$ for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high-temperatures, followed by an exponential increase of the conductivity $\ln \sigma \sim 1/T$ at intermediate temperatures and, finally, $\sigma \propto 1/T^{2-2(2-{\Delta_X})}$ at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.