Electrical transport near quantum criticality in low dimensional organic superconductors

TL;DR

This paper develops a theoretical model for the temperature-dependent resistivity in quasi-one-dimensional organic superconductors near a quantum critical point, highlighting the role of umklapp scattering and comparing with experimental data.

Contribution

It introduces a numerical solution of the Boltzmann equation incorporating renormalization group derived umklapp scattering to explain resistivity behavior near quantum criticality.

Findings

Resistivity is linear in temperature near the quantum critical point.

Resistivity evolves towards Fermi liquid behavior away from criticality.

The theory aligns with experimental results on (TMTSF)$_2$PF$_6$ under pressure.

Abstract

We propose a theory of longitudinal resistivity in the normal phase of quasi-one-dimensional organic superconductors near the quantum critical point where antiferromagnetism borders with superconductivity under pressure. The linearized semi-classical Boltzmann equation is solved numerically, fed in by the half-filling electronic umklapp scattering vertex as derived from one-loop renormalization group calculations for the quasi-one-dimensional electron gas model. The momentum and temperature dependence of umklapp scattering has an important impact on the behaviour of longitudinal resistivity in the the normal phase. Resistivity is found to be linear in temperature around the quantum critical point at which spin-density-wave order joins superconductivity along the antinesting axis, to gradually evolve towards the Fermi liquid behaviour in the limit of weak superconductivity. A comparison is made between theory and experiments performed on the (TMTSF)$_2$PF$_6$ member of the Bechgaard salt series under pressure.