Collision-dominated spin transport in graphene and Fermi liquids

TL;DR

This paper investigates spin transport in graphene and Fermi liquids, revealing how electron-electron interactions and Coulomb coupling influence spin conductivity, especially near the Dirac point, with implications for understanding strongly coupled quantum systems.

Contribution

It provides an analytical calculation of collision-limited spin conductivity in graphene, highlighting the effects of Coulomb interactions and the breakdown of symmetry at higher orders.

Findings

Spin conductivity reaches a minimum at the Dirac point.

Strong Coulomb interactions lead to near-maximal inelastic scattering rates.

Transport time is parametrically smaller than collision time in gated graphene.

Abstract

In a clean Fermi liquid, due to spin up/spin down symmetry, the dc spin current driven by a magnetic field gradient is finite even in the absence of impurities. Hence, the spin conductivity sigma_s assumes a well-defined collision-dominated value in the disorder-free limit, providing a direct measure for the inverse strength of electron-electron interactions. In neutral graphene, with Fermi energy at the Dirac point, the Coulomb interactions remain unusually strong, such that the inelastic scattering rate comes close to a conjectured upper bound 1/\tau_{inel} <= k_B T/\hbar, similarly as in strongly coupled quantum critical systems. The strong scattering is reflected by a minimum of the spin conductivity at the Dirac point, where it reaches sigma_s = (0.121/alpha^2) * (mu_B^2/\hbar) at weak Coulomb coupling alpha. Up to the replacement of quantum units, e^2/\hbar -> mu_s^2/\hbar, this result equals the collision-dominated electrical conductivity obtained previously. This accidental symmetry is, however, broken to higher orders in the interaction strength. For gated graphene, and 2d metals in general, we show that the transport time is parametrically smaller than the collision time. We exploit this to compute the collision-limited sigma_s analytically as sigma_s= (1/C) * (mu/T)^2 * (mu_B^2/\hbar) with C=4 pi^2 alpha^2 [2/3 ln(1/(2\alpha))-1] for weak Coulomb coupling alpha.