Viscous corrections to the resistance of nano-junctions: a dispersion relation approach

TL;DR

This paper introduces a dispersion relation approach to estimate viscous effects in nanojunctions, linking high-frequency shear modulus to zero-frequency viscosity, revealing potentially significant contributions to resistance.

Contribution

It proposes a novel method based on dispersion relations and time-dependent current-density functional theory to quantify viscous corrections in nanojunctions.

Findings

Viscous effects can significantly increase resistance in low-conductance junctions.

The approach connects high-frequency shear modulus to zero-frequency viscosity.

Viscous contributions may be larger than previously estimated.

Abstract

It is well known that the viscosity of a homogeneous electron liquid diverges in the limits of zero frequency and zero temperature. A nanojunction breaks translational invariance and necessarily cuts off this divergence. However, the estimate of the ensuing viscosity is far from trivial. Here, we propose an approach based on a Kramers-Kr\"onig dispersion relation, which connects the zero-frequency viscosity, $\eta(0)$, to the high-frequency shear modulus, $\mu_{\infty}$, of the electron liquid via $\eta(0) =\mu_{\infty} \tau$, with $\tau$ the junction-specific momentum relaxation time. By making use of a simple formula derived from time-dependent current-density functional theory we then estimate the many-body contributions to the resistance for an integrable junction potential and find that these viscous effects may be much larger than previously suggested for junctions of low conductance.