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

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-Krönig dispersion relation, which connects the zero-frequency viscosity, $η(0)$, to the high-frequency shear modulus, $μ_{\infty}$, of the electron liquid via $η(0) =μ_{\infty} τ$, with $τ$ 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.