Viscous corrections to the resistance of nanojunctions: 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-Kronig dispersion relation, which connects the zero-frequency viscosity eta(0) to the high-frequency shear modulus mu(infinity) of the electron liquid via eta(0) = mu(infinity)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.