Kosterlitz-Thouless vortex-scaling equations with nonzero current drives

Abstract

The Kosterlitz-Thouless (KT) scaling procedure for the two-dimensional planar spin model is generalized to include an x-axis-applied current density I. Scaling equations for vortex coupling K_l and vortex pair fugacity y_l at a general minimum scale a≡e^l are derived, with current density acting as a y-axis "topological electric field" E_l on the ±₁ vortex "topological charges." A vortex-unbinding onset scale l=l_c is defined by E_lc=K_lc, where the current-driven repulsion of the ±1 vortex pairs begins to exceed their attraction. The nonlinear resistance R(T¯,I¯)=2πR_lc is related to the finite-scale phase-slip resistance R_l that has a minimum at l=l_c. Above transition, the zero-current resistance R(T¯,I¯=0) shows KT-like exponential inverse square-root temperature dependence, and is a universal function of dimensionless temperature T¯. The current-voltage exponent α(T¯,I¯) curves (where V~I^1+α) are universal in T¯ and I¯≡ħI/(2ek_BT). Below transition, the α curves are weakly dependent on I¯, with α(T¯,I¯) close to ΠK_∞(T¯). Above transition, non-Ohmic behavior α(T¯,I¯)≠0 is predicted for strong current.