Spontaneous Symmetry-Breaking of Nonequilibrium Steady-States Caused by Nonlinear Electrical Transport

Negative differential resistance (NDR) in certain materials has been attributed to spontaneous emergence of symmetry-breaking electrical current density localization from a previously homogeneous distribution, which is postulated to occur due to the nonequilibrium thermodynamic force of minimization of entropy production. However, this phenomenon has not been quantitatively predicted based on intrinsic material properties and an applied electrical stimulus. Herein an instability criterion is derived for localization of current density and temperature from a thermal fluctuation in a parallel conductor model of a thin film that is subject to Newton's law of cooling. The conditions for steady-state electro-thermal localization is predicted, verifying a decrease in entropy production upon localization. Electro-thermal localization accompanied by a decrease of entropy production is confirmed in a multiphysics simulation of current flow in a thin film. The instability criterion predicts conditions for spontaneous current density localization, relating symmetry breaking fundamentally to dynamical instability via Local Activity theory.