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Current-induced atomic dynamics, instabilities, and Raman signals: Quasi-classical Langevin equation approach

We derive and employ a semi-classical Langevin equation obtained from path-integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective non-equilibrium bath. The bath results in random forces describing Joule heating,current-induced forces including the non-conservative wind force,dissipative frictional forces, and an effective Lorentz-like force due to the Berry phase of the non-equilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway "waterwheel" modes) and investigate the signature of these in the Raman signals.