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We study current-induced vibrational cooling, heating, and instability in adonor-acceptor rectifying molecular junction using a full counting statisticsapproach. In our model, electron-hole pair excitations are coupled to a givenmolecular vibrational mode which is either harmonic or highly anharmonic. Thismode may be further coupled to a dissipative thermal environment. Adopting amaster equation approach, we confirm the charge and heat exchange fluctuationtheorem in the steady-state limit, for both harmonic and anharmonic models.Using simple analytical expressions, we calculate the charge current andseveral measures for the mode effective temperature. At low bias, we observethe effect of bias-induced cooling of the vibrational mode. At higher bias, themode effective temperature is higher than the environmental temperature, yetthe junction is stable. Beyond that, once the vibrational mode (bias-induced)excitation rate overcomes its relaxation rate, instability occurs. We identifyregimes of instability as a function of voltage bias and coupling to anadditional phononic thermal bath. Interestingly, we observe a reentrantbehavior where an unstable junction can properly behave at a high enough bias.The mechanism for this behavior is discussed.

Vibrational cooling, heating, and instability in molecular conducting junctions: Full counting statistics analysis