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Stability and Relaxation of Electron-Phonon Systems at Strong Coupling

I will discuss possible limits on the stability of electron-phonon systems at strong coupling and possible fundamental limits on the superconducting Tc. Specifically, I will present a study of Migdal-Eliashberg theory (MET) for electron-phonon interactions at strong coupling. Within the Markovian Boltzmann approximation, this description was found to be dynamically unstable at large couplings, leading to a claim about a fundamental upper bound on the dimensionless coupling constant. Using the quasiclassical Kadanoff-Baym equation, we show that this instability is absent when non-Markovian effects are correctly taken into account. Having established the validity of the strong-coupling limit, we analyze the long-time relaxation dynamics. We find a clear imprint of the non-Markovian nature of the dynamics: in an intermediate temperature range between the Debye frequency and the coupling strength, the relaxation rate becomes linear in temperature with Planckian slope, while the leading relaxation mode acquires a large imaginary component, producing strongly oscillatory decay. Our results imply that any instability which preempts superconductivity must arise from effects beyond MET, such as phonon softening or polaronic effects at finite electronic bandwidth. This leaves open the possibility of parametrically unbounded superconducting Tc in multi-flavor electron-phonon models.