Quantum Matter Seminar

Is there a fundamental upper bound on the superconducting transition temperature in electron–phonon systems? At strong coupling, the Migdal–Eliashberg gap equations predict a superconducting $T_c$ that increases indefinitely with interaction strength. In most real materials, however, this growth is cut off at a model-dependent coupling by competing effects such as phonon softening, charge order, and polaron or bipolaron formation. A natural question remains: if these competing tendencies are sufficiently suppressed, is Migdal–Eliashberg theory intrinsically stable at arbitrarily strong coupling?

We show that it is, and that the Fermi energy is the only fundamental scale limiting $T_c$. We establish this through a careful analysis of the Kadanoff–Baym equations, avoiding spurious instabilities that invariably arise in Markovian reductions such as the quantum Boltzmann equation. The same non-Markovian framework also gives access to normal-state kinetic properties at strong-couplings, revealing a new perspective on the emergence of "Planckian" bounds on equilibration.