Finite-temperature transition of the edge pair-density wave

Determine whether the finite mean-field onset of the edge pair-density wave in the superconducting Peierls mechanism corresponds to a sharp finite-temperature phase transition or only a crossover once thermal and low-dimensional fluctuations are included.

Background

The paper establishes the superconducting Peierls instability in an effectively zero-temperature mean-field treatment, where counter-propagating zero-energy Andreev bound states produce a finite-wavevector pairing instability and an edge pair-density wave. The authors note that thermal broadening weakens the finite-wavevector quasiparticle response, suggesting a finite mean-field onset temperature for the edge modulation.

Because the edge is effectively low-dimensional, fluctuations beyond mean field may alter the finite-temperature behavior. The unresolved issue is whether the mean-field onset survives as a genuine thermodynamic transition or is replaced by a crossover.