Pokrovsky--Talapov and Berezinskii--Kosterlitz--Thouless Phase Transitions in Bilayer Superconducting Films under an In-Plane Magnetic Field

Abstract

We study finite-temperature phase transitions in a Josephson-coupled bilayer superconducting film with compact layer phases under an in-plane magnetic field. At zero temperature, where thermally excited layer vortices are absent, the relative-phase sector undergoes a Pokrovsky--Talapov (PT) commensurate--incommensurate (C--IC) transition from a commensurate Fulde--Ferrell (C/FF) state to an incommensurate Bloch superconducting (IC/Bloch SC) state. At finite temperature, compactness separates two distinct defect mechanisms. The C--IC boundary remains a PT soliton-entry line: interlayer Josephson vortex--antivortex-pair solitons enter with the square-root onset $ρ_{\rm sol}\propto [k_0-k_0^c(T)]^{1/2}$. Thermal melting is instead Berezinskii--Kosterlitz--Thouless (BKT)-like, with correlation exponent $η=1/4$ at the boundary, but the active vortex channel changes across the phase diagram. Josephson locking suppresses elementary layer vortices in the C/FF state and selects a same-vorticity layer-pair BKT channel, whereas elementary layer vortices control melting of the IC/Bloch SC state.