First order phase transition in a two-dimensional superconductor

N. J. Jabusch; E. K. Kokkinis; A. V. Chubukov

doi:10.1103/PhysRevB.111.174507

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First order phase transition in a two-dimensional superconductor

N. J. Jabusch, E. K. Kokkinis, A. V. Chubukov

DOI 10.1103/PhysRevB.111.174507 · Physical Review B

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Abstract

We consider a superconductor under external perturbation, which forces Cooper pairs to develop with a finite total momentum q. The condensation energy of such a state decreases with q and vanishes at a critical qc. We analyze how superconducting order evolves at q≈qc. In three dimensions, the result is well known: the pairing susceptibility diverges at q=qc+0, and the gap amplitude Δ(q) gradually increases as q decreases below qc and reaches its largest value Δ0 at q=0. In two dimensions (2D), we find different behavior. Namely, for a parabolic dispersion, the pairing susceptibility also diverges at q=qc+0, but at q=qc−0, the gap amplitude jumps to the maximal Δ0 and remains equal to it for all q<qc. For a nonparabolic dispersion ɛk=ck2α, we find that for α>1 the transition becomes second order, but the gap evolution is rather sharp, whereas for α<1 it becomes first order, but Δ(q) is nonmonotonic. This is similar, but not identical, to the behavior of magnetization near a Stoner transition in 2D.