Ginzburg-Landau theory for unconventional surface superconductivity in PtBi$_2$

TL;DR

This paper develops a Ginzburg-Landau theoretical framework for understanding unconventional surface superconductivity in PtBi₂, focusing on the symmetry of order parameters and their response to magnetic fields, aiding experimental identification.

Contribution

It introduces a systematic method to derive the Ginzburg-Landau functional for the three irreducible representations of PtBi₂'s point group, including magnetic coupling and field effects.

Findings

Identifies the likely irreducible representations $A_1$ and $A_2$ for the order parameters.

Derives the symmetry-allowed terms up to fourth order in the Ginzburg-Landau functional.

Predicts field-induced helical superconductivity and effects on nodal structures.

Abstract

Recent experimental evidence suggests the presence of an unconventional, nodal surface-su\-per\-con\-duc\-ting state in trigonal PtBi\textsubscript{2}. We construct a Ginzburg--Landau theory for the three superconducting order parameters, which correspond to the three irreducible representations of the point group $C_{3v}$. The irreducible representations $A_1$ and $A_2$ are the most likely. We develop a systematic method to determine the symmetry-allowed terms and apply it to derive all terms up to fourth order in the three order parameters. The Ginzburg--Landau functional also includes coupling to the magnetic field. The functional is employed to determine the effect of an applied uniform magnetic field on the nodal structure for $A_1$ and $A_2$ pairing. The results facilitate clear-cut experimental differentiation between these symmetries. We also predict field-induced helical superconductivity.