# Ground state of the three-dimensional BCS d-wave superconductor

## TL;DR

This paper determines the mean-field ground state of a three-dimensional d-wave superconductor, revealing a non-inert, time-reversal symmetry-breaking state with high magnetization, minimally affected by parasitic s-wave coupling.

## Contribution

It provides a detailed characterization of the 3D d-wave superconductor's ground state, including symmetry properties and effects of s-wave coupling, using Ginzburg--Landau theory.

## Key findings

- Ground state breaks time reversal symmetry almost maximally.
- State is invariant under only C2 symmetry.
- Parasitic s-wave component has negligible effect.

## Abstract

We determine the mean-field ground state of the three-dimensional rotationally symmetric d-wave ($\ell=2$) superconductor at weak coupling. It is a non-inert state, invariant under the symmetry $C_{2}$ only, which breaks time reversal symmetry almost maximally, and features a high, but again less than maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg--Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic s-wave component has only a minuscule quantitative and no qualitative effect on the ground state.