Competition of Superconductivity and Antiferromagnetism in a d-Wave Vortex Lattice

TL;DR

This paper investigates the coexistence and competition of d-wave superconductivity and antiferromagnetic order in vortex lattices using BdG mean field theory, revealing how magnetic order influences local electronic properties.

Contribution

It introduces a self-consistent study of AFM and d-wave SC orders in vortex states, showing their spatial interplay and impact on electronic states.

Findings

AFM order peaks at vortex centers and changes sign

AFM order decays over a length scale larger than the coherence length

Coexistence suppresses local density of states at vortex cores

Abstract

The d-wave vortex lattice state is studied within the framework of Bogoliubov-de Gennes (BdG) mean field theory. We allow antiferromagnetic (AFM) order to develop self-consistently along with d-wave singlet superconducting (dSC) order in response to an external magnetic field that generates vortices. The resulting AFM order has strong peaks at the vortex centers, and changes sign, creating domain walls along lines where $\nabla \times j_s \approx 0$. The length scale for decay of this AFM order is found to be much larger than the bare d-wave coherence length, $\xi$. Coexistence of dSC and AFM order in this system is shown to induce $\pi$-triplet superconducting order. Competition between different orders is found to suppress the local density of states at the vortex center and comparison to recent experimental findings is discussed.