Coexistence of superconductivity and incommensurate magnetic order

TL;DR

This paper investigates how incommensurate spin density waves affect superconductivity, revealing that SDWs induce inhomogeneity in the order parameter and can lead to FFLO states under magnetic fields, with implications for unconventional superconductors.

Contribution

It introduces an efficient approach to solve BdG equations for large inhomogeneous systems and demonstrates the impact of SDWs and magnetic fields on superconducting states.

Findings

SDWs induce inhomogeneity in the superconducting order parameter.

External magnetic fields can suppress homogeneous order and induce FFLO states.

Magnetic fields reduce the destructive effect of SDWs on superconductivity in s-wave pairing.

Abstract

The influence of incommensurate spin density waves (SDW) on superconductivity in unconventional superconductors is studied by means of the Bogolubov-de Gennes (BdG) equations. Exploiting translational symmetries of a magnetically ordered two-dimensional system we propose an approach that allows to solve the BdG equations on much larger clusters than it is usually possible for inhomogeneous systems. Applying this approach we demonstrate that the presence of incommensurate spin density waves induces real-space inhomogeneity of the superconducting order parameter even in the absence of external magnetic field. In this case a homogeneous order parameter of the Bardeen-Cooper-Schrieffer-type superconducting state is slightly modulated, or equivalently, a small fraction of the charge carriers form Cooper pairs with non-zero total momentum. However, when a sufficiently strong magnetic field is applied, the homogeneous component of the order parameter is suppressed and the system transits to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where the order parameter oscillates changing sign. We show that for s-wave pairing the presence of external magnetic field diminishes the destructive influence of the SDW order on superconductivity. A simple explanation of this effect is also proposed.