Magnetic field behaviour in $s+is$ and $s+id$ superconductors: twisting of applied and spontaneous fields

TL;DR

This paper investigates magnetic field screening and spontaneous magnetic fields in $s+is$ and $s+id$ superconductors, revealing non-standard decay behaviors, field twisting, and domain wall solutions with unique magnetic properties.

Contribution

It introduces a linearized model coupling order parameter moduli to magnetic modes, predicting non-monotonic decay and field twisting in $s+is$ and $s+id$ superconductors, with new domain wall solutions.

Findings

Magnetic fields decay non-monotonically in the bulk.

Field twisting occurs in $s+id$ systems.

Two distinct domain wall solutions are identified.

Abstract

We consider magnetic field screening and spontaneous magnetic fields in $s+is$ and $s+id$ superconductors both analytically and numerically. We show that in general, the linearized model couples the moduli of order parameters to the magnetic modes. This causes magnetic field screening that does not follow the standard exponential law and hence cannot be characterized by a single length scale: the London penetration length. We also demonstrate that the resulting linear mixed modes, correctly predict spontaneous fields and their orientation. We show that these mixed modes cause external fields to decay non-monotonically in the bulk. This is observed as the magnetic field twisting direction, up to an angle of $\pi/2$, as it decays in the nonlinear model. Finally, we demonstrate that there are two non-degenerate domain wall solutions for any given parameter set. These are distinguished by either clockwise or anti-clockwise interpolation of the inter-component phase difference, each producing a different solution for the other fields. However, only domain wall solutions in $s+id$ systems exhibit magnetic field twisting.