Magnetic field behavior in s+is and s+id superconductors: Twisting of applied and spontaneous fields

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 nonmonotonically in the bulk. This is observed as the magnetic field twisting direction, up to an angle of π/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.

Symmetries, length scales, magnetic response, and skyrmion chains in nematic superconductors

“…We will first consider |H| < H c1 and magnetic field screening. We will show that the mixed modes cause the local magnetic field B to locally twist direction, as has been demonstrated for s + is and s + id superconductors [21]. We will then consider vortex solutions in the bulk, which for many orientations exhibit fractional vortex splitting, forming Skyrmions.…”

“…a density excitation can only be excited through coupled modes and hence induces magnetic field fluctuations. This leads to excitations that in the isotropic model would feature purely excited matter fields, such as domain walls and defects, spontaneously inducing localised magnetic field, as seen in [21,28] and noted in [29].…”

“…If this process is repeated for the anisotropic case however, the equations of motion will not decouple into separate magnetic and matter equations and are in general mixed. It has been shown that this leads to mixed modes [21], meaning the familiar London penetration depth and coherence lengths do not exist. Hence in this paper, the London model will not describe the magnetic response of the system.…”

“…If C is invertible (as assumed in [21]), then Ξ is invertible allowing eq. 35 to be written as an eigenvalue problem.…”

“…It is important to note that we have retained all three components for p i , as it was shown in [21] that reducing to a single component does not, in general, yield a solution of the equations of motion.…”