Chiral p -wave superconductors have complex coherence and magnetic field penetration lengths

Abstract

We show that in superconductors that break time reversal symmetry and have anisotropy, such as p + ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa. Correspondingly the long-range decay of the magnetic field and order parameter are in general given by the same exponent. Thus one cannot characterize p + ip superconductors by the usual coherence and magnetic field penetration lengths. Instead the system has normal modes that are associated with linear combinations of magnetic fields, moduli of and phases of the order parameter components. Each such normal mode has its own decay length that plays the role of a hybridized coherence/magnetic field penetration length. On a large part of the parameter space these exponents are complex. Therefore the system in general has damped oscillatory decay of the magnetic field accompanied by damped oscillatory variation of the order parameter fields. PACS numbers:arXiv:1905.07296v1 [cond-mat.supr-con]

Magnetic signatures of domain walls in s+is and s+id superconductors: Observability and what that can tell us about the superconducting order parameter

“…In isotropic superconductors, domain walls are associated with zero magnetic field, unless the domain wall is attached to an inhomogeneous pinning center or there is an underlying density inhomogeneity [9,12,13]. However, in the presence of anisotropies, it has been shown that the magnetic field is coupled with phase difference gradients [15,[26][27][28] and with matter field density gradients [30]. This would suggest that anisotropies could principally alter the magnetic signatures of domain walls in s + is and s + id systems.…”

First-order superconducting phase transition in a chiralp+ipsystem

“…II B. The decay of magnetic fields in this model usually involves multiple modes and multiple length scales [52], that yields further differences compared to s + is models previously studied in Monte Carlo simulations [36,37]. In what follows we will not distinguish between the subdominant electromagnetic scales.…”

“…The London limit is commonly used for similar models [40,41]. However, in the case of a multicomponent order parameter, and with the addition of Ising anisotropy and MGT, such an approach requires considerable care and is generally not applicable [52].…”

“…We will first explicitly assess the validity of this approach, following a similar but not identical method to the one presented in Ref. [52]. To this end, we expand all fluctuating fields to second order in deviations from their mean-field values, introducing…”

“…Above this value amplitude fluctuations become important as the − mode corresponds to the lowest eigenvalue. The effect of MGT is that the eigenvectors become mixed modes with multiple nonzero entries for nonzero momentum [52]. To investigate the degree of mixing, we plot the k dependence of the nonzero entries in ψ * in Fig.…”