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Abstract
We discuss transport properties of fully spin-polarized triplet superconductors, where only electrons of one spin component (along a certain axis) are paired. Due to the structure of the order parameter space, wherein phase and spin rotations are intertwined, a configuration where the superconducting phase winds by $4\pi$ in space is topologically equivalent to a configuration with no phase winding. This opens the possibility of supercurrent relaxation by a smooth deformation of the order parameter, where the order parameter remains non-zero at any point in space throughout the entire process. During the process, a spin texture is formed. We discuss the conditions for such processes to occur and their physical consequences. In particular, we show that when a voltage is applied, they lead to an unusual alternating-current Josephson effect whose period is an integer multiple of the usual Josephson period. These conclusions are substantiated in a simple time-dependent Ginzburg-Landau model for the dynamics of the order parameter. One of the potential applications of our analysis is for moir\'e systems, such as twisted bilayer and double bilayer graphene, where superconductivity is found in the vicinity of ferromagnetism.
Highlights
Spin-triplet superconductors (SCs) and superfluids are predicted to exhibit rich phenomena owing to the interplay between the spin and phase degrees of freedom of their order parameters
Triplet superconductivity remains scarce in electronic systems, ; possible examples include uranium heavy-fermion compounds where superconductivity is found to coexist with ferromagnetism [3,4,5], and Sr2RuO4 [6], the latter has recently been contested [7]
We focus on a particular state which is natural for twisted bilayer graphene (TBG) and related graphene-based moiré materials: a fully spin-polarized triplet superconductor, in which only electrons of one spin component are paired
Summary
Spin-triplet superconductors (SCs) and superfluids are predicted to exhibit rich phenomena owing to the interplay between the spin and phase degrees of freedom of their order parameters. A small voltage applied across the SC results in a time-dependent current with a direct-current (DC) component of magnitude close to this critical current, and an alternating-current (AC) component with a fundamental frequency ω J = eV/h, i.e., half of the usual Josephson frequency across a SC weak link; see Fig. 1(c) This doubled periodicity is directly related to the Z2 topological structure of the order parameter space. For sufficiently lar√ge applied Zeeman field, the critical current scales as Jc ∝ B independently of system size We demonstrate these phenomena within a time-dependent Ginzburg-Landau model, where we assume that the system is coupled to a bath with which it can exchange both energy and spin angular momentum. The Appendices contain technical details of the solution of the time-dependent Ginzburg-Landau (TDGL) equations
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