On the theory of nonhomogeneous nonequilibrium superconductivity in 2D systems with massless fermions

We analyze static and nonequilibrium superconducting properties of a 2D relativistic-like model system with local electron-electron interaction, Rashba spin-orbit interaction αR in presence of time-dependent in-plane magnetic field H(t). It is shown that similar to the 2D case with ordinary massive quasiparticle dispersion ε ( k ) ∼ | k | 2 at large fields, such a system demonstrates a nonhomogeneous superconducting stripe phase with the order parameter Δ ( r ) = Δ ( 0 ) cos ( 2 [ μ B B × r ] n / ℏ υ F ) (B is the magnetic induction, υF is the Fermi velocity, n is the normal to the plane, μB is the Bohr magneton, and α R ≪ υ F) where the stripes are oriented along the B direction. In the considered system, the inter-stripe period L and the magnitude of the magnetic field B are related by a universal relation B L = ℏ υ F / μ B ≃ 0.714 ⋅ 10 − 4 T m. Contrary to the case of massive quasiparticles, where the condition α R ∼ υ F can be, in principle, satisfied by increasing αR or by charge doping (Fermi velocity decreasing), in a relativistic-like system, where υF is doping-independent and one-two orders of magnitude larger than typical Fermi velocity in the “standard” 2D systems, the stripe phase can be the ground state at a rather low doping level. We also analyzed the nonequilibrium properties of the system with a focus on the melting of the stripe order (when the magnetic field is quenched to a lower value) and stripe dynamics (when the field is rotated by 90° degrees) and found several notable results. In particular, it was shown that the stripe domains melt according to law R ∼ 1 t at initial times, while at longer times they shrink exponentially. In the case of the flipped magnetic field, the stripe orientation gradually turns from x- to y-direction, and the intermediate “crossed-stripe” phase takes place during times of order of picoseconds. Such a crossed phase is built of periodic superconducting bubbles that potentially may have applications in modern ultrafast superconducting technologies.