Magnetoelectrics in disordered topological insulator Josephson junctions

We study theoretically the coupling of electric charge and spin polarization in an equilibrium and nonequilibrium electric transport across a two-dimensional Josephson configuration comprised of disordered surface channels of a three-dimensional topological insulator. In the equilibrium state of the system, we predict the Edelstein effect, which is much more pronounced than its counterpart in conventional spin-orbit coupled materials. Employing a quasiclassical Keldysh technique, we demonstrate that the ground state of the system can be shifted experimentally into arbitrary macroscopic superconducting phase differences other than the standard 0 or pi, constituting a phi(0) junction, solely by modulating a quasiparticle flow injection into the junction. We propose a feasible experiment in which the quasiparticles are injected into the topological insulator surface by means of a normal electrode and voltage gradient so that oppositely oriented stationary spin densities can be developed along the interfaces and allow for direct use of the spin-momentum locking nature of Dirac fermions in the surface channels. The phi(0) state is proportional to the voltage difference applied between the injector electrode and superconducting terminals that calibrates the injection rate of particles and, therefore, the phi(0) shift.