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 ${\varphi }_0$ 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 ${\varphi }_0$ 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 ${\varphi }_0$ shift.

• Received 10 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.134506