Spontaneous vortex lattice due to orbital magnetization in valley polarized superconductors

Abstract: In this work, we study the spontaneous formation of a vortex lattice in two-dimensional valley polarized superconductors due to orbital magnetization. The screening of magnetic field is weak for two-dimension superconductors, allowing for the magnetic flux associated with vortices to penetrate deep into the superconducting region. The Zeeman coupling between orbital magnetization and magnetic fields associated with vortices leads to the formation of a vortex lattice, once the vortex self-energy is lower than the Zeeman energy. We study the phase diagram and the vortex lattice configuration, and discuss the consequences of the vortex lattice formation in various experimental setups.