Spontaneous vortex lattice due to orbital magnetization in valley polarized superconductors

TL;DR

This paper investigates how valley polarization in 2D superconductors leads to spontaneous vortex lattice formation driven by orbital magnetization and Zeeman coupling, affecting magnetic properties and phase behavior.

Contribution

It introduces a mechanism for vortex lattice formation in valley polarized superconductors due to orbital magnetization and analyzes the resulting phase diagram and configurations.

Findings

Vortex lattice forms when Zeeman energy exceeds vortex self-energy.

Weak magnetic screening allows flux penetration deep into the superconductor.

Vortex configurations depend on valley polarization and magnetic interactions.

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.