# Effect of Spin-Orbit Coupling on 2d Superconductors

I studied the effect of spin orbit coupling due to parallel external magnetic fields on interfacial superconductivity in oxide interfaces. I assumed an XY Hamiltonian with an extra term depending on the sine of the angle between neighbouring spins. I then did Monte-Carlo simulation of this system, for zero temperature to finite temperatures. I found that for constant uniform spin-orbit coupling, there is no change in the Berezinskii-Kosterlitz-Thouless (BKT) phase transition for the 2D XY Model.  I then assumed uncorrelated quenched disorder states. For each realization, I simulated the expected results. After this, I had to do disorder averaging over all the different realizations to find the observed results.

This project taught me

• to use computational clusters and write parallelized code running on a large number of cores (256).
• associated theory in Condensed Matter Physics like Ginzburg-Landau theory and its applications, phase transitions in the XY model
• Monte-Carlo methods for simulations in statistical physics.

I will also study the theory of disordered-systems to theoretically analyze the problem.

[Reference: (Aviram Steinbok and Karen Michaeli, https://doi.org/10.1103/PhysRevB.95.184515)
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.184515 ]