p-wave superconductivity in weakly repulsive 2D Hubbard model with Zeeman splitting and weak Rashba spin-orbit coupling

TL;DR

This paper investigates p-wave superconductivity in a 2D Hubbard model with weak repulsion, Zeeman field, and Rashba spin-orbit coupling, revealing how filling and magnetic orientation influence pairing symmetry and critical temperature.

Contribution

It introduces an effective low-energy interaction framework showing how spin-orbit coupling and filling fraction affect p-wave pairing in the Hubbard model.

Findings

Superconductivity arises from Kohn-Luttinger interactions.

Pairing symmetry depends on filling and magnetic field orientation.

Critical temperature varies with filling and band dominance.

Abstract

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the non-interacting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger type interaction, while the pairing symmetry of the bands are indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$ of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning $n$. Moreover, $n$ also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral $p_x \pm i p_y$ type state for out-of-plane fields, to a nodal p-wave type state for purely in-plane fields.