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

• Published in: Physical review. B 2018-01, Vol.97 (2), Article 024515
• Main Authors: Hugdal, Henning G., Sudbø, Asle
• Format: Article
• Language: English
• Subjects: Dependence; Mathematical models; Momentum; Order parameters; Spin-orbit interactions; Superconductivity; Transition temperature; Two dimensional models; Zeeman effect
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.97.024515

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 noninteracting 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 is 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 px±ipy type state for out-of-plane fields, to a nodal p-wave-type state for purely in-plane fields.