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The weak-coupling renormalization group method is an asymptotically exact method to find superconducting instabilities of a lattice model of correlated electrons. Here we extend it to spin-orbit coupled lattice systems and study the emerging superconducting phases of the Rashba-Hubbard model. Since Rashba type spin-orbit coupling breaks inversion symmetry, the arising superconducting phases may be a mixture of spin-singlet and spin-triplet states. We study the two-dimensional square lattice as a paradigm and discuss the symmetry properties of the arising spin-orbit coupled superconducting states including helical spin-triplet superconductivity. We also discuss how to best deal with split energy bands within a method which restricts paired electrons to momenta on the Fermi surface.
We investigate the Hubbard model on a two-dimensional square lattice by the perturbation expansion to the fourth order in the on-site Coulomb repulsion U. Numerically calculating all diagrams up to the fourth order in self-energy, we examine the conv
The discovery of superconductivity in twisted bilayer graphene has triggered a resurgence of interest in flat-band superconductivity. Here, we investigate the square-octagon lattice, which also exhibits two perfectly flat bands when next-nearest neig
Motivated by recent studies on ferroelectric-like order coexisting with metallicity, we investigate ferroelectric (FE) superconductivity in which a FE-like structural phase transition occurs in the superconducting state. We consider a two-dimensional
Heterostructures containing strongly correlated electron systems provide a platform to clarify interplay of electron correlation and Rashba spin-orbit coupling in unconventional superconductors. Motivated by recent fabrication of artificially-enginee
Interplay between antiferromagnetism and superconductivity is studied by using the 3-dimensional nearly half-filled Hubbard model with anisotropic transfer matrices $t_{rm z}$ and $t_{perp}$. The phase diagrams are calculated for varying values of th