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Register a new userSpin-orbit coupled superconductivity: Rashba-Hubbard model on the square lattice
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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.
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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 convergence of perturbation series in the lattice system. We indicate that the coefficient of each order term rapidly decreases as in the impurity Anderson model for T > 0.1t in the half-filled case, but it holds in the doped case even at lower temperatures. Thus, we can expect that the convergence of perturbation expansion in U is very good in a wide parameter region also in the lattice system, except for T < 0.1t in the half-filled case. We next calculate the density of states in the fourth-order perturbation. In the half-filled case, the shape in a moderate correlation regime is quite different from the three peak structure in the second-order perturbation. Remarkable upper and lower Hubbard bands locate at w = +(-)U/2, and a pseudogap appears at the Fermi level w=0. This is considered as the precursor of the Mott-Hubbard antiferromagnetic structure. In the doped case, quasiparticles with very heavy mass are formed at the Fermi level. Thus, we conclude that the fourth-order perturbation theory overall well explain the asymptotic behaviors in a strong correlation regime.
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 neighbour hopping or an external magnetic field are added to the system. We calculate the superconducting phase diagram in the presence of on-site attractive interactions and find two superconducting domes, as observed in several types of unconventional superconductors. The critical temperature shows a linear dependence on the coupling constant, suggesting that superconductivity might reach high temperatures in the square-octagon lattice. Our model could be experimentally realized using photonic or ultracold atoms lattices.
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 s-wave superconductor with Rashba-type antisymmetric spin-orbit coupling (ASOC). Assuming linear relationship between polar lattice displacement and strength of the ASOC, we treat the Rashba-type ASOC as a molecular field of FE-like order. It is shown that the FE-like order is induced by the magnetic field when the system is superconducting. Furthermore, we clarify the FE superconductivity in a low carrier density regime, which was recently discovered in doped SrTiO$_3$. It is demonstrated that the FE superconducting state can be stable in this regime in the absence of the magnetic field. Our results open a way to control the electric polarization by superconductivity, that is, superconducting multiferroics.
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-engineered heavy fermion superlattices and high-temperature cuprate superconductors, we conduct a thorough study on superconductivity in Rashba-Hubbard model. In contrast to previous weak coupling approaches, we employ fluctuation-exchange approximation to describe quantum critical magnetic fluctuations and resulting superconductivity. As a result, robust Fermi surfaces against magnetic fluctuations, incommensurate spin fluctuations, and a strongly parity-mixed superconducting phase are demonstrated in a wide range of electron filling from type-II van Hove singularity to half-filling. We also clarify impacts of type-II van Hove singularity on magnetic fluctuations and superconductivity. Whereas the $d_{x^2-y^2}$-wave pairing always dominant, subdominant spin-triplet pairing with either $p$-wave or $f$-wave symmetry shows a comparable magnitude, especially near the type-II van Hove singularity. Our results resolve unsettled issues on strongly correlated Rashba systems and uncover candidate systems of nonreciprocal transport and topological superconductivity.
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 the ratio $r_{rm z}=t_{rm z}/t_{perp}$ using the spin fluctuation theory within the fluctuation-exchange approximation. The antiferromagnetic phase around the half-filled electron density expands while the neighboring phase of the anisotropic $d_{x^{2}-y^{2}}$-wave superconductivity shrinks with increasing $r_{rm z}$. For small $r_{rm z}$ $T_{rm c}$ decreases slowly with increasing $r_{rm z}$. For moderate values of $r_{rm z}$ we find the second order transition, with lowering temperature, from the $d_{x^{2}-y^{2}}$-wave superconducting phase to a phase where incommensurate SDW coexists with $d_{x^{2}-y^{2}}$-wave superconductivity. Resonance peaks as were discussed previously for 2D superconductors are shown to survive in the $d_{x^{2}-y^{2}}$-wave superconducting phase of 3D systems. Soft components of the incommensurate SDW spin fluctuation mode grow as the coexistent phase is approached.
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