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Register a new userInducing and controlling superconductivity in Hubbard honeycomb model using an electromagnetic drive
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The recent successful experimental observation of quantum anomalous Hall effect in graphene under laser irradiation demonstrates the feasibility of controlling single particle band structure by lasers. Here we study superconductivity in a Hubbard honeycomb model in the presence of an electromagnetic drive. We start with Hubbard honeycomb model in the presence of an electromagnetic field drive, both circularly and linearly polarized light and map it onto a Floquet $t$-$J$ model. We explore conditions on the drive under which one can induce superconductivity (SC) in the system. We study the Floquet $t$-$J$ model within the mean-field theory in the singlet pairing channel and explore superconductivity for small doping in the system using the Bogoliubov-de Gennes approach. We uncover several superconducting phases, which break lattice or time reversal symmetries in addition to the standard $U(1)$ symmetry. We show that the unconventional chiral SC order parameter ($d pm id$) can be driven to a nematic SC order parameter ($s+d$) in the presence of a circularly polarized light. The $d+id$ SC order parameter breaks time reversal symmetry and is topologically nontrivial, and supports chiral edge modes. We further show that the three-fold nematic degeneracy can be lifted using linearly polarized light. Our work, therefore, provides a generic framework for inducing and controlling SC in the Hubbard honeycomb model, with possible application to graphene and other two-dimensional materials.
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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.
Using a dynamical cluster quantum Monte Carlo approximation we investigate the d-wave superconducting transition temperature $T_c$ in the doped 2D repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings $tp$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2times2$ plaquette and $tp$ is the hopping between the plaquettes. We find inhomogeneity suppresses $T_c$. The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing $T_c$ suggesting a strong correlation between these quantities.
In order to discuss superconductivity in orbital degenerate systems, a microscopic Hamiltonian is introduced. Based on the degenerate model, a strong-coupling theory of superconductivity is developed within the fluctuation exchange (FLEX) approximation where spin and orbital fluctuations, spectra of electron, and superconducting gap function are self-consistently determined. Applying the FLEX approximation to the orbital degenerate model, it is shown that the $d_{x^2-y^2}$-wave superconducting phase is induced by increasing the orbital splitting energy which leads to the development and suppression of the spin and orbital fluctuations, respectively. It is proposed that the orbital splitting energy is a controlling parameter changing from the paramagnetic to the antiferromagnetic phase with the $d_{x^2-y^2}$-wave superconducting phase in between.
We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number $pm 1$ with equal-spin-pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of three different interactions, onsite attraction $U$, nearest-neighbor density-density attraction $V$, and nearest-neighbor antiferromagnetic exchange $J$, within self-consistent Bogoliubov--de Gennes theory. Transition metal dichalcogenides and cold atom experiments are promising platforms to explore these phases.
Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and d-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the four-fold symmetric Fermi surface becomes unstable against a spontaneous distortion into two-fold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk distorted Fermi surface is modified from the d-wave pairing to (d+s)-wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature $T_{rm c}^{rm PI}$ of Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting $T_{rm c}^{rm SC}$. This implies that the filling region for strong Pomeranchuk instability and that for strong superconducting fluctuations can be separated, and Pomeranchuk instability can appear even if the peak of $T_c^{rm PI}$ is lower than the peak of $T_c^{rm SC}$. An interesting observation is that the Fermi surface distortion can enhance the superconducting $T_{rm c}^{rm SC}$ in the overdoped regime, which is explained with a perturbation picture for small distortions.
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