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Register a new userd-wave superconductivity from electron-phonon interactions
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J.P.Hague
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I examine electron-phonon mediated superconductivity in the intermediate coupling and phonon frequency regime of the quasi-2D Holstein model. I use an extended Migdal-Eliashberg theory which includes vertex corrections and spatial fluctuations. I find a d-wave superconducting state that is unique close to half-filling. The order parameter undergoes a transition to s-wave superconductivity on increasing filling. I explain how the inclusion of both vertex corrections and spatial fluctuations is essential for the prediction of a d-wave order parameter. I then discuss the effects of a large Coulomb pseudopotential on the superconductivity (such as is found in contemporary superconducting materials like the cuprates), which results in the destruction of the s-wave states, while leaving the d-wave states unmodified.
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Determinant quantum Monte Carlo (DQMC) simulations are used to study non-linear electron-phonon interactions in a two-dimensional Holstein-like model on a square lattice. We examine the impact of non-linear electron-lattice interactions on superconductivity and on Peierls charge-density-wave (CDW) correlations at finite temperatures and carrier concentrations. We find that the CDW correlations are dramatically suppressed with the inclusion of even a small non-linear interaction. Conversely, the effect of the non-linearity on superconductivity is found to be less dramatic at high temperatures; however, we find evidence that the non-linearity is ultimately detrimental to superconductivity. These effects are attributed to the combined hardening of the phonon frequency and a renormalization of the effective linear electron-phonon coupling towards weaker values. These results demonstrate the importance of non-linear interactions at finite carrier concentrations when one is addressing CDW and superconducting order and have implications for experiments that drive the lattice far from equilibrium.
We present the numerical solution of the renormalization group (RG) equations derived in Ref. [1], for the problem of superconductivity in the presence of both electron-electron and electron-phonon coupling at zero temperature. We study the instability of a Fermi liquid to a superconductor and the RG flow of the couplings in presence of retardation effects and the crossover from weak to strong coupling. We show that our numerical results provide an ansatz for the analytic solution of the problem in the asymptotic limits of weak and strong coupling.
We study by Variational Monte Carlo an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange $J$ favoring d-wave superconductivity and a repulsion $V$ opposing against it. We find that the on-site repulsion $U$ effectively enhances the strength of $J$ meanwhile suppressing that of $V$, thus favoring superconductivity. This result shows that attractions which do not involve charge fluctuations are very well equipped against strong electron-electron repulsion so much to get advantage from it.
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.
The nature of unconventional superconductivity is intimately linked to the microscopic nature of the pairing interactions. In this work, motivated by cubic heavy fermion compounds with embedded multipolar moments, we theoretically investigate superconducting instabilities instigated by multipolar Kondo interactions. Employing multipolar fluctuations (mediated by RKKY interaction) coupled to conduction electrons via two-channel Kondo and novel multipolar Kondo interactions, we uncover a variety of superconducting states characterized by higher-angular momentum Cooper pairs, $J=0,1,2,3$. We demonstrate that both odd and even parity pairing functions are possible, regardless of the total angular momentum of the Cooper pairs, which can be traced back to the atypical nature of the multipolar Kondo interaction that intertwines conduction electron spin and orbital degrees of freedom. We determine that different (point-group) irrep classified pairing functions may coexist with each other, with some of them characterized by gapped and point node structures in their corresponding quasiparticle spectra. This work lays the foundation for discovery and classification of superconducting states in rare-earth metallic compounds with multipolar local moments.
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