We examine the effect of repulsion on superconductivity in a three-dimensional system with a Bardeen-Pines-like interaction in the low-density limit, where the chemical potential $μ$ is much smaller than the phonon frequency $ω_L$. We parameterize the strength of the repulsion by a dimensionless parameter $f$, and find that the superconducting transition temperature $T_c$ approaches a nonzero value in the $μ= 0$ limit as long as $f$ is below a certain threshold $f^*$. In this limit, we find that $T_c$ goes to zero as a power of $f^*-f$, in contrast to the high density limit, where $T_c$ goes to zero exponentially quickly as $f$ approaches $f^*$. For all nonzero $f$, the gap function $Δ(ω_m)$ changes sign along the Matsubara axis, which allows the system to partially overcome the repulsion at high frequencies. We trace the position of the gap node with $f$ and show that it approaches zero frequency as $f$ approaches $f^*$. To investigate the robustness of our conclusions, we then go beyond the Bardeen-Pines model and include full dynamical screening of the interaction, finding that $T_c$ still saturates to a non-zero value at $μ= 0$ when $f < f^*$.
Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the onsite term is paramount. Recently, the onset of superconductivity at 4.7K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial t…
We study superconductivity driven by screened Coulomb repulsion in three-dimensional Luttinger semimetals with a quadratic band touching and strong spin-orbit coupling. In these semimetals, the Cooper pairs are formed by spin-3/2 fermions with non-trivial wavefunctions. We numerically solve the linear Eliashberg equation to obtain the critical temperature of a singlet s-wave gap function as a function of doping, with account of spin-orbit and self-energy corrections. In order to understand the underlying mechanism of superconductivity, we compute the sensitivity of the critical temperature to …
Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of $d$-wave pairing when a near neighbor Coulomb repulsion $V$ is present in addition to the on-site Coulomb repulsion $U$. We find that $d$-wave pairing and the superconducting transition temperature $T_c$ are only weakly suppressed as long as $V$ does not exceed $U/2$. This stability is traced to the strongly retarded nature of pairing that allows the $d$-wave pairs to minimize the repulsive effect of $V$. When $V$ approaches $U/2$, large momentum c…
We discuss superconducting pairing in a narrow conduction band sandwiched between unoccupied and occupied bands, an arrangement that enables an unconventional pairing mechanism governed by Coulomb repulsion. Pairing interaction originates from repulsion-assisted scattering between far-out pair states in the higher-energy bands and those at the Fermi level. Optimizing the bandstructure design and carrier density in order to bring plasma frequency below the bandgap renders the repulsion unscreened for the processes with a large frequency transfer. This allows the pairing to fully benefit from th…
We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moiré band electrons, we find that phonons generate attractive interactions in both $s$ and $d$ wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the $s$-wave channel is more favorable; however, on-site Coulomb repulsion can suppress $s$-wave pairing relative to $d$-wave. The pair amplitude varies spatially with the moiré period…
We present a novel mechanism of s-wave pairing in Fe-based superconductors. The mechanism involves holes near dxz/dyz pockets only and is applicable primarily to strongly hole doped materials. We argue that as long as the renormalized Hund's coupling J exceeds the renormalized inter-orbital Hubbard repulsion U', any finite spin-orbit coupling gives rise to s-wave superconductivity. This holds even at weak coupling and regardless of the strength of the intra-orbital Hubbard repulsion U. The transition temperature grows as the hole density decreases. The pairing gaps are four-fold symmetric, but…
The experimental observation of superconductivity in doped semimetals and semiconductors, where the Fermi energy is comparable to or smaller than the characteristic phonon frequencies, is not captured by the conventional theory. In this paper, we propose a mechanism for superconductivity in ultralow-density three-dimensional Dirac materials based on the proximity to a ferroelectric quantum critical point. We derive a low-energy theory that takes into account both the strong Coulomb interaction and the direct coupling between the electrons and the soft phonon modes. We show that the Coulomb rep…
We review recent theoretical progress in understanding spatially uniform $s$-wave superconductivity which arises from a fermion-fermion interaction, which is repulsive on the Matsubara axis, where it is real, but does depend on the transferred frequency. Such a situation holds, e.g., for systems with a screened Coulomb and retarded electron-phonon interaction. We show that despite repulsion, superconductivity is possible in a certain range of system parameters. However, at $T=0$ the gap function on the Matsubara axis, $Δ(ω_m)$, must pass through zero and change sign at least once. These zeros …
We analyze in detail the superconductivity that arises in an extended Hubbard model describing a multiband system with repulsive interactions. We show that virtual interband processes induce an effective attractive interaction for small momentum transfers, a situation not found in most models of superconductivity from repulsion. This attraction can be traced back, in real space, to the presence of correlated hopping terms induced by interband polarization. We reveal this physics with both strong-coupling expansion and many-body perturbation theory, supplemented by numerical calculations. Final…
Monovalent metals contain half filled band (HFB) of s-electrons. Emphasizing importance of Coulomb repulsions in HFB in 2D and 1D monovalent systems we sketched a theory (2018) for ambient temperature granular superconductivity reported by Thapa and Pandey (2018) in Au-Ag nanostructures (updated by Thapa et al., 2019). Sharpening our theory, we suggest that \textit{Coulomb repulsions in certain structurally perturbed regions (atomic clusters, stacking faults, grain boundaries etc.) create nanoscale reservoirs of singlet electron pairs}. These low dimensional patches are hybridized to a backgro…
Perturbation Theory for a Repulsive Hubbard Model in Quasi-One-Dimensional Superconductors
研究了准一维排斥哈伯德模型的对对称性和相变温度。我们用三阶微扰展开法求解了Eliashberg方程，并考虑了在位排斥$U$ .我们发现，当电子数密度从半充满的，过渡到非常规超导预期。当一维性较弱时，自旋单重态是有利的。相比之下，当一维性强且电子数密度远离半填充时，自旋三重态稳定。最后，我们讨论了在$β$ -Na $_{0.33}$ V $_2$ O $_5$中由在位库仑排斥引起的非常规超导电性的可能性。
Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optic phonons decouple from the electron charge. In the resulting vacuum, the residual interactions between quasiparticles are carried by energy fluctuations of the polar medium, resembling the gravitational interactions of a dark matter universe. Here we demonstrate that pairing inevitably emerges from "gravitational'…
The two-dimensional Hubbard model is studied for small values of the interaction strength (U of the order of the hopping amplitude t), using a variational ansatz well suited for this regime. The wave function, a refined Gutzwiller ansatz, has a BCS mean-field state with d-wave symmetry as its reference state. Superconducting order is found for densities n <1 (but not for n=1). This resolves a discrepancy between results obtained with the functional renormalization group, which do predict superconducting order for small values of U, and numerical simulations, which did not find superconductivit…
Recently, Prakash et. al. have discovered bulk superconductivity in single crystals of bismuth, which is a semi metal with extremely low carrier density. At such low density, we argue that conventional electron-phonon coupling is too weak to be responsible for the binding of electrons into Cooper pairs. We study a dynamically screened Coulomb interaction with effective attraction generated on the scale of the collective plasma modes. We model the electronic states in bismuth to include three Dirac pockets with high velocity and one hole pocket with a significantly smaller velocity. We find a w…
A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a general mechanism for spin-triplet superconductivity in multi-band systems, where a non-retarded pairing interaction between conduction electrons is produced by their electronic repulsion to a third-electron undergoing a virtual interband transition. Our theory is analytically controlled by an interband hybridization parameter, and explicitly demonstrated in doped band insulators…
