We study the influence of the repulsive Coulomb interactions on thermodynamic properties of the boson fermion model with an anisotropic (d-wave, and extended s-wave) order parameter. Superconductivity is induced in this model from the anisotropic charge exchange interaction between the conduction band fermions (electrons or holes) and the immobile hard-core bosons (the localized electron pairs). The on-site Coulomb repulsion competes with this pairing interaction and hence is expected to have a detrimental influence on superconductivity. We analyze this effect in some detail considering the two opposite limits of: the weak and strong repulsion. A possible crossover between both these regimes is also discussed.
We study vortex lattices (VLs) in superconducting weak-pinning platelet-like crystals of $β$-Bi$_{2}$Pd in tilted fields with a Scanning Tunneling Microscope. We show that vortices exit the sample perpendicular to the surface and are thus bent beneath the surface. The structure and orientation of tilted VL in the bulk are, for large tilt angles, strongly affected by Coulomb-type intervortex repulsion at the surface due to stray fields.
Within the spin-fermion model for cuprate superconductors, the influence of the intersite Coulomb interactions $V_2$ and $V_2'$ between holes located at the next-nearest-neighbor oxygen ions of CuO$_2$ plane on the implementation of the d_{x^2-y^2}-wave pairing is studied. It is shown that d-wave pairing can be suppressed only for unphysically large values of $V_2$ and $V_2'$.
It is shown that an account for the space separatedness of the two-orbital subsystem of the oxygen holes and the subsystem of the localized spins of copper ions in high-T$_c$ cuprate superconductors leads to the stability of the superconducting $d_{x^2-y^2}$-wave pairing towards the strong Coulomb repulsion between holes located at the nearest oxygen ions. This effect is due to the fact that the Coulomb potential slips out of the equation for the Cooper pairing in the $d_{x^2-y^2}$-wave channel owing to the properties of symmetry.
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 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 t…
We theoretically study ferromagnetic (FM) fluctuations that are experimentally observed in the heavily overdoped region of cuprate superconductors. To explore the origin of FM fluctuations, we evaluate the spin susceptibilities of a single-band Hubbard model within the fluctuation exchange approximation. Model parameters are derived using the Wannierization technique and the constrained random phase approximation method based on the maximally localized Wannier functions. The constrained random phase approximation calculations reveal that the on-site Coulomb interaction decreases with an increa…
The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin-polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO$_2$ plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin-fermion coupling. The investigation of the possibility of implementation superconducting phases with d-wave and s-wave pairing of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-con…
We demonstrate the instability of the normal state of purely repulsive fermionic systems towards the transition to the Kohn-Luttinger superconducting state. We construct the superconducting phase diagrams of these systems in the framework of the Hubbard and Shubin-Vonsovsky models on the square and hexagonal lattices. We show that an account for the long-range Coulomb interactions, as well as the Kohn- Luttinger renormalizations lead to an increase in the critical superconducting temperatures in various materials, such as high-temperature superconductors, idealized monolayer and bilayer of dop…
We study the effect of Coulomb repulsion between oxygen holes on the London penetration depth $λ$ based on the concept of spin-polaron nature of Fermi quasiparticles in cuprates superconductors. It is shown that for the generally accepted values of the parameters of the spin-fermion model, taking into account the Coulomb interaction, both the one-site Hubbard $U_p$ and interaction between the holes on next-nearest-neighbor oxygen ions $V_2$, allows one to achieve a much better agreement of the calculated temperature dependencies of the value $λ^{-2}$ with the experimental data in La$_{2-x}$Sr$…
We study analytically and numerically dynamics and eigenstates of two electrons with Coulomb repulsion on a tight-binding lattice in one and two dimensions. The total energy and momentum of electrons are conserved and we show that for a certain momentum range the dynamics is exactly reduced to an evolution in an effective narrow energy band where the energy conservation forces the two electrons to propagate together through the whole system at moderate or even weak repulsion strength. We argue that such a mechanism of electron pair formation by the repulsive Coulomb interaction is rather gener…
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…
The majority of fulleride superconductors with unusually high transition-temperature to kinetic-energy ratios have a face-centred-cubic (FCC) structure. We demonstrate that, within extended Hubbard models with strong Coulomb repulsion, paired fermions in FCC lattices have qualitatively different properties than pairs in other three-dimensional cubic lattices. Our results show that strongly bound, light, and small pairs can be generated in FCC lattices across a wide range of the parameter space. We estimate that such pairs can Bose condense at high temperatures even if the lattice constant is l…
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 …
The superconducting properties of small metallic grains has been a topic of active research for half a century now. Early experiments demonstrated a remarkable rise in the critical temperature, $T_{c}$, with reducing grain size in a variety of materials. In two dimensional diffusive superconductors, $T_{c}$ is decreased due to enhanced Coulomb repulsion. We propose that in finite size grains, the diffusive enhancement of the Coulomb repulsion is weakened and leads ultimately to an increase in $T_{c}$ in isolated, disordered two dimensional grains. Our mechanism is superimposed on the possible …
We study the effect of interlayer Coulomb interaction in an electronic double layer. Assuming that each of the layers consists of a bipartite lattice, a sufficiently strong interlayer interaction leads to an interlayer pairing of electrons with a staggered order parameter. We show that the correlated pairing state is dual to the excitonic pairing state with uniform order parameter in an electron-hole double layer. The interlayer pairing of electrons leads to strong current-current correlations between the layers. We also analyze the interlayer conductivity and the fluctuations of the order par…
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…
Idealized graphene monolayer is considered neglecting the van der Waals potential of the substrate and the role of the nonmagnetic impurities. The effect of the long-range Coulomb repulsion in an ensemble of Dirac fermions on the formation of the superconducting pairing in a monolayer is studied in the framework of the Kohn-Luttinger mechanism. The electronic structure of graphene is described in the strong coupling Wannier representation on the hexagonal lattice. We use the Shubin-Vonsowsky model which takes into account the intra- and intersite Coulomb repulsions of electrons. The Cooper ins…
Cooper pairing and Coulomb repulsion are antagonists, producing distinct energy gaps in superconductors and Mott insulators. When a superconductor exchanges unpaired electrons with a quantum dot, its gap is populated by a pair of electron-hole symmetric Yu-Shiba-Rusinov excitations between doublet and singlet many-body states. The fate of these excitations in the presence of a strong Coulomb repulsion in the superconductor is unknown, but of importance in applications such as topological superconducting qubits and multi-channel impurity models. Here we couple a quantum dot to a superconducting…
We investigate the superconductivity of 3D Luttinger semimetals, such as YPtBi, where Cooper pairs are constituted of spin-3/2 quasiparticles. Various pairing mechanisms have already been considered for these semimetals, such as from polar phonons modes, and in this work we explore pairing from the screened electron-electron Coulomb repulsion. In these materials, the small Fermi energy and the spin-orbit coupling strongly influence how charge fluctuations can mediate pairing. We find the superconducting critical temperature as a function of doping for an s-wave order parameter, and determine i…
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…
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…
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…
With the discovery of strong coupling physics and superconductivity in Moiré superlattices, it's essential to have an understanding of strong coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here we use density matrix renormalization group (DMRG) to investigate the domininant superconducting channels in the hole-doped…
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…
The influence of antiadiabatic phonons on the temperature of superconducting transition is considered within Eliashberg - McMillan approach in the model of discrete set of (optical) phonon frequencies. A general expression for superconducting transition temperature $T_c$ is proposed, which is valid in situation, when one (or several) of such phonons becomes antiadiabatic. We study the contribution of such phonons into the Coulomb pseudopotential $μ^{\star}$. It is shown, that antiadiabatic phonons do not contribute to Tolmachev's logarithm and its value is determined by partial contributions f…
