Superconductivity in a disordered metal with Coulomb interactions
Svetlana V. Postolova, Alexey Yu. Mironov, Víctor Barrena, Jose Benito-Llorens, Jose Gabriel Rodrigo, Hermann Suderow, Mikhail R. Baklanov, Tatyana I. Baturina, Valerii M. Vinokur
We study the electronic densities of states (DOS) of strongly disordered superconducting thin films of TiN. We find, using Scanning Tunneling Microscopy (STM) that the DOS decreases towards the Fermi level in the normal phase obtained by applying magnetic fields. The DOS shows spatial fluctuations whose length scale is related to the energy dependent DOS and is similar in normal and superconducting phases. This suggests that Coulomb interactions lead to a spatially varying DOS in the normal phase of a disordered superconductor.
We numerically study the interplay between superconductivity and disorder on the graphene honeycomb lattice with on-site Hubbard attractive interactions U using a spatially inhomogeneous self-consistent Bogoliubov-de Gennes (BdG) approach. In the absence of disorder there are two phases at charge neutrality. Below a critical value Uc for attractive interactions there is a Dirac semimetal phase and above it there is a superconducting phase. We add scalar potential disorder to the system, while remaining at charge neutrality on average. Numerical solution of the BdG equations suggests that while…
Gaplessness was observed in the disordered films of MoC on approaching to the superconductor to insulator transition by reducing the film thickness. The gaplessness is attributed to the enhanced Coulomb interactions due to the loss of screening in the presence of strong disorder in the films.
In the last years ample experimental evidence has shown that charge carriers in high-temperature superconductors are strongly correlated but also coupled with lattice vibrations (phonons), signaling that the true origin of high-Tc superconductivity can only be found in a proper combination of Coulomb and electron-phonon interactions. On this basis, we propose and study a model for high-Tc superconductivity, which accounts for realistic Coulomb repulsion, strong electron-phonon (Fröhlich) interaction and residual on-site (Hubbard \tilde{U}) correlations without any ad-hoc assumptions on their r…
The theory of electron-phonon superconductivity depends on retardation drastically reducing effects of the strong Coulomb repulsion. The standard theory only treats the lowest order diagram, which is an uncontrolled approximation. We study retardation in the Hubbard-Holstein model in a controlled way using perturbation theory and dynamical mean-field theory. We calculate analytically second order results for the pseudopotential $μ^*$ and demonstrate the validity up to intermediate couplings by comparison with non-perturbative results. Retardation effects are still operative, but less efficient…
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 …
In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling $λ$ as well as the Coulomb pseudopotential $μ^*$ are important to determine the transition temperature $T_c$ and other properties. We calculate corrections to the conventional result for the Coulomb pseudopotential. Our calculation are based on the Hubbard-Holstein model, where electron-electron and electron-phonon interactions are local. We develop a perturbation expansion, which accounts for the important renormalization effects for the electrons, the phonons, and the electron-phonon vertex.…
We theoretically study the competition among different electronic phases in molecular conductors $κ$-(BEDT-TTF)$_2$X. The ground-state properties of a 3/4-filled extended Hubbard model with the $κ$-type geometry are investigated by a variational Monte Carlo method. We find various competing phases: dimer-Mott insulator, polar charge-ordered insulator, 3-fold charge-ordered metal, and superconductivity, whose pairing symmetry is an "extended-$s$+$d_{x^2-y^2}$"-wave type. Our results show that the superconducting phase is stabilized not on the verge of the Mott metal-insulator transition but nea…
We use quasiclassical methods of superconductivity to study the superconducting proximity effect from a topological $p$-wave superconductor into a disordered one-dimensional metallic wire. We demonstrate that the corresponding Eilenberger equations with disorder reduce to a closed non-linear equation for the superconducting component of the matrix Green's function. Remarkably, this equation is formally equivalent to a classical mechanical system (i.e., Newton's equations), with the Green function corresponding to a coordinate of a fictitious particle and the coordinate along the wire correspon…
The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. Using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb …
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 nature of superconductivity in monolayer transition metal dichalcogenides is still an object of debate. It has already been argued that repulsive Coulomb interactions, combined with the disjoint Fermi surfaces around the $K$, $K'$ valleys and at the $Γ$ point, can lead to superconducting instabilities in monolayer NbSe$_2$. Here, we demonstrate the two bands nature of superconductivity in NbSe$_2$. It arises from the competition of repulsive long range intravalley and short range intervalley interactions together with Ising spin-orbit coupling. The two distinct superconducting gaps, one fo…
The disorder-induced Superconductor-to-Insulator Transition in amorphous Nb$_{x}$Si$_{1-x}$ two-dimensional thin films is studied for different niobium compositions $x$ through a variation of the sample thickness $d$. We show that the critical thickness $d_c$, separating a superconducting regime from an insulating one, increases strongly with diminishing $x$, thus attaining values of over 100 Å. The corresponding phase diagram in the $(d, x)$ plane is inferred and related to the three-dimensional situation. The two-dimensional Superconductor-to-Insulator Transition well connects with the three…
In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength $|u|$ is larger than some critical value $|u_{c}|$ because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders…
Superconducting instability can occur in three-dimensional quadratic band crossing semimetals only at a finite coupling strength, due to the vanishing of density of states at the quadratic band touching point. Since realistic materials are always disordered to some extent, we study the effect of short-ranged correlated disorder on this superconducting quantum critical point, using a controlled loop-expansion applying dimensional regularization. The renormalization group (RG) scheme allows us to determine the RG flows of the various interaction strengths, and shows that disorder destroys the su…
Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range inter-electron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further …
Recently, in certain flat band lattice systems at commensurate fillings, fractional quantum Hall states have been found -- which have anyonic excitations. We study such systems away from commensuration, i.e. the ground state of an anyon gas in such a system. The presence of the underlying lattice allows access to an entirely new regime where the anyon kinetic energy can be larger than their interaction energy. Within the flux-attachment approach, using mean-field then adding fluctuations, we find several possible superfluid states. Two have intrinsic topological order, i.e. fractionalized quas…
The pair-fluctuation contribution reduces the electrostatic screening length in superconductivity as compared to the normal state. When a conductor possesses a static background charge distribution, superconductivity arises even in the absence of an explicit pairing interaction, such that the Coulomb repulsion is reduced and the total energy is lowered. We demonstrate that the superconducting gap increases with increased background charge at first, after which the mixing of the Higgs and plasma modes suppresses superconductivity in the pseudogap phase. This indicates that the mechanism may be …
We represent the superconducting ceramic compounds by the single band extended Hubbard model. We solve this model for the simultaneous presence of antiferromagnetism and the d-wave superconductivity in the Hartree-Fock (H-F) and in the coherent potential (CP) approximation, which is applied to the on-site Coulomb repulsion U. The hopping interaction used in addition to the Coulomb repulsion causes rapid expansion of the band at carrier concentrations departing from unity. This expansion shifts the d-wave superconductivity away from the half filled point reducing its occupation range approximat…
The influence of weak disorder on the superconductivity in ordinary metals can be formally described by the Abrikosov-Gorkov diagrammatic approach. The vertex correction is ignored in this approach because an inequality $k_F l \gg 1$, where $k_F$ is the Fermi momentum and $l$ mean free path, is satisfied in ordinary metals with a large Fermi surface. In a Dirac semimetal that has discrete Fermi points, this inequality may break down even for arbitrarily weak disorder since $k_F \rightarrow 0$, and thus the vertex correction could be important. We incorporate the vertex correction into the self…
We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density ($n_{el} \rightarrow 0$) on simple cubic (square) lattice. We show that in a realistic strong-coupling case $U\gg V\gg W$ ($U$ and $V$ are the onsite and the intersite Coulomb repulsions, $W$ the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V=0.
Superconductivity in Electron Liquids: Precision Many-Body Treatment of Coulomb Interaction
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Department of Physics, University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校物理系）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Center for Computational Quantum Physics, Flatiron Institute（西蒙斯平顿研究所计算量子物理中心）；Department of Physics, Columbia University（哥伦比亚大学物理系）
Synthesizing a polarizable environment surrounding a low-dimensional metal to generate superconductivity is a simple theoretical idea that still awaits a convincing experimental realization. The challenging requirements are satisfied in a metallic bilayer when the ratio between the Fermi velocities is small and both metals have a similar, low carrier density. In this case, the slower electron gas acts as a retarded polarizable medium (a "dielectric" environment) for the faster metal. Here we show that this concept is naturally optimized for the case of an atomically thin bilayer consisting of …
The topic of superconductivity in strongly disordered materials has attracted a significant attention. In particular vivid debates are related to the subject of intrinsic spatial inhomogeneity responsible for non-BCS relation between the superconducting gap and the pairing potential. Here we report experimental study of electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. We find that conventional models based on phase slip concept provide reasonable fits for the shape of the R(T) transition curve. Temperature dep…
Superconductivity was recently observed in boron-doped ($\sqrt{3}\times\sqrt{3}$)Sn/Si(111). The material can be described by an extended Hubbard model on a triangular lattice. Here, we use the random-phase approximation to investigate the charge and spin fluctuations as well as the superconducting properties of the system with respect to filling and the relative strength of the extended versus the on-site Hubbard interactions. Our calculations reveal that near half-filling and weak extended Hubbard interactions, the superconducting ground state exhibits chiral $d$-wave pairing. Far from half-…
In contrast to conventional s-wave superconductivity, unconventional (e.g. p or d-wave) superconductivity is strongly suppressed even by relatively weak disorder. Upon approaching the superconductor-metal transition, the order parameter amplitude becomes increasingly inhomogeneous leading to effective granularity and a phase ordering transition described by the Mattis model of spin glasses. One consequence of this is that at low enough temperatures, between the clean unconventional superconducting and the diffusive metallic phases, there is necessarily an intermediate superconducting phase whi…
Nonreciprocal transport phenomena have attracted much attention in modern condensed matter physics. In the field of superconductivity, the superconducting diode effect (SDE) has been one of the central topics. Recent theoretical studies for the SDE in intrinsic mechanism revealed the relation between the SDE and helical superconductivity, for which experimental clarification has been awaited. In this work, we establish a microscopic theory of the intrinsic SDE in disordered systems. We show that the sign reversal of the nonreciprocal critical current is suppressed under moderate impurity conce…
We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a disordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological st…
The critical effect of disorder on the two-dimensional (2D) surface superconductor Si(111)-($\sqrt{7}\times\sqrt{3}$)-In is clarified by comparing two regions with different degrees of disorder. Low-temperature scanning tunneling microscopy measurements reveal that superconductivity is retained in the less disordered region, judging from the characteristic differential conductance ($dI/dV$) spectra and from the formation of vortices under magnetic fields. In striking contrast, the absence of those features in the highly disordered region shows that superconductivity is strongly suppressed ther…
The parent compound of an unconventional superconductor must contain unusual correlated electronic and magnetic properties of its own. In the high-Tc potassium intercalated FeSe, there has been significant debate regarding what the exact parent compound is. Our studies unambiguously show that the Fe-vacancy ordered K2Fe4Se5 is the magnetic, Mott insulating parent compound of the superconducting state. Non-superconducting K2Fe4Se5 becomes a superconductor after high temperature annealing, and the overall picture indicates that superconductivity in K2-xFe4+ySe5 originates from the Fe-vacancy ord…
Layered three-dimensional centrosymmetric crystals can exhibit characteristics of noncentrosymmetric materials. This happens when each individual layer alone lacks inversion, but, when combined, inversion symmetry is restored; hence the designation: locally noncentrosymmertic superconductors (LNCSs). In LNCSs, the effects of impurities and subdominant magnetic field induced pairing channels remain unexplored. Using a minimal model, we examine all pairing channels and show that there is always a subdominant superconducting instability that is favored at high magnetic fields, which can substanti…
Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the $T_c$ suppression arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift $δT_c/T_{c0} \sim - 1/k_Fl$…
Monolayer NbSe$_2$ is a nodal topological Ising superconductor at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. Here, we use a combined numerical and group-theoretical approach in real-space to characterize the unconventional superconducting state in monolayer transition metal dichalcogenides. Even with a conventional pairing interaction, the superconducting state is intrinsically parity-mixed and robust against on-site disorder. The interplay between the Zeeman magnetic field, strong spin-orbit interaction, and ele…
