A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusive-like transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function $α^{2}F(ω)$ in comparison with experiments, and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on one hand drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale $ω_{log}$ in the Allen-Dynes formula. As a consequence, the non-monotonicity of $T_{c}$ as a function of alloying (disorder) in $\text{Pb}$-based systems can be rationalized. The case of $\text{Al}$-based systems, where disorder increases $T_{c}$ from the start, is also analyzed. General material-design principles for enhancing $T_{c}$ in amorphous superconductors are presented.
Following our previous investigations on superconductivity in amorphous carbon (aC) based systems; we have prepared thin composite aC-W films using electron-beam induced deposition. The films did not show any sign for superconductivity above 5 K. However, local, non-percolative, superconductivity emerged at Tc = 34.4 K after treatment with sulfur at 250 C for 24 hours. The superconducting features in the magnetization curves were by far sharper compared to our previous results, and the shielding fraction increased by about an order of magnitude. Our data suggest that pairing and localized supe…
Structural and superconducting transitions of layered van der Waals (vdW) hydrogenated germanene (GeH) were observed under high-pressure compression and decompression processes. GeH possesses a superconducting transition at critical temperature (Tc) of 5.41 K at 8.39 GPa. A crystalline to amorphous transition occurs at 16.80 GPa while superconductivity remains. An abnormally increased Tc up to 6.1 K has been observed in the decompression process while the GeH remained amorphous. Thorough in-situ high-pressure synchrotron X-ray diffraction and in-situ high-pressure Raman spectroscopy with the d…
Topological states of matter support quantized nondissipative responses and exotic quantum particles that cannot be accessed in common materials. The exceptional properties and application potential of topological materials have triggered a large-scale search for new realizations. Breaking away from the popular trend focusing almost exclusively on crystalline symmetries, we introduce the Shiba glass as a platform for amorphous topological quantum matter. This system consists of an ensemble of randomly distributed magnetic atoms on a superconducting surface. The collection of magnetic moments g…
We report the growth, characterization and superconducting properties of a new amorphous superconductor, RexZr ( x ~ 6 ), in thin film form. Films were grown by pulsed laser deposition with the substrate kept at room temperature. Films with thickness larger than 40 nm showed a superconducting transition temperature (Tc) of 5.9 K. Superconducting properties were measured for films with varying thickness from 120 to 3 nm. The normal state resistance scales linearly with inverse of thickness. The transition temperature, critical field, coherence length, penetration depth and superconducting energ…
In general, conventional superconductivity and magnetism are competing phenomena. In some alloys this competition is a function of the concentration of the elements. Here we show that in the palladium alloys Pd$_{1-c}$(H/D/T)$_{c}$ (Pd-ides) the increase in the concentration $c$ of the ides: hydrogen, deuterium, tritium (H/D/T), lowers the predicted magnetism of amorphous palladium ($a$-Pd) gradually, allowing superconductivity to appear for $ c \approx 40\%$. This magnetism explains why superconductivity does not manifest for smaller values of $c$ ($c \leq 40\%$) in these Pd alloys. Also, the…
(abridged) We present results of the disorder-induced metal-insulator-transition (MIT) in three-dimensional amorphous indium-oxide films. The amorphous version studied here differs from the one reported earlier [PRB 46, 10917 (1992)] in that it has a much lower carrier concentration. As a measure of the static disorder we use the dimensionless parameter kFl. Thermal annealing is employed as the experimental handle to tune the disorder. On the metallic side of the transition, the low temperature transport exhibits weak-localization and electron-electron correlation effects characteristic of dis…
The interplay between disorder and interactions can dramatically influence the physical properties of thin-film superconductors. In the most extreme case, strong disorder is able to suppress superconductivity as an insulating phase emerges. Due to the known pair-breaking potential of magnetic disorder on superconductors, the research focus is on the influence of non-magnetic disorder. Here we provide direct evidence that magnetic disorder is also present at the surface of amorphous superconducting films. This magnetic disorder is present even in the absence of magnetic impurity atoms and is in…
We discuss the destruction of superconductivity in quasi-one-dimensional systems due to the interplay between disorder and Coulomb repulsion. We argue that to understand the behavior of the system one has to study both fermionic and bosonic mechanisms of suppression of superconductivity. The former describes reduction in the mean field critical temperature $T_c$, while the latter refers to thermal and quantum fluctuations in the order parameter. A change in parameters such as wire width and disorder strength significantly affects both mechanisms.
The phonon spectra of solids, described through the measurable vibrational density of states (VDOS), provide a wealth of information about the underlying atomic structure and bonding, and they determine fundamental macroscopic properties such as specific heat, thermal conductivity and superconductivity. In amorphous solids, structural disorder generates a number of poorly understood phenomena that are absent in crystals. Starting from an effective field theory description which accounts for disorder in terms of momentum diffusion, we provide a unified theoretical description of the VDOS of amo…
We introduce a model describing vortices in strongly disordered three-dimensional superconductors. The model focuses on the topological defects, i.e., dislocation lines, in an elastic description of the vortex lattice. The model is studied using Monte Carlo simulations, revealing a glass phase at low temperatures, separated by a continuous phase transition to the high temperature resistive vortex liquid phase. The critical exponents nu ~ 1.3 and eta ~ -0.4 characterizing the transition are obtained from finite size scaling.
In contact with a superconductor, a normal metal modifies its properties due to Andreev reflection. In the current work, the local density of states (LDOS) of superconductor - normal metal Mo$_{78}$Ge$_{22}$ - Au bilayers are studied by means of STM applied from the Au side. Three bilayers have been prepared on silicate glass substrate consisting of 100, 10 and 5 nm MoGe thin films covered always by 5 nm Au layer. The tunneling spectra were measured at temperatures from 0.5 K to 7 K. The two-dimensional cross-correlation between topography and normalized zero-bias conductance (ZBC) indicates a…
We present resistivity, magnetization and specific heat measurements on flux grown single crystals of NiBi3. We find typical behavior of a type-II superconductor, with, however, a sizable magnetic signal in the superconducting phase. There is a hysteretic magnetization characteristic of a ferromagnetic compound. By following the magnetization as a function of temperature, we find a drop at temperatures corresponding to the Curie temperature of ferromagnetic amorphous Ni. Thus, we assign the magnetism in NiBi$_3$ crystals to amorphous Ni impurities.
Bismuth displays puzzling superconducting properties. In its crystalline equilibrium phase, it does not seem to superconduct at accessible low temperatures. However, in the amorphous phase it displays superconductivity at ~ 6 K. Under pressure bismuth has been found to superconduct at Tcs that go from 3.9 K to 8.5 K depending on the phase obtained. So the question is: what electronic or vibrational changes occur that explains this radical transformation in the conducting behavior of this material? In a recent publication we argue that changes in the density of electronic and vibrational states…
Traces of superconductivity (SC) at elevated temperatures (up to 65 K) were observed by magnetic measurements in three different inhomogeneous sulfur doped amorphous carbon (a-C) systems: (a) in commercial and (b) synthesized powders and (c) in a-C thin films. (a) Studies performed on commercial (a-C) powder which contains 0.21% of sulfur, revealed traces of non-percolated superconducting phases below Tc = 65 K. The SC volume fraction is enhanced by the sulfur doping. (b) a-C powder obtained by pyrolytic decomposition of sucrose did not show any sign for SC above 5 K. This powder was mixed wit…
We studied the effect of magnetic doping with Gd atoms on the superconducting properties of amorphous Mo70Ge30 films. We observed that in uniform films deposited on amorphous Ge, the pair-breaking strength per impurity strongly decreases with film thickness initially and saturates at a finite value in films with thickness below the spin-orbit scattering length. The variation is likely caused by surface induced magnetic anisotropy and is consistent with the fermionic mechanism of superconductivity suppression. In thin films deposited on SiN the pair-breaking strength becomes zero. Possible reas…
High-entropy alloys are made from random mixtures of principal elements on simple lattices, stabilized by a high mixing entropy. The recently discovered BCC Ta-Nb-Hf-Zr-Ti high entropy alloy superconductor appears to display properties of both simple crystalline intermetallics and amorphous materials, e.g. it has a well defined superconducting transition along with an exceptional robustness against disorder. Here we show that the valence-electron count dependence of the superconducting transition temperature in the high entropy alloy falls between those of analogous simple solid solutions and …
In superconductivity, electrons exhibit unique macroscopic collective quantum behavior that is the key for many modern quantum technologies. This electron behavior stems vastly from coupling to a correlated motion of atoms in the material, as well as from synchronized directional movement that screens external magnetic fields perfectly. Hence, the inter-atomic distance and material geometry are expected to affect fundamental superconductive characteristics. These parameters are tunable with strain, but strain application is hindered by the rigidity of superconductors, which in turn increases a…
We have studied the magnetic-field-tuned superconductivity destroying quantum transition in amorphous In-O films with the onset of superconductivity in zero field at about 2 K. At temperatures down to 30 mK the critical resistance R_c=R(T,B_c) has been found to change approximately linearly with temperature, which is in contradiction to a standard description where zero slope dR_c/dT = 0 is assumed near T=0. To make the data R(T,B) collapse in the vicinity of transition against scaling variable (B-B_c)/T^{1/y}, one has either to allow for the intrinsic temperature dependence of R_c or to postu…
We present results on disordered amorphous films which are expected to undergo a field-tuned Superconductor-Insulator Transition. Based on low-field data and I-V characteristics, we find evidence of a low temperature Metal-to-Superconductor transition. This transition is characterized by hysteretic magnetoresistance and discontinuities in the I-V curves. The metallic phase just above the transition is different from the "Fermi Metal" before superconductivity sets in.
Current-voltage characteristics in the insulator bordering superconductivity in disordered thin films exhibit current jumps of several orders of magnitude due to the development of a thermally bistable electronic state at very low temperatures. In this high-resolution study we find that the jumps can be composed of many (up to 100) smaller jumps that appear to be random. This indicates that inhomogeneity develops near the transition to the insulator and that the current breakdown proceed via percolative paths spanning from one electrode to the other.
MgB2 thin films were cold-grown on sapphire substrates by pulsed laser deposition (PLD), followed by post-annealing in mixed, reducing gas, Mg-rich, Zr gettered, environments. The films had Tcs in the range 29 K to 34 K, Jcs (20K, H=0) in the range 30 kA/cm2 to 300 kA/cm2, and irreversibility fields at 20 K of 4 T to 6.2 T. An inverse correlation was found between Tc and irreversibility field. The films had grain sizes of 0.1-1 micron and a strong biaxial alignment was observed in the 950C annealed film.
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…
Kagome lattice systems have been proposed to host rich physics, which provide an excellent platform to explore unusual quantum states. Here, we report on the discovery of superconductivity in van der Waals material Pd3P2S8 under pressure. The superconductivity is observed in Pd3P2S8 for those pressures where the temperature dependence of the resistivity changes from a semiconducting-like behavior to that of a normal metal. The superconducting transition temperature Tc increases with applied pressure and reaches ~ 6.83 K at 79.5 GPa. Combining high-pressure XRD, Raman spectroscopy and theoretic…
We briefly review earlier and report original experimental results in the context of metastable or possible superconducting materials. We show that applied electric field induces conducting state in Copper Chloride (CuCl) whose characteristics resemble behavior of sliding charge-density-wave(s) (CDW). We discuss whether the sliding CDW or collective transport of similar ordered charge phase(s) may account for the problem of "high-temperature superconductivity" observed in this and other materials, including Cadmium Sulfide (CdS), metal-ammonia solutions, polymers, amorphous carbon and tungsten…
High temperature superconductivity in doped Mott insulators such as the cuprates contradicts the conventional wisdom that electron repulsion is detrimental to superconductivity. Because doped fullerene conductors are also strongly correlated, the recent discovery of high-critical-temperature, presumably s-wave, superconductivity in C$_{60}$ field effect devices is even more puzzling. We examine a dynamical-mean-field solution of a model for electron doped fullerenes which shows how strong correlations can indeed enhance superconductivity close to the Mott transition. We argue that the mechanis…
The intimate connection between antiferromagnetism and superconductivity is at the core of high-temperature superconductivity. Here, we put forward the projected BCS theory for the unification of antiferromagnetism at half filling and strongly correlated superconductivity at moderate doping. Specifically, it is shown that the projected BCS theory provides excellent trial states for the exact ground states of the $t$-$J$ model in the square lattice, generating the unified phase diagram as a continuous function of hole concentration. Precisely capturing antiferromagnetism at half filling, which …
We consider a strongly spin-orbit-coupled metal, one of whose Fermi surfaces is close to a Lifshitz (topological) transition. Via a renormalization group analysis of the square-lattice Hubbard model with strong Rashba spin-orbit coupling, we show that such a metal is generically unstable to the formation of mixed-parity superconductivity with a helical triplet component.
Specific heat studies of CeRhIn5 as functions of pressure and magnetic field have been used to explore the relationship between magnetism and unconventional superconductivity, both of which involve the 4f electron of Ce. Results of these studies cannot be understood as a simple competition for Fermi-surface states and require a new conceptual framework.
We study the spin-fluctuation-mediated $s\pm$-wave superconductivity in the bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the two-leg ladder model with diagonal hoppings, studied previously by the present authors, superconductivity is strongly enhanced when one of the bands lies just below (or touches) the Fermi level, that is, when the band is incipient. The strong enhancement of superconductivity is because large weight of the spin fluctuations lies in an appropriate energy range, whereas the low energy, pair-breaking spin fluctuations are suppressed. The optimi…
Heterostructures containing strongly correlated electron systems provide a platform to clarify interplay of electron correlation and Rashba spin-orbit coupling in unconventional superconductors. Motivated by recent fabrication of artificially-engineered heavy fermion superlattices and high-temperature cuprate superconductors, we conduct a thorough study on superconductivity in Rashba-Hubbard model. In contrast to previous weak coupling approaches, we employ fluctuation-exchange approximation to describe quantum critical magnetic fluctuations and resulting superconductivity. As a result, robust…
We discuss a physical mechanism of a non-BCS nature which can stabilize a superconducting state in a {\it strongly repulsive} electronic system. By considering the two-dimensional Hubbard model with spatially modulated electron hoppings, we demonstrate how kinetic-energy frustration can lead to robust d-wave superconductivity at {\it arbitrarily} large on-site repulsion. This phenomenon should be observable in experiments using fermionic atoms, e.g. ${}^{40}K$, in specially prepared optical lattices.
This is a "perspective" inspired by the forthcoming article, "What makes the $T_c$ of monolayer FeSe on SrTiO so high: a sign-problem free quantum Monte Carlo study," by Z-X. Li, F. Wang, H. Yao, and D-H. Lee, arXiv:1512.06179.
We review recent studies for superconductivity using diagrammatic extensions of dynamical mean field theory. These approaches take into account simultaneously both, the local correlation effect and spatial long-range fluctuations, which are essential to describe unconventional superconductivity in a quasi-two-dimensional plane. The results reproduce and predict the experimental phase diagrams of strongly correlated system such as cuprates and nickelates. Further studies reveal that the dynamical screening effect of the pairing interaction vertex has dramatic consequences for the transition tem…
We report an unusual persistence of superconductivity against high magnetic fields in the iron chalcogenide film FeTe:O$_{x}$ below ~ 2.5 K. Instead of saturating like a mean-field behavior with a single order parameter, the measured low-temperature upper critical field increases progressively, suggesting a large supply of superconducting states accessible via magnetic field or low-energy thermal fluctuations. We demonstrate that superconducting states of finite momenta can be realized within the conventional theory, despite its questionable applicability. Our findings reveal a fundamental cha…
The existence of topological superconductors preserving time-reversal symmetry was recently predicted, and they are expected to provide a solid-state realization of itinerant massless Majorana fermions and a route to topological quantum computation. Their first concrete example, CuxBi2Se3, was discovered last year, but the search for new materials has so far been hindered by the lack of guiding principle. Here, we report point-contact spectroscopy experiments showing that the low-carrier-density superconductor Sn_{1-x}In_{x}Te is accompanied with surface Andreev bound states which, with the he…
On the basis of the recently proposed self-consistent theory of metal- insulator transition in strongly disordered systems, taking into account interaction effects, we study transition temperature $T_{c}$ suppression in disordered superconductors for the wide disorder interval --- from weakly disordered metal up to Anderson insulator, induced by "Coulomb pseudogap" formation in the density of states. It is shown that for a number of systems this theory provides rather satisfactory fit of experimental data.
In the correlated electron system with the pseudogap, there are full-gapped domains and Fermi-arced domains coexisting. Those domains are created by the quantum-fluctuated antiferromagnetic fluctuations that generate the short-ranged attractive potential to produce the Fermi arcs and the superconductivity. In the full-gapped domains, s-wave or (d_{x^2-y^2}\pm id_{xy})-wave symmetry of the electron pairs is favored. In the Fermi-arced domains, only d_{x^2-y^2}-wave symmetry of pairs is stable. Superconductivity of different pairing symmetry coexists in different domains, as well. Different from…
In a recent X-ray absorption study in boron doped diamond, Nakamura et al. have seen a well isolated narrow boron impurity band in non-superconducting samples and an additional narrow band at the chemical potential in a superconducting sample. We interpret the beautiful spectra as evidence for upper Hubbard band of a Mott insulating impurity band and an additional metallic `mid-gap band' of a conducting `self-doped' Mott insulator. This supports the basic framework of a recent theory of the present author of strongly correlated impurity band superconductivity (SCIBS) in a template of a wide-ga…
We present a novel route for attaining unconventional superconductivity (SC) in a strongly correlated system without doping. In a simple model of a correlated band insulator (BI) at half-filling we demonstrate, based on a generalization of the projected wavefunctions method, that SC emerges when e-e interactions and the bare band-gap are both much larger than the kinetic energy, provided the system has sufficient frustration against the magnetic order. As the interactions are tuned, SC appears sandwiched between the correlated BI followed by a paramagnetic metal on one side, and a ferrimagneti…
Disproportionation in 3d compounds can give rise to an unconventional electron-hole Bose liquid with a very rich phase diagram from a Bose metal, charge ordering insulator to an inhomogeneous Bose superfluid. Optimal conditions for the disproportionation driven high-T_c superconductivity are shown to realize only for several Jahn-Teller d^n configurations that permit the formation of well defined local composite bosons. These are the high-spin d^4, low-spin d^7, and d^9 configurations given the octahedral crystal field, and the d^1, high-spin d^6 configurations given the tetrahedral crystal fi…
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…
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id'-type mediated by the antiferromagnetic exchange is found. The superconducting Tc as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange …
Unconventional superconductivity (SC) is said to occur when Cooper pair formation is dominated by repulsive electron-electron interactions, so that the symmetry of the pair wavefunction is other than isotropic s-wave. The strong, on-site, repulsive electron-electron interactions that are the proximate cause of such superconductivity are more typically drivers of commensurate magnetism. Indeed, it is the suppression of commensurate antiferromagnetism (AF) that usually allows this type of unconventional superconductivity to emerge. Importantly, however, intervening between these AF and SC phases…
In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivi…
Confirmation of the phononic origin of Cooper pair formation in superconductors came with the demonstration that the interaction was retarded and that the corresponding energy scales were associated with phonons. Using cellular dynamical mean-field theory for the two-dimensional Hubbard model, we identify such retardation effects in d-wave pairing and associate the corresponding energy scales with short-range spin fluctuations. We find which frequencies are relevant for pairing as a function of interaction strength and doping and show that the disappearance of superconductivity on the overdope…
A new organic superconductor, possibly with formula $K_3$ p-terphenyl, has been discovered by Wang, Gao, Huang and Chen, reaching a very high $T_c$ of about 120~K. Besides a clear diamagnetic signal, most other details such as stoichiometry and structure are yet unknown. However, pristine p-terphenyl has a familiar $P2_1/a$ staggered bimolecular structure, and it can be reasonably assumed that a similar bimolecular structure could be retained by hypothetical $K_3$ p-terphenyl. We point out that the resulting 2-narrow band metal would support the same $s_{\pm}$ superconductivity recently propos…
We extend the rotationally invariant formulation of the slave-boson method to superconducting states. This generalization, building on the recent work by Lechermann et al. [Phys. Rev. B {\bf 76}, 155102 (2007)], allows to study superconductivity in strongly correlated systems. We apply the formalism to a specific case of strongly correlated superconductivity, as that found in a multi-orbital Hubbard model for alkali-doped fullerides, where the superconducting pairing has phonic origin, yet it has been shown to be favored by strong correlation owing to the symmetry of the interaction. The metho…
MgB$(p^{n_σ}p^{n_π})_{2}$ is classified as a system with strongly interacting $σ$-electrons and non-correlated $π$-electrons of boron ions. The kinematic and Coulomb interaction V between the orbitally degenerated $σ$-electrons provide the superconducting state with an anisotropic gap of s*-wave symmetry. The critical temperature $T_c$ has a non-monotonic dependence on the distance r between the centers of gravity of $σ$- and $π$-bands. MgB$_2$ corresponds to r=0.085 eV and V=0.45 eV in our model with flat bands. The derived superconducting density of electronic states is in good agreement wit…
We use a Luttinger-Ward functional approach to study the problem of phonon-mediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams for the EEI and the resulting theory is therefore nonperturbative in the strength of the latter. We show that one of the building blocks of the theory is the irreducible six-leg vertex related to EEIs. Diagrammatically, this implies five contributions (one of the Fock and four of the Hartree type) to the electronic self-energy, which, to the best of our knowl…
We present a lattice field theory of spins coupled to Dirac fermions, as a model for the doped copper oxide compounds. Both the fermionic and spin degrees of freedom are treated dynamically. The influence of the charge carriers on the magnetic ordering follows automatically. The magnetic phase diagram at zero temperature is studied numerically and with Mean-Field methods. The Hybrid Monte Carlo algorithm is adapted to the O(3) non-linear sigma model constraint. The charged excitations in the various phases are studied at the Mean-Field level. Bound states of two charged fermions are found in a…
