A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen-Cooper-Schrieffer theory, on Fröhlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to stabilization of such states in its vicinity and a possibility of their Bose-Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition $T^*$ from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition $T_c$ which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of $T_c$ for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing $T_c$ and producing new room-temperature superconductors are discussed on the basis of the theory suggested.
We show that objections raised by Chakraverty $et$ $al$ (Phys. Rev. Lett. 81, 433 (1998)) to the bipolaron model of superconducting cuprates are the result of an incorrect approximation for the bipolaron energy spectrum and misuse of the bipolaron theory. The consideration, which takes into account the multiband energy structure of bipolarons and the unscreened electron-phonon interaction clearly indicates that cuprates are in the Bose-Einstein condensation regime with mobile charged bosons.
Large-bipolaron superconductivity is plausible with carrier densities well below those of conventional metals. Bipolarons form when carriers self-trap in pairs. Coherently moving large-bipolarons require extremely large ratios of static to optical dielectric-constants. The mutual Coulomb repulsion of a planar large-bipolarons paired carriers drives it to a four-lobed shape. A phonon-mediated attraction among large-bipolarons propels their condensation into a liquid. This liquids excitations move slowly with a huge effective mass. Excitations concomitant weak scattering by phonons produces a mo…
It is shown that the translation-invariant bipolaron theory of superconductivity can explain the dependence of the isotope coefficient in high-temperature superconductors on the critical temperature of a superconducting transition: in the case of strong electron-phonon interaction, the isotope coefficient is low when doping is optimal and high when it is weak. It is demonstrated that in the case of London penetration depth, the absolute value of the isotope coefficient behaves in the opposite way. A conclusion of the great role of non-adiabaticity in the case of weak doping is made. The criter…
We have calculated the tunneling conductance of a superconductor-insulator-superconductor junction based on the polaron-bipolaron theory of superconductivity. The predicted incoherent hump features are in quantitative agreement with tunneling spectra of optimally doped Bi2Sr2CaCu2O8+y and Bi2Sr2Ca2Cu3O10+y. We further show that angle-resolved photoemission spectra of underdoped cuprates are consistent with the Bose-Einstein condensation of inter-site bipolarons and that the superconducting gap symmetry is d-wave, which is determined by the anomalous kinetic process rather than by the pairing i…
Developing a theory of high-temperature superconductivity in copper oxides is one of the outstanding problems in physics. Twenty-five years after its discovery, no consensus on the microscopic theory has been reached despite tremendous theoretical and experimental efforts. Attempts to understand this problem are hindered by the subtle interplay among a few mechanisms and the presence of several nearly degenerate and competing phases in these systems. Here we provide unified parameter-free explanation of the observed oxygen-isotope effects on the critical temperature, the magnetic-field penetra…
The explanation of the nature of superconducting gap in high temperature superconductors (HTSC) is a fundamental task which solution can lead to the understanding of superconducting mechanism. However, it has not been fully solved yet. From the mid of the twentieth century when Bardeen, Cooper and Schrieffer constructed their theory it has been believed that a superconducting gap is a collective phenomenon of electron excitations. In this work it is demonstrated that according to translation-invariant bipolaron theory of HTSC the different types of experiments measure for the gap different val…
Large diameter single-wall boron nanotubes (SWBNT) produced by 2%Mg-mesoporous Al2O3 catalysis show diamagnetic transition at ~ 40 K and ~ 80 K, which is a serious indication for possible superconductivity (J.Phys.Chem.C113, (2009) 17661). Theoretical study which explains or disproves possibility of superconductivity in boron is so far absent, however. Here we apply first-principles formulation of nonadiabatic theory of electron-vibration interactions in study of band structure of boron nanotubes. The ab initio results show that electron-vibration coupling induces in SWBNT with diameter larger…
It is shown that the bipolaron ground state is described by a delocalized wave function. For a two-parameter wave function, the lowest variation estimate of the ground state energy in the strong coupling limit is found to be $E=- 0,414125 α^2$. This is much lower than that derived with the use of the localized bipolaron wave function. The results obtained testify to the possibility of a bipolaron mechanism of high-temperature superconductivity.
A correlation is established between the theories of superconductivity based on the concept of charge density waves (CDW) and the translation invariant (TI) bipolaron theory. It is shown that CDW are originated from TI-bipolaron states in the pseudogap phase due to Kohn anomaly and form a pair density wave (PDW) for wave vectors corresponding to nesting. Emerging in the pseudogap phase, CDW coexist with superconductivity at temperatures below that of superconducting transition while their wave amplitudes decrease as a Bose condensate is formed from TI-bipolarons, vanishing at zero temperature.
Dynamical equations for a polaron and bipolaron in a DNA duplex are obtained on the basis of Holstein-Hubbard Hamiltonian. It is shown that in a PolyA/PolyT duplex especially stable is a bipolaron state in which holes are localized on different chains of the duplex. With the use of the polaron and bipolaron free energy, the temperature of bipolaron decay is found to be T_d \approx 350 K which can serve as an approximate estimate of the superconducting transition temperature. The way of constructing superconducting nanowires on the basis of DNA is suggested.
We show that spontaneous breaking of the translational symmetry (SBTS) of strongly interacting electron and phonon fields acknowledged in lightly doped cuprates to interpret broad bands in their ARPES and optical conductivity spectra influences the carrier distribution function as charge carrier momentum is no longer certain. We develop appropriate distribution and use it to calculate the carrier concentration in different states in essentially doped systems with SBTS. This allows studying doping and temperature evolution of ARPES spectra of such systems. We reveal that at increasing both temp…
Quantum Monte Carlo Simulation of Bipolaron Superconductivity in Extended Hubbard--Holstein models on Face-Centered-Cubic and Body-Centered-Cubic Lattices
Extending the BCS theory towards the strong electron-phonon interaction (EPI), a charged Bose liquid of small bipolarons has been predicted by us with a further prediction that the highest superconducting critical temperature is found in the crossover region of the EPI strength from the BCS-like to bipolaronic superconductivity. Later on we have shown that the unscreened (infinite-range) Froehlich EPI combined with the strong Coulomb repulsion create \emph{superlight} small bipolarons, which are several orders of magnitude lighter than small bipolarons in the Holstein-Hubbard model (HHM) with …
Electron-lattice interactions play a prominent role in quantum materials, making a deeper understanding of direct routes to phonon-mediated high-transition-temperature ($T_{\mathrm{c}}$) superconductivity desirable. However, it has been known for decades that weak electron-phonon coupling gives rise to low values of $T_{\mathrm{c}}$, while strong electron-phonon coupling leads to lattice instability or formation of bipolarons, generally assumed to be detrimental to superconductivity. Thus, the route to high-$T_{\mathrm{c}}$ materials from phonon-mediated mechanisms has heretofore appeared to b…
Polarons originating from phonon displacement modulated hopping have relatively light masses and, thus, are of significant current interest as candidates for bipolaron mechanism of high-temperature superconductivity [Phys. Rev. Lett. {\bf 121}, 247001 (2018)]. We observe that the bond model, when the dominant coupling comes from atomic vibrations on lattice bonds, can be solved by efficient sign-free Monte Carlo methods based on the path-integral formulation of the particle sector in combination with either the (real-space) diagrammatic or Fock-path-integral representation of the phonon sector…
The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron…
Planar large-bipolarons can form if the ratio of the surrounding mediums static to high-frequency dielectric constants is especially large. A large-bipolaron in p-doped La2CuO4 is modeled as two electrons being removed from the out-of-plane orbitals of four oxygen ions circumscribed by four copper ions of a CuO2 layer. These oxygen dianions relax inwardly as they donate electrons to the surrounding outwardly relaxing copper cations. This charge transfer generates the strong in-plane electron-lattice interaction needed to stabilize a large-bipolaron with respect to decomposing into polarons. Th…
The BCS theory has been extended by us to the strong-coupling regime where carriers are small lattice polarons and bipolarons. Here I review the multi-polaron strong-coupling theory of superconductivity. Attractive electron correlations, prerequisite to any superconductivity, are caused by an almost unretarded electron-phonon interaction sufficient to overcome the direct Coulomb repulsion in this regime. Low energy physics is that of small polarons and bipolarons, which are itinerant quasiparticles existing in the Bloch states at temperatures below the characteristic phonon frequency. I identi…
Developing a theory of high-temperature superconductivity in copper oxides is one of the outstanding problems in physics. It is a challenge that has defeated theoretical physicists for more than twenty years. Attempts to understand this problem are hindered by the subtle interplay among a few mechanisms and the presence of several nearly degenerate and competing phases in these systems. Here we present some crucial experiments that place essential constraints on the pairing mechanism of high-temperature superconductivity. The observed unconventional oxygenisotope effects in cuprates have clear…
We report the observation of an exceptionally large room-temperature electrical conductivity in silver and aluminum layers deposited on a lead zirconate titanate (PZT) substrate. The surface resistance of the silver-coated samples also shows a sharp change near 313 K. The results are strongly suggestive of a superconductive interfacial layer, and have been interpreted in the framework of Bose-Einstein condensation of bipolarons as the suggested mechanism for high-temperature superconductivity in cuprates.
We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte-Carlo (CTQMC) algorithm extended to the Coulomb-Frohlich model with two particles. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and bipolaron radius are computed. Lattice bipolarons on such lattices have a novel crablike motion, and are small but very light in a wide range of…
Various mechanisms have been put forward for cuprate superconductivity, which fit largely into two camps: spin-fluctuation and electron-phonon (el-ph) mechanisms. However, in spite of a large effort, electron-phonon interactions are not fully understood away from clearly defined limits. To this end, we use a numerically exact algorithm to simulate the binding of bipolarons. We present the results of a continuous-time quantum Monte-Carlo (CTQMC) algorithm on a tight-binding lattice, for bipolarons with arbitrary interaction range in the presence of strong coulomb repulsion. The algorithm is suf…
Soon after the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 the late Sir Nevill Mott answering his own question "Is there an explanation?" [Nature v 327 (1987) 185] expressed a view that the Bose-Einstein condensation (BEC) of small bipolarons, predicted by us in 1981, could be the one. Several authors then contemplated BEC of real space tightly bound pairs, but with a purely electronic mechanism of pairing rather than with the electron-phonon interaction (EPI). However, a number of other researchers criticized the bipolaron (or any real-spac…
An analytical method of studying strong long-range electron-phonon and Coulomb interactions in complex lattices is presented. The method is applied to a perovskite layer with anisotropic coupling of holes to the vibrations of apical atoms. Depending on the relative strength of the polaronic shift, Ep, and the inter-site Coulomb repulsion, Vc, the system is either a polaronic Fermi liquid, Vc > 1.23 Ep, a bipolaronic superconductor, 1.16 Ep < Vc < 1.23 Ep, or a charge segregated insulator, Vc < 1.16 Ep. In the superconducting window, the carriers are mobile bipolarons with a remarkably low effe…
After a short review of the different physics in the weak and strong coupling regime, resulting in amplitude fluctuation controlled Cooper pair superconductivity and phase fluctuation controlled superfluidity of tightly bound local polaron pairs, we suggest a scenario for the cross-over regime between those two. It is based on the idea of resonating Bipolarons inside a Fermi sea of uncorrelated electrons, similar to the Feshbach resonance in Fermionic gases in optical traps. Due to the competition between amplitude and phase correlations such systems in the cross-over regime can exhibit a supe…
It is widely accepted that phonon-mediated high-temperature superconductivity is impossible at ambient pressure, because of the very large effective masses of polarons/bipolarons at strong electron-phonon coupling. Here we challenge this belief by showing that strongly bound yet very light bipolarons appear for strong Peierls/Su-Schrieffer-Heeger interaction. These bipolarons also exhibit many other unconventional properties, e.g. at strong coupling there are two low-energy bipolaron bands that are stable against strong on-site Hubbard repulsion. Using numerical simulations and analytical argu…
An understanding of high temperature superconductivity clearly requires the nature of its normal state, however the normal state of the cuprates is poorly understood. One possible explanation is the bipolaronic model where mobile, heavily phonon-dressed holes (polarons) are paired in real space. The ground state is made up of intersite singlet bipolarons where excitations can be made to triplet bipolaron and polaron bands. Based on this model I derive the Nernst coefficient and the Thermoelectric power for the cuprates. The Nernst coefficient shows an interesting interference term due to the t…
We use the Density Matrix Renormalization Group method to study a one-dimensional chain with Peierls electron-phonon coupling, which describes the modulation of the electron hopping by lattice distortions. We demonstrate that this system is stable against phase separation in the dilute density limit. We only find phase separation numerically for large couplings for which the linear approximation for the electron-phonon coupling becomes invalid; this behavior can be stabilized in a narrow sliver of the physical parameter space if the dispersion of the phonons is carefully tuned. These results i…
Inspired by the discovery of high temperature superconductivity in potassium-doped $p$-terphenyl, we examine the possibility of superconductivity in $p$-quaterphenyl with one more phenyl ring than $p$-terphenyl. The Meissner effect with critical temperatures ranging from 3.5 K to 120 K is found by the magnetic susceptibility measurements in $p$-quaterphenyl upon doping potassium in the condition of annealing or just pestling. The primary superconducting phase with critical temperature of 7.2 K can be reduplicated in several superconducting samples. In both the annealed and pestled superconduct…
Most of the proposed models of high-temperature superconductivity (HTSC) are based on the short-range electron-electron correlations or/and on a short-range electron-phonon interaction. However, in the cuprates the screening is poor due to a low carrier density, layered crystal structure, and high ionicity of the lattice. We develop further the bipolaron model of HTSC, which explicitly takes into account the long-range origin of all interactions. The long-range electron-phonon (Froehlich) interaction binds carriers into real space pairs (small bipolarons) with surprisingly low mass but suffici…
We introduce a generic Froehlich-Coulomb model of the oxides, which also includes infinite on-site (Hubbard) repulsion, and describe a simple analytical method of solving the multi-polaron problem in complex lattice structures. Two particular lattices, a zig-zag ladder and a perovskite layer, are studied. We find that depending on the relative strength of the Froehlich and Coulomb interactions these systems are either polaronic Fermi (or Luttinger)-liquids, bipolaronic superconductors, or charge segregated insulators. In the superconducting phase the carriers are superlight mobile bipolarons. …
Over the last decade several competing models of high-temperature superconductivity were proposed, most of them with short-range interactions. We review a more realistic model with strong on-site repulsive correlations, the Coulomb and strong finite-range electron-phonon interactions. Bipolarons in the model exist in the itinerant Bloch states at temperatures below about half of the characteristic phonon frequency. Depending on the ratio of the inter-site Coulomb repulsion and the polaron level shift the ground state of the model is a polaronic Fermi (or Luttinger) liquid, bipolaronic high-Tc …
We argue that the extension of the BCS theory to the strong-coupling regime describes the high-temperature superconductivity of cuprates and the colossal magnetoresistance (CMR) of ferromagnetic oxides if the phonon dressing of carriers and strong attractive correlations are taken into account. The long-range Froehlich electron-phonon interaction has been identified as the most essential in cuprates providing "superlight" lattice polarons and bipolarons. Here some kinetic, magnetic, and more recent thermomagnetic normal state measurements are interpreted in the framework of the strong-coupling…
It is discussed some problems of normal states of high temperature superconductors (HTS's) with d-wave pairing and next suppositions: 1) at pseudogap temperature it occurs the dimensional crossover from 3D incoherent normal state to quasi 2D system of Cu O2 layers; 2) "naked holes" are bed quasiparticles for system with Janh-Teller and mixed valent Cu ions, strong electron correlations and fluctuations, and inherent strong p-d hybridization of copper and oxygen orbitals; 3) this leads to reducing of "naked holes" to two types of magneto-elastic polarons. It is shown that one of them, ferromagn…
The intermediate coupling regime in polaronic systems, situated between the adiabatic and the anti-adiabatic limit, is characterized by resonant pairing between quasi-free electrons which is induced by an exchange interaction with localized bipolarons. The onset of this resonant pairing takes place below a characteristic temperature T* and is manifest in the opening of a pseudogap in the density of states of the electrons. The variation of T* is examined here as a function of (i) the typical frequency ω_0 of the local lattice modes, which determines the binding energy of the bipolarons, and (i…
Free energy of a two-liquid system of charge carriers in strongly coupled electron and phonon fields and common nature of three phases in hole-doped cuprates
Structures and parameters of some high and low temperature superconductors (HTSC, LTSC) are considered basing on the alternative estimate of the O2- ion radius magnitude (0.5-0.6) A. Phase transitions into the superconducting state are considered as the Bose-Einstein condensation (BEC). The super HTSC with Tc = 371 K (YBa2Cu3Se7) and TC ~ 400K (Ag2(Ag3Pb2H2O6)) and LTSC with Tc~0.3K (SrNbxTi(1-x)O3) are shown to be of the BEC type. Instability of the structure of the first one results from higher magnitude of the Se2- ion radius in comparison with the O2- radius. The second one forms quasi one…
We discuss the shape resonance in the superconducting gaps of a two band superconductor by tuning the chemical potential at a Lifshitz transition for Femi surface neck collapsing and for spot appearing. The high temperature superconducting scenario for complex matter shows the coexistence of a first BCS condensate made of Cooper pairs in the first band and a second boson-like condensate made of bosons like bipolarons, in the second band where the chemical potential is tuned near a Lifshitz transition. The interband coupling controls the shape resonance in the pair exchange between the two cond…
Recent renewal of the highest transition temperature in a conventional superconductor of the sulfer hydride attracts much attention to exploring simple compounds with the lighter elements, situated in unconventional conditions. We report the discovery of superconductivity in simple oxides of Ti4O7 and g-Ti3O5 in a thin-film form having deliberately tuned epitaxial structures and off-stoichiometry. These higher titanium oxides join in a class of simple-oxide superconductors, and g-Ti3O5 now holds the highest superconducting transition temperature of 7.1 kelvin among them. The mechanism behind t…
Recent advanced Monte Carlo simulations have not found superconductivity and phase separation in the Hubbard model with on-site repulsive electron-electron correlations. We argue that microscopic phase separations in cuprate superconductors and colossal magnetoresistance (CMR) manganites originate from a strong electron-phonon interaction (EPI) combined with unavoidable disorder. Attractive electron correlations, caused by an almost unretarded EPI, are sufficient to overcome the direct inter-site Coulomb repulsion in these charge-transfer Mott-Hubbard insulators, so that low energy physics is …
We derive an effective Hamiltonian for spin polarons forming in weakly doped antiferromagnets and demonstrate that the system becomes superconducting at finite doping. We argue that the driving mechanism which gives rise to superconductivity is lowering of the kinetic energy by formation of mobile antiferromagnetic spin bipolarons. That source of attraction between holes is by definition effective if the antiferromagnetic correlation length is longer than the radius of forming polarons. Notwithstanding that the attraction is strongest in the undoped system with long range order, the supercondu…
It has been recently shown that the competition between unscreened Coulomb and Fröhlich electron-phonon interactions can be described in terms of a short-range spin exchange $J_p$ and an effective on-site interaction $\tilde{U}$ in the framework of the polaronic $t$-$J_p$-$\tilde{U}$ model. This model, that provides an explanation for high temperature superconductivity in terms of Bose-Einstein condensation (BEC) of small and light bipolarons, is now studied as a charged Bose-Fermi mixture. Within this approximation, we show that a gap between bipolaron and unpaired polaron bands results in a …
In this review we examine the experimental evidence for dynamic inhomogeneity, defining the length, time and energy scales of the relevant elementary excitations. The dynamics of the objects below and above Tc are examined in detail with femtosecond spectroscopy and compared with magnetic and other measurements. The dynamically inhomogeneous state is described theoretically by considering an interaction between electrons, spins and the lattice. By symmetry, only electrons in degenerate states can couple to the lattice and spins to give an anisotropic, d-wave symmetry interaction. The proposed …
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…
In the last two decades there have been tremendous attempts to built an adequate theory of high-temperature superconductivity. Most studies (including our efforts) used some model Hamiltonians with input parameters not directly related to the material. The dielectric response function of electrons in strongly correlated high-temperature superconductors is apriori unknown. Hence one has to start with the generic Hamiltonian including unscreened Coulomb and Froehlich electron-phonon interactions operating on the same scale since any ad-hoc assumption on their range and relative magnitude might f…
We study $\mathbb{Z}_2$ topologically ordered states enriched by translational symmetry by employing a recently developed 2D bosonization approach that implements an exact $\mathbb{Z}_2$ charge-flux attachment in the lattice. Such states can display `weak symmetry breaking' of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is `broken' by its anyon quasi-particles, in the sense that its action maps them into a different super-selection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak top…
Taking into account microscopic properties of most usual high-$T_{c}$ superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the two-dimensional square lattice. We establish that these model Hamiltonians can show d-wave paring at the bottom of their spectrum, despite their space isotropy. This phenomenon appear when a "giant electron-phonon anomaly" is present at the boundaries of the Brillouin zone ("half breathing" bond-stretching mode), like in doped cuprates. Our results can be used to derive ef…
A major pathway towards understanding complex systems is given by exactly solvable reference systems that contain the essential physics of the system. For the $t-t'-U$ Hubbard model, the four-site plaquette is known to have a quantum critical point in the $U-μ$ space where states with electron occupations $N=2, 3, 4$ per plaquette are degenerate [Phys. Rev. B {\bf 94}, 125133 (2016)]. We show that such a critical point in the lattice causes an instability in the particle-particle singlet d-wave channel and manifests some of the essential elements of the cuprate superconductivity. For this purp…
