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 identify the long-range Froehlich electron-phonon interaction with c-axis polarised optical phonons as the most essential for pairing in superconducting cuprates. A number of key observations have been predicted or explained with polarons and bipolarons including unusual isotope effects and upper critical fields, normal state (pseudo)gaps, kinetic properties and diamagnetism, and giant proximity effects. These and some other observations provide strong evidence for a novel state of electronic matter in layered cuprates, which is a charged Bose-liquid of small mobile bipolarons.
The single bipolaron problem is examined in the context of the 1D Holstein-Hubbard model, emphasizing analogies and differences with respect to the complementary single polaron physics. The bipolaron band structure below the phonon threshold is revealed, showing a complex relationship between numerous excited bands as the adiabatic limit is approached. Light bipolarons with significant binding energy, the stability of large bipolarons, the small to large bipolaron crossover as a function of the Hubbard repulsion, as well as the bipolaron dissociation, are investigated in detail, disentangling …
The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined…
We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion, U, and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large U at intermediate and large…
A Lorentz invariant version of a mass-gap graphene-like planar quantum electrodynamics, the parity-preserving $U(1)\times U(1)$ massive QED$_3$, exhibits attractive interaction in low-energy electron-polaron--electron-polaron $s$-wave scattering, favoring quasiparticles bound states, the $s$-wave bipolarons.
It is remarkable how the Froehlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article …
Superconductivity is a fascinating example of how "more is different". It is due to electrons binding into bosonic Cooper pairs, which exhibit coherent behavior across a macroscopic sample. Finding the mechanism responsible for this binding is one of the more difficult tasks of condensed matter physics. For conventional superconductors the solution was given by the BCS theory as being due to exchange of phonons. For the cuprate high-Tc superconductors a widely-accepted explanation is still missing despite intense effort. The recently discovered Fe-based high-Tc superconductors pose now a new c…
Strong electron-phonon interaction in cuprates has gathered support over the last decade in a number of experiments. While phonons remain almost unrenormalised, electrons are transformed into itinerent bipolarons and thermally excited polarons when the electron-phonon interaction is strong. We calculate the Lorenz number of the system to show that the Wiedemann-Franz law breaks down because of the interference of polaron and bipolaron contributions in the heat flow. The model fits numerically the experimental Hall Lorenz number, which provides a direct evidence for bipolarons in the cuprates.
Bismuth perovskites ABiO$_3$ (A = Sr, Ba) host a variety of peculiar phenomena including bond-disproportionated insulating phases and high-temperature superconductivity upon hole doping. While the mechanisms underlying these phenomena are still debated, off-diagonal electron-phonon ($e$-ph) coupling originating from the modulation of the orbital overlaps has emerged as a promising candidate. Here, we employ classical Monte Carlo simulations to study a semiclassical three-orbital model with off-diagonal $e$-ph interactions. We demonstrate the existence of a (bi)polaron correlations that persist…
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…
The bound states of two electrons in the adiabatic Holstein-Hubbard model are studied numerically in one and two dimensions from the anticontinuous limit. This model involves a competition between a local electron-phonon coupling (with a classical lattice) which tends to form pairs of electrons and the repulsive Hubbard interaction $U \geq 0$ which tends to break them. In 1D, the ground-state always consists in a pair of localized polarons in a singlet state. They are located at the same site for U=0. Increasing U, there is a first order transition at which the bipolaron becomes a spin singlet…
The possibility of formation of a new type of polaron based on the quantum aniferromagnet (AF) model is reported. We take into account exchange interactions between localized d-d spins of the AF, as well as the p-d interaction of the AF with p-carriers. The energy minimum is found when maximum charge density occurs on every second spin. The formation of such ``comb''-like polarons results from the damping of quantum fluctuations and the appearance of Van Vleck-like staggered magnetization. Such polarons tend to form pairs coupled by an AF ``glue''.
We report analytical and numerical results on the two-particle states of the polaronic t-Jp model derived recently with realistic Coulomb and electron-phonon (Frohlich) interactions in doped polar insulators. Eigenstates and eigenvalues are calculated for two different geometries. Our results show that the ground state is a bipolaronic singlet, made up of two polarons. The bipolaron size increases with increasing ratio of the polaron hopping integral t to the exchange interaction Jp but remains small compared to the system size in the whole range 0<t/Jp<1. Furthermore, the model exhibits a pha…
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 …
he formation of the optical polaron and bipolaron in two-dimensional (2D) systems are studied in the intermediate electron-phonon coupling regime. The total energies of 2D polaron and bipolaron are calculated by using the Buimistrov-Pekar method of canonical transformations and analyzed in the weak, intermediate and strong coupling regimes. It is shown that the electron-phonon correlation significantly reduces the total energy of 2D polaron in comparison with the energy of the strong-coupling (adiabatic) polaron. A charge carrier in polar crystals remains localized in a 2D potential well when …
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 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…
We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram, where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), w…
Bipolaron energies are calculated as a function of wave vector by a variational method of Gurari appropriate for weak or intermediate coupling strengths, for a model with electron-phonon interactions independent of phonon wave vectors and a short-ranged Coulomb repulsion. It is assumed that the bare electrons have a constant effective mass. A two-parameter trial function is taken for the relative motion of the two electrons in the bipolaron. Energies of bipolarons are compared with those of two single polarons as a function of wave vector for various parameter values. Results for effective mas…
The properties of a Bose gas of translation-invariant (TI) bipolarons analogous to Cooper pairs are considered. As in the BCS theory, the description of a TI-bipolaron gas is based on the electron-phonon interaction and Froehlich Hamiltonian. As distinct from the BCS theory, when the correlation length greatly exceeds the mean distance between the pairs, here we deal with the opposite case when the correlation length is much less than the distance between the pairs. We calculate the critical temperature of the transition of a TI-bipolaron Bose-gas into the superconducting state, its energy, he…
A large polaron is a quasiparticle that consists of a nearly free electron interacting with the phonons of a material, whose lattice parameters are much smaller than the polaron scale. The electron-phonon interaction also leads to an attractive interaction between electrons, which can allow two polarons to pair up and form a bipolaron. It has been shown that large bipolarons can form in theory due to strong 1-electron-1-phonon coupling, but they have not been seen in real materials because the critical value of the required electron-phonon interaction is too large. Here, we investigate the eff…
We present details of a continuous-time quantum Monte-Carlo algorithm for the screened Hubbard-Froehlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Froehlich bipolarons and we compare the properties of bipolaro…
Here we consider an interacting electron-phonon system within the framework of extended Holstein-Hubbard model at strong enough electron-phonon interaction limit in which (bi)polarons are the essential quasiparticles of the system. It is assumed that the electron-phonon interaction is screened and its potential has Yukawa-type analytical form. An effect of screening of the electron-phonon interaction on the temperature of Bose-Einstein condensation of the intersite bipolarons is studied for the first time. It is revealed that the temperature of Bose-Einstein condensation of intersite bipolaron…
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…
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…
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…
There is a growing understanding that transport properties of complex oxides and individual molecules are dominated by polaron physics. In superconducting oxides the long-range Froehlich and short-range Jahn-Teller electron-phonon interactions bind carriers into real space pairs - small bipolarons with surprisingly low mass but sufficient binding energy, while the long-range Coulomb repulsion keeps bipolarons apart preventing their clustering. The bipolaron theory numerically explains high Tc values without any fitting parameters and describes other key features of the cuprates. The same appro…
With the superconducting cuprates in mind, a set of unitary transformations was used to decouple electrons and phonons in the strong-coupling limit. While phonons remain almost unrenormalised, electrons are transformed into itinerent singlet and triplet bipolarons and thermally excited polarons. The triplet/singlet exchange energy and the binding energy of the bipolarons are thought to account for the spin and charge pseudogaps in the cuprates, respectively. We calculated the Hall Lorenz number of the system to show that the Wiedemann-Franz law breaks down due to the interference of the polaro…
The seminal work by Bardeen, Cooper and Schrieffer taken further by Eliashberg to the intermediate coupling solved the problem of conventional superconductors about half a century ago. The Froehlich and Jahn-Teller electron-phonon interactions were identified as an essential piece of physics in all novel superconductors. The BCS theory provides a qualitatively correct description of some of them like magnesium diborade and doped fullerenes (if the polaron formation is taken into account). However, cuprates remain a problem. Here I show that the bipolaron extension of the BCS theory to the stro…
The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction $\upsilon \geq 0$, which tends to break them, generates many different ground-states. There are four domains in the $g,\upsilon$ phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electro…
It is shown that the bipolaron theory of Cooper pairs suggests that there is a possibility for a superconducting phase to exist at low and high levels of doping and be absent at intermediate level of doping. The results obtained imply possibly universal character of 1/8 anomaly.
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…
There is strong experimental evidence for pairing of polaronic carriers in the normal state, two distinct energy scales, d-wave superconducting order parameter,and charge segregation in the form of stripes in several cuprates.All these remarkable phenomena might be unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Extending the BCS theory towards an intermediate and strong-coupling regime we show that there are two energy scales in this regime, a temperature independent incoherent gap and…
Persistent current generation by small polarons embedded in a spin-density wave background in a two dimensional lattice is theoretically studied. When the embedded small polarons become cores of merons and antimerons (vortices in spin configuration with winding numbers +1 and -1, respectively), a spin Berry phase arises from the spiral spin texture of the merons and antimerons, and generates a spin current around the polarons. Electric current is, however, absent due to the exact cancellation of the up- and down-spin electron currents. By addition of an imaginary magnetic flux that negates the…
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…
Consideration is given to thermodynamical properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons). The critical temperature of transition, energy, heat capacity and the transition heat of TI-bipolaron gas are calculated. The results obtained are used to explain experiments on high-temperature superconductors.
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…
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 …
Electrons coupled to local lattice deformations end up in selftrapped localized molecular states involving their binding into bipolarons when the coupling is stronger than a certain critical value. Below that value they exist as essentially itinerant electrons. We propose that the abrupt crossover between the two regimes can be described by resonant pairing similar to the Feshbach resonance in binary atomic collision processes. Given the intrinsically local nature of the exchange of pairs of itinerant electrons and localized bipolarons, we demonstrate the occurrence of such a resonance on a fi…
Consideration is given to thermodynamical properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons) in magnetic field. The critical temperature of transition, critical magnetic fields, energy, heat capacity and the transition heat of TI-bipolaron gas are calculated. Such values as maximum magnetic field, London penetration depth and their temperature dependencies are calculated. The results obtained are used to explain experiments on high-temperature superconductors.
Materials containing high densities of exceptionally displaceable ions (e.g. perovskites) have extremely large ratios of their static to high-frequency dielectric constants, > 2. Large polarons form in such materials as their electronic charge carriers self-trap by displacing surrounding ions. Large polarons are very heavy-massed slow-moving quasi-particles that are very weakly scattered by ambient phonons. Large-polaron mobilities, e.g. 1 cm2/V-sec at 300 K, are much smaller than the minimum possible for conventional electronic charge carriers. The minimum mobility for an itinerant charge car…
We study the Coulomb-Fröhlich model on a triangular lattice, looking in particular at states with angular momentum. We examine a simplified model of crab bipolarons with angular momentum by projecting onto the low energy subspace of the Coulomb-Fröhlich model with large phonon frequency. Such a projection is consistent with large long-range electron-phonon coupling and large repulsive Hubbard $U$. Significant differences are found between the band structure of singlet and triplet states: The triplet state (which has a flat band) is found to be significantly heavier than the singlet state (whic…
Polarons are composite quasiparticles comprising electronic charge carriers taken together with the alterations they induce in surrounding condensed matter. Strong-coupling polarons form when electronic charge carriers become self-trapped: bound within potential wells stabilized by carriers presence. Distinctively, exciting these bound carriers generates broad absorption bands. Strong-coupling polarons are slow and massive since moving them requires atomic motion. Their transport differs qualitatively from that of conventional electronic charge carriers. Large (strong-coupling) polarons move c…
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…
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…
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 …
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…
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…
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 …
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
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 show that bipolaron formation leads to a d-wave Bose-Einstein condensate in cuprates. It is the bipolaron energy dispersion rather than a particular pairing interaction which is responsible for the d-wave symmetry. The unusual low-temperature dependence of the magnetic field penetration depth in cuprates is explained by the localisation of bosons in the random potential. The temperature dependence of the penetration depth is linear with positive or negative slope depending on the random field profile.
Distinctive normal-state properties of cuprate superconductors follow from their charge carriers forming a large-bipolaron liquid. The very weak scattering of the slow-moving heavy-massed excitations of the liquid by acoustic phonons yields a scattering rate that is less than the Debye frequency. The moderate liquid mobility, greater than 1 cm2/V-sec at 300 K, results as the weak scattering of the liquid compensates for its large mass. In resolution of a long-standing dilemma, the dc resistivity resulting from scattering by acoustic phonons remains nearly proportional to temperature to well be…
Within a two component approach to high Tc copper oxides including polaronic couplings, we identify the pseudogap phase as the onset of polaron ordering. This ordering persists in the superconducting phase. A huge isotope effect on the pseudogap onset temperature is predicted and in agreement with experimental data. The anomalous temperature dependence of the mean square copper oxygen ion displacement observed above, at and below Tc stems from an s-wave superconducting component of the order parameter, whereas a pure d-wave order parameter alone can be excluded.
Two-dimensional (2D) crystals have emerged as a class of materials with tuneable carrier density. Carrier doping to 2D semiconductors can be used to modulate manybody interactions and to explore novel composite particles. Holstein polaron is a small composite particle of an electron carrying a cloud of self-induced lattice deformation (or phonons), which has been proposed to play a key role in high-temperature superconductivity and carrier mobility in devices. Here, we report the discovery of Holstein polarons in a surface-doped layered semiconductor, MoS2, where a puzzling 2D superconducting …
The properties of an electron in a typical solid are modified by the interaction with the crystal ions, leading to the formation of a quasiparticle: the polaron. Such polarons are often described using the Fröhlich Hamiltonian, which assumes the underlying lattice phonons to be harmonic. However, this approximation is invalid in several interesting materials, including the recently discovered high-pressure hydrides which superconduct at temperatures above $200$K. In this paper, we show that Fröhlich theory can be extended to eliminate this problem. We derive four additional terms in the Fröhli…
