Long-range Electron-phonon Interaction Research Articles

Dispersion interactions in proposed covalent superhydride superconductors

Recent developments in high temperature superconducting materials under high pressure have made numerical evaluation of the superconducting transition temperature (${T}_{c}$) of predicted materials critically important as a means to identification. Existing methods of calculating ${T}_{c}$ often do not agree with each other or experiment, often due to the large number of complex factors that contribute to this property; among them is the neglect of dispersion interactions in commonly used density functionals. Here, we evaluate the effect of including dispersion interactions on the predicted superconducting properties of two examples of the covalent superhydride class of very high-${T}_{c}$ superconducting materials. In both cases, dispersion is found to have sizable effects, increasing the electron-phonon coupling as compared to the reference case of elemental niobium. A detailed investigation traces the origin of this effect in a 270 GPa $R3m\phantom{\rule{4pt}{0ex}}\mathrm{C}\mathrm{S}{\mathrm{H}}_{7}$ [Cui et al., Phys. Rev. B 101, 134504 (2020)] structure to structural distortions driven by long-range electron-phonon interactions rather than novel bonding networks.

Significant suppression of phonon transport in polar semiconductors owing to electron-phonon-induced dipole coupling: An effect of breaking centrosymmetry

Thermal resistance induced by long-range electron-phonon interaction is often considered negligible. Here, by combining ab initio calculations with analytical modeling, we show that the scattering rate of acoustic phonons due to the electron-phonon-induced dipole (EPID) interaction varies asymptotically as the reciprocal of the phonon wavevector (∝q–1), and surpasses the short-range deformation-potential scattering as the wavevectors reduce to tens of reciprocal centimeters. This strong EPID coupling can significantly suppress the thermal conductivity in wurtzite zinc oxide, which originates from the absence of a mirror plane perpendicular to the c-axis that breaks the inversion symmetry of the out-of-plane vibrational modes. In contrast, such an effect does not occur in the zinc-blende gallium arsenide because no piezoelectric field can be generated along the three principal axes. This work highlights the effect of centrosymmetry breaking on tailoring phonon transport in polar semiconductors.

Formation of strong-coupling (bi)polarons and related in-gap states in lightly-doped cuprate superconductors

The formation of large polarons and bipolarons and related in-gap states in lightly-doped cuprates is studied in the strong electron–phonon coupling regime. The ground-state energies, binding energies and binding radius of strong-coupling large (bi)polarons are calculated using the continuum model and adiabatic approximation taking into account both the short- and long-range electron–phonon interactions. The obtained results show that the binding energies of such large (bi)polarons in the cuprates are progressively increased with decrease in the high frequency dielectric constant [Formula: see text] and ratio [Formula: see text] (where [Formula: see text] is the static dielectric constant). As a result, large (bi)polarons become nearly small (bi)polarons. It is shown that hole carriers strongly interact with acoustic and optical phonons and their self-trapping leads to the formation of (bi)polaronic states in the charge-transfer (CT) gap of the cuprates. As the cuprate system is doped, the CT gap of the parent compound is filled in with low-energy (bi)polaronic states. The calculated energies of such (bi)polaronic states are in good agreement with the experimentally observed energies of new states appearing in the CT gap of the parent cuprates. The calculated values of the binding radius of large polarons are also well consistent with the existing experimental data.

Strong long-range electron–phonon interaction as possible driving force for charge ordering in cuprates

A model resulting in charge ordering (CO) similar to that observed in cuprate superconductors is under study. It includes strong long-range electron–phonon interaction (EPI) and high density of correlated carriers. Coexistence of large bipolarons and delocalized carriers is a feature of such system. We develop generalized variation method to calculate the bipolaron size (CO period) in the ground normal state of such system at various doping. The approach allows the revealing of a possible physical reason of strongly different doping behavior of the CO wave vector in different cuprates. Obtained doping dependences of the CO period and temperature of the CO decay demonstrate quantitative agreement with those observed in cuprates. Predicted in the suggested approach ratio of the CO wave vector to the wave vector of the high-energy anomaly (HEA) in ARPES spectrum is in consent with that in cuprates. Calculated resonant x-rays scattering on the CO emerging in the model is in good agreement with experiments on cuprates including the asymmetry of the CO peaks’ cross-section. A gap arises in the spectrum of delocalized carriers near antinodal direction due to their scattering on the periodic potential created by autolocalized carriers, analogously to photon crystal effect.

Electron-Phonon Systems on a Universal Quantum Computer.

We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The additional number of qubits required by the presence of phonons scales linearly with the size of the system. The additional circuit depth is constant for systems with finite-range electron-phonon and phonon-phonon interactions and linear for long-range electron-phonon interactions. Our algorithm for a Holstein polaron problem was implemented on an Atos quantum learning machine quantum simulator employing the quantum phase estimation method. The energy and the phonon number distribution of the polaron state agree with exact diagonalization results for weak, intermediate, and strong electron-phonon coupling regimes.

Relaxation of strongly coupled electron and phonon fields after photoemission and high-energy part of ARPES spectra of cuprates

An approach to considering systems with a high concentration of correlated carriers and strong long-range electron–phonon interaction and to calculating the high-energy part of the angle-resolved photoemission spectroscopy (ARPES) spectra of such systems is suggested. Joint relaxation of strongly coupled fields—a field of correlated electrons and phonon field—after photoemission is studied to clarify the nature of characteristic features observed in the high-energy part of the ARPES spectra of cuprate superconductors. Such relaxation occurs in systems with strong predominantly long-range electron–phonon interaction at sufficiently high carrier concentration due to the coexistence of autolocalized and delocalized carriers. A simple method to calculate analytically a high-energy part of the ARPES spectrum arising is proposed. It takes advantage of using the coherent states basis for the phonon field in the polaron and bipolaron states. The approach suggested yields all the high-energy spectral features like broad Gaussian band and regions of ‘vertical dispersion’ being in good quantitative agreement with the experiments on cuprates at any doping with both types of carriers. Demonstrated coexistence of autolocalized and delocalized carriers in superconducting cuprates changes the idea about their ground state above the superconducting transition temperature that is important for understanding transport and magnetic properties. High density of large-radius autolocalized carriers revealed may be a key to the explanation of charge ordering in doped cuprates.

Polaron mobility obtained by a variational approach for lattice Fröhlich models

Charge carrier mobility for a class of lattice models with long-range electron–phonon interaction was investigated. The approach for mobility calculation is based on a suitably chosen unitary transformation of the model Hamiltonian which transforms it into the form where the remaining interaction part can be treated as a perturbation. Relevant spectral functions were then obtained using Matsubara Green’s functions technique and charge carrier mobility was evaluated using Kubo’s linear response formula. Numerical results were presented for a wide range of electron–phonon interaction strengths and temperatures in the case of one-dimensional version of the model. The results indicate that the mobility decreases with increasing temperature for all electron–phonon interaction strengths in the investigated range, while longer interaction range leads to more mobile carriers.

Cold Rydberg Atoms for Quantum Simulation of Exotic Condensed Matter Interactions

Quantum simulators could provide an alternative to numerical simulations for understanding minimal models of condensed matter systems in a controlled way. Typically, cold atom systems are used to simulate e.g. Hubbard models. In this paper, we discuss a range of exotic interactions that can be formed when cold Rydberg atoms are loaded into optical lattices with unconventional geometries; such as long-range electron-phonon interactions and extended Coulomb like interactions. We show how these can lead to proposals for quantum simulators for complex condensed matter systems such as superconductors. Continuous time quantum Monte Carlo is used to compare the proposed schemes with the physics found in traditional condensed matter Hamiltonians for systems such as high temperature superconductors.

Strictly localised triplet dimers on one- and two-dimensional lattices

Electrons may form inter-site pairs (dimers) by a number of mechanisms. For example, long-range (Fröhlich) electron-phonon interactions and strong on-site Hubbard U allow formation of small light bipolarons in some lattices. We identify circumstances under which triplet dimers are strictly localised by interference in certain one- and two-dimensional lattices. We assume a U-V Hamiltonian with nearest- and next-nearest-neighbour hopping integrals t and t′, large positive U and attractive nearest- and next-nearest-neighbour interactions V and V′. In the square ladder and some two-dimensional bilayers, if the dimer Hilbert space is restricted to nearest- and next-nearest-neighbour dimers, triplet dimers become strictly localised for certain values of these parameters. For example, in a square ladder with t′ = t and V′ = V, all triplet bands become flat due to exact cancellation of hopping paths. We identify the localised eigenstates for all flat bands in each lattice. We show that many of the flat bands persist for arbitrary t/t′ so long as other restrictions still apply.

Bipolarons from long-range interactions: Singlet and triplet pairs in the screened Hubbard-Fröhlich model on the chain

We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich 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 Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.

Superconductivity in a Hubbard-Fröhlich model and in cuprates

Using the variational Monte Carlo method, we find that a relatively weak long-range electron-phonon interaction induces a $d$-wave superconducting state in doped Mott-Hubbard insulators and/or strongly correlated metals with a condensation energy significantly larger than can be obtained with Coulomb repulsion only. Moreover, the superconductivity is shown to exist for infinite on-site Coulomb repulsion without the need for additional mechanisms such as spin fluctuations to mediate $d$-wave superconductivity. We argue that our superconducting state is robust with respect to a more intricate choice of the trial-wave function and that a possible origin of high-temperature superconductivity lies in a proper combination of strong electron-electron correlations with poorly screened Fr\"ohlich electron-phonon interaction.

Two-site model for a small polaron: Mass renormalization and optical conductivity

The renormalization of the mass of an electron interacting with many ions of a lattice via the long-range (Frohlich) electron-phonon interaction and optical absorption of electrons are studied at zero temperature. Ions are assumed to be isotropic three-dimensional oscillators. The optical conductivity and the renormalized mass of small adiabatic Frohlich polarons are calculated and compared with those of small adiabatic Holstein polarons.

Long-range electron-phonon interactions lead to superlight small bipolarons

A finite-range Fröhlich electron-phonon interaction (EPI) with c-axis polarized optical phonons has been identified in cuprate superconductors by photoemission spectroscopy, in agreement with an earlier proposal by Alexandrov and Kornilovitch [1]. In this article, we discuss the consequences of long-range interactions on phonon-mediated local pairing. First, we examine the effects of modifying interaction range and lattice geometries with regard to analytical strong-coupling/non-adiabatic results for ladder systems. To test the applicability of the analytic results to experimentally achievable couplings and phonon frequencies, we apply a continuous time quantum Monte-Carlo algorithm (CTQMC) to the computation of the effective mass and pairing radius of lattice bipolarons. We demonstrate that bipolarons can be simultaneously small and light due to a novel crab-like motion. Such light, small bipolarons are a necessary precursor to high-temperature Bose-Einstein condensation in solids.

Path-integral approach to lattice polarons

The basic principles behind a path integral approach to the lattice polaron are reviewed.Analytical integration of phonons reduces the problem to one self-interactingimaginary-time path, which is then simulated by Metropolis Monte Carlo. Projectionoperators separate states of different symmetry, which provides access to various excitedstates. Shifted boundary conditions in imaginary time enable calculation of the polaronmass, spectrum and density of states. Other polaron characteristics accessible by themethod include the polaron energy, number of excited phonons and isotope exponent onmass. Monte Carlo updates are formulated in continuous imaginary time on infinite latticesand as such provide statistically unbiased results without finite-size and finite time-steperrors. Numerical data are presented for models with short-range and long-rangeelectron–phonon interactions.

Nature of the charge carriers and their pairing state in the anisotropic three-dimensional lightly doped cuprates

The self-trapping and pairing of carriers in the three-dimensional (3D) isotropic and anisotropic high-Tc cuprates are studied in the strong electron–phonon coupling limit. It is shown that the relevant charge carriers in these systems are large (bi)polarons. The ground-state energies of large polarons and bipolarons in the doped cuprates are calculated variationally as a function of the ratio of the optic to the static dielectric constant η=ε∞/ε0, taking into account the short- and long-range electron–phonon interactions and Coulomb correlation in the continuum model and adiabatic approximation. It is found that the formation of a large acousto-optic bipolaron is possible in a broad region of η.

Superlight Small Bipolarons in the Presence of a Strong Coulomb Repulsion

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 algorithm to solve the two-particle Coulomb-Fröhlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.

High Temperature Superconductivity Due to a Long-Range Electron–Phonon Interaction, Application to Isotope Effects, Thermomagnetic Transport and Nanoscale Heterogeneity in Cuprates

Strong electron-phonon interactions in cuprates and other high-temperature superconductors have gathered support over the last decade in a large number of experiments. Here I briefly introduce the Froehlich-Coulomb multi-polaron model of high-temperature superconductivity, which includes strong on-site repulsive correlations and the long-range Coulomb and electron-phonon (e-ph) interactions. Our extension of the BCS theory to the strong-coupling regime with the long-range \emph{unscreened} electron-phonon interaction could naturally explain the isotope effects, unconventional thermomagnetic transport, and checkerboard modulations of the tunnelling density of states in cuprates.

FORMATION AND STABILITY OF A STRONG-COUPLING LARGE BIPOLARON IN THE LIGHTLY DOPED CUPRATES

The ground-state energies of large polaron Ep and bipolaron EB in three-dimensional lightly doped cuprates are calculated variationally taking into account the short- and long-range electron-phonon interactions and Coulomb correlation in the continuum model and adiabatic approximation. The binding energy of a large bipolaron and its stability region are determined as a function of the ratio of dielectric constants η = ε∞/ε0. It is found that the large bipolaron is stable in a broad region of η.

Effects of electron-phonon coupling range on the polaron formation

The polaron features due to electron-phonon interactions with different coupling ranges are investigated by adopting a variational approach. The ground-state energy, the spectral weight, the average kinetic energy, the mean number of phonons, and the electron-lattice correlation function are discussed for the system with coupling to local and nearest-neighbor lattice displacements comparing the results with the long-range case. For large values of the coupling with nearest-neighbor sites, most physical quantities show a strong resemblance with those obtained for the long-range electron-phonon interaction. Moreover, for intermediate values of interaction strength, the correlation function between electron and nearest-neighbor lattice displacements is characterized by an upturn as function of the electron-phonon coupling constant.

Polaron features for long-range electron–phonon interaction

The polaron features for long-range electron–phonon interaction are investigated byextending a variational approach previously proposed for the study of systems with localcoupling. The ground state spectral weight, the average kinetic energy, the mean number ofphonons, and the electron–lattice correlation function are discussed for a wide range ofmodel parameters focusing on the adiabatic regime and comparing the results with theshort-range case (Holstein model). A strong mixing of electronic and phononic degrees offreedom for small values of the electron–phonon coupling constant is found in the adiabaticcase due to the long-range interaction. Finally a polaron ‘phase diagram’ is proposed.