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Journal of Physics Conference Series

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

J. P. Hague, P. E. Kornilovitch, John H. Samson, A. S. Alexandrov

Published Dec 1, 2007• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/92/1/012118

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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.
We report analytical and numerical results on the two-particle states of the polaronic ttt-Jp{J}_{p}Jp​ model derived recently with realistic Coulomb and electron-phonon (Fr\"ohlich) 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 ttt to the exchange interaction Jp{J}_{p}Jp​ but remains small in the whole range $0\ensuremath{\leqslant}t/{J}_{p}\ensuremath{\leqslant}1$. Furthermore, the model exhibits a phase transition to a superconducting state with a critical temperature well in excess of 100 K since the small bipolarons are perfectly mobile. In the range $t/{J}_{p}\ensuremath{\leqslant}1$, there are distinct charge and spin gaps opening in the density of states, specific heat, and magnetic susceptibility well above Tc{T}_{c}Tc​.
We compute the properties of singlet and triplet bipolarons on two-dimensional lattices using the continuous-time quantum Monte Carlo algorithm. Properties of the bipolaron including the total energy, inverse mass, bipolaron radius, and number of phonons associated with the bipolaron demonstrate the qualitative difference between models of electron-phonon interaction with long-range interaction (screened Fr\"ohlich) and those with purely local (Holstein) interaction. A major result of our survey of the parameter space is the existence of extra-light hybrid singlet bipolarons consisting of an on-site and an off-site component on both square and triangular lattices. We also compute triplet properties of the bipolarons and the pair dispersion. For pair momenta on the edge of the Brillouin zone of the triangular lattice, we find that triplet states are more stable than singlets.
Light-mass bipolarons in off-diagonally coupled electron-phonon systems provide a potential route to bipolaronic high-Tc superconductivity. While there has been numerical progress in the physically relevant limit of slow phonons, more insights are needed to fully understand to what extent this mechanism survives at finite densities and in different regimes. We address these questions using advanced tensor-network methods applied to the Su-Schrieffer-Heeger model. Studying both the spectral properties of isolated bipolarons as well as the pairing correlations at small finite densities, we find evidence that the conventional picture of bipolarons as molecular bound states which undergo Bose-Einstein condensation may need to be reconsidered. Instead, our findings suggest correlation-driven formation of a fragmented condensate with spatially separated polaron pairs, stabilized by strong repulsive electron-electron interactions at moderate values of the electron-phonon coupling. These spatially modulated charge clouds exhibit pairing with a typical length-scale set by the Fermi momentum.
We present the numerically exact ground-state energy, effective mass, and isotope exponents of a one-dimensional lattice polaron, valid for any range of electron-phonon interaction, applying a continuous-time quantum Monte Carlo (QMC) technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strong-coupling $1∕\ensuremath{\lambda}$ expansion. We show that the exact results agree well with the canonical Fr\"ohlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased (less adiabatic) phonon frequency: specifically, a reduction in the effective mass.