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arXiv:1112.3230 · Physical Review B

Superlight small bipolarons from realistic long-range Coulomb and Fröhlich interactions

A. S. Alexandrov, John H. Samson, Gerardo Sica

Published Mar 26, 2012• 14 citations
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Abstract

We report analytical and numerical results on the two-particle states of the polaronic $t$-${J}_{p}$ 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 $t$ to the exchange interaction ${J}_{p}$ 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 ${T}_{c}$.

DOI
10.1103/physrevb.85.104520

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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⩽t/Jp\ensuremath⩽10\ensuremath{\leqslant}t/{J}_{p}\ensuremath{\leqslant}10\ensuremath⩽t/Jp​\ensuremath⩽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/Jp\ensuremath⩽1t/{J}_{p}\ensuremath{\leqslant}1t/Jp​\ensuremath⩽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​.
It has been recently shown that the competition between unscreened Coulomb and Fr\"{o}hlich electron-phonon interactions can be described in terms of a short-range spin exchange JpJ_pJp​ and an effective on-site interaction U~\tilde{U}U~ in the framework of the polaronic ttt-JpJ_pJp​-U~\tilde{U}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 strong suppression of low-temperature spin susceptibility, specific heat and tunneling conductance, signaling the presence of normal state pseudogap without any assumptions on preexisting orders or broken symmetries in the normal state of the model.
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 JpJ_pJp​ and an effective on-site interaction U~\tilde{U}U~ in the framework of the polaronic ttt-JpJ_pJp​-U~\tilde{U}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 strong suppression of low-temperature spin susceptibility, specific heat and tunneling conductance, signaling the presence of normal state pseudogap without any assumptions on preexisting orders or broken symmetries in the normal state of the model.
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.
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 in the framework of the polaronic t - J p - 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 strong suppression of low-temperature spin susceptibility, specific heat and tunnelling conductance, signalling the presence of a pseudogap regime in the normal state without any assumptions on pre-existing orders or broken symmetries in the normal state of the model.
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≥0U \geq 0U≥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 pair of two polarons bounded by a magnetic interaction. The pinning mode of the bipolaron soften in the vicinity of this transition leading to a higher mobility of the bipolaron which is tested numerically. In 2D, and for any UUU, the electron-phonon coupling needs to be large enough in order to form small polarons or bipolarons instead of extended electrons. We calculate the phase diagram of the bipolaron involving first order transitions lines with a triple point. A pair of polarons can form three types of bipolarons: a) on a single site at small UUU, b) a spin singlet state on two nearest neighbor sites for larger UUU as in 1D and c) a new intermediate state obtained as the resonant combination of four 2-sites singlet states sharing a central site, called quadrisinglet. The breathing and pinning internal modes of bipolarons in 2D generally only weakly soften and thus, they are practically not mobile. On the opposite, in the vicinity of the triple point involving the quadrisinglet, both modes exhibit a significant softening. However, it was not sufficient for allowing the existence of a classical mobile bipolaron (at least in that model).
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.