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Europhysics Letters (EPL)

Pseudogap in high-temperature superconductors from realistic Fröhlich and Coulomb interactions

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

Published Nov 1, 2012• 3 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/100/37005

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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.
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 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 review a series of exact, analytical and numerical results obtained on the adiabatic Holstein–Hubbard model, many of which are new and non-trivial. We study next the role of the quantum lattice fluctuations that were initially neglected. The possibility of having high- T c bipolaronic superconductors is analysed on the basis of these results. We suggest that models that involve only electron–phonon coupling are very unlikely to produce bipolaronic superconductivity, which is prevented by the spatial ordering of the bipolarons associated with a lattice instability. This is due to a very large effective mass of the bipolarons that can be related to the large Peierls–Nabarro energy barrier required to move these bipolarons through the lattice in the adiabatic limit. We conjecture that high- T c superconductivity originates specifically from the exceptionally well-balanced competition between electron–phonon coupling and electron–electron repulsion. In the restricted region in which, within the mean field approach, the energy of a bipolaron is close to those of two polarons, a new type of electron pairing occurs by formation of pairs of polarons in the spin singlet state. Such a polaron pair, called a spin resonant bipolaron (SRB), is not the standard bipolaron (both could exist in the adiabatic case). Its Peierls–Nabarro energy barrier can be sharply depressed, almost to zero. As a result of quantum lattice fluctuations, its tunnelling energy is sharply enhanced. Then, superconductivity could persist for a relatively large electron–phonon coupling, with an unusually large critical temperature as a Bose condensate of SRBs before becoming, at larger coupling and in any case, an insulating spin–Peierls polaronic phase.
An extended boson–fermion (BF) model is introduced describing the evolution of attractively interacting single electrons into a binary mixture of unpaired electrons plus incoherent bosonic Cooper pairs as absolute temperature is lowered. The new model is employed to determine how the system, upon cooling, exhibits critical temperatures for: a) incoherent boson formation below as well as b) for creating a coherent boson fluid below . Critical temperatures and are related with the dynamical parameters of the attractively interacting fermion system. It is shown that the introduction of a uniform Coulomb interaction in an anisotropic BF binary gas mixture model allows finding not only a self-consistent description of a pseudogap and a dome-shaped -vs-doping behaviour, but also to predict, even in a phonon-mediated many-electron dynamics, of an energy–momentum dispersion that is either gapped or not depending on direction. This manifests itself in high- superconductors as curves in momentum space along which the superconducting gap vanishes, hence giving rise to the so-called “Fermi arcs” observed in angle-resolved-photoemission spectroscopy experiments.
In this paper, we try to understand the pseudogap phenomenon observed in the cuprate superconductor through a model study. Specifically, we explore the so-called low-temperature pseudogap state by turning off the superconducting (SC) off diagonal long range order in an ansatz state for the t – J model (Weng 2011 New J. Phys. 13 103039 ). Besides strong non-Gaussian SC fluctuations, the resulting state also exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous 'normal state' properties are found in qualitative consistency with experimental measurements in the cuprates. Such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the SC ground state. A critical comparison with other approaches to the doped Mott insulator is also made.