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Existence of “$d$-wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors

Antonio Delgado de Pasquale

Published Mar 21, 2018• 0 citations
OpenAlex

Abstract

High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows the presence of symmetry $d$-wave in a class of superconductors of high $T_c$, as well as the condition for the existence of density waves in the states of equilibrium. We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit. It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian .

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High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter.In this work we present a model that shows the presence of symmetry d-wave in a class of superconductors of high T c , as well as the condition for the existence of density waves in the states of equilibrium.We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit.It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian .

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The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.

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S. Aubry

At large electron-phonon coupling, the phonon of the Holstein-Hubbard model can be (generally) treated classically. Exact results can be obtained for this model at any band filling and any finite dimension where the Hubbard term with coefficient U is treated rigorously. The existence of chaotic bipolaronic states is proven when U is smaller than a certain value Uc and for an electron-phonon coupling k sufficiently large. The existence of magnetic polaronic states is also proven for positive U and k sufficiently large. For 0<U<Uc, there exists an overlap region with chaotic mixed polaronic-bipolaronic states. There is a region for U=Uc/2 and large k of special interest, where the bipolarons in their ground-state become singlet pairs of polarons bounded by a magnetic resonance. Then, the Peierls-Nabarro barrier which usually pins polarons and bipolarons to the lattice depresses to almost zero and the validity of the classical lattice approximation breaks down so that the initial exact results do not apply in that specific region. The formation of a superconducting state with possibly a high critical temperature, is then conjectured at a large coupling k in a narrow domain in-between the two insulating domains corresponding to Bipolaronic Charge Density Waves and to magnetic Polaronic Spin Density Waves respectively.

Journal de Physique IV (Proceedings)•Jul 1, 1993•7 citations
Existence of “ddd-wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors
High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows the presence of symmetry ddd-wave in a class of superconductors of high TcT_cTc​, as well as the condition for the existence of density waves in the states of equilibrium. We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit. It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian .
High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter.In this work we present a model that shows the presence of symmetry d-wave in a class of superconductors of high T c , as well as the condition for the existence of density waves in the states of equilibrium.We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit.It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian .
Taking into account microscopic properties of most usual high- T c superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the two-dimensional square lattice. We establish that these model Hamiltonians can show d -wave pairing at the bottom of their spectrum, despite their space isotropy. This phenomenon appears when a 'giant electron–phonon anomaly' is present at the boundaries of the Brillouin zone ('half breathing' bond-stretching mode), as in doped cuprates. Our results can be used to derive effective electron–electron interactions mediated by bipolarons and we discuss regimes where the corresponding model is relevant for the physics of high-temperature superconductivity and can be mathematically rigorously studied.
It is very important to clarify the mechanism of high-temperature superconductivity in strongly correlated electron systems. The mechanism of superconductivity in high temperature cuprate superconductors has been studied extensively since their discovery. We investigate the properties of correlated electron systems and mechanism of superconductivity by using the optimization quantum variational Monte Carlo method. The many-body wave function is constructed by multiplying by correlation operators of exponential type. We show that d-wave superconducting phase exists in the strongly correlated region where the on-site repulsive interaction is as large as the bandwidth or more than the bandwidth. The d-wave pairing correlation function is shown as a function of lattice sites, showing that the long-range order indeed exists.
Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.
The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.
At large electron-phonon coupling, the phonon of the Holstein-Hubbard model can be (generally) treated classically. Exact results can be obtained for this model at any band filling and any finite dimension where the Hubbard term with coefficient U is treated rigorously. The existence of chaotic bipolaronic states is proven when U is smaller than a certain value Uc and for an electron-phonon coupling k sufficiently large. The existence of magnetic polaronic states is also proven for positive U and k sufficiently large. For 0<U<Uc, there exists an overlap region with chaotic mixed polaronic-bipolaronic states. There is a region for U=Uc/2 and large k of special interest, where the bipolarons in their ground-state become singlet pairs of polarons bounded by a magnetic resonance. Then, the Peierls-Nabarro barrier which usually pins polarons and bipolarons to the lattice depresses to almost zero and the validity of the classical lattice approximation breaks down so that the initial exact results do not apply in that specific region. The formation of a superconducting state with possibly a high critical temperature, is then conjectured at a large coupling k in a narrow domain in-between the two insulating domains corresponding to Bipolaronic Charge Density Waves and to magnetic Polaronic Spin Density Waves respectively.