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arXiv:cond-mat/9406019

Condensation of Hard-Core Pairs on a Lattice: A Model of the Superconducting State in Cuprates

Morten Holm Pedersen, T. Schneider

Published Jun 3, 1994• 0 citations
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Abstract

Using the Monte Carlo technique we study the dependence of transition temperature, penetration depth and specific heat singularity on the pair concentration in the Bose Hubbard model. We observe remarkable agreement with the corresponding properties of cuprates. This points uniquely to Bose condensation of hard-core pairs on a lattice as the mechanism that drives the transition.

DOI
10.48550/arxiv.cond-mat/9406019

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Using the Monte Carlo technique we study the dependence of transition temperature, penetration depth and specific heat singularity on the pair concentration in the Bose Hubbard model. We observe remarkable agreement with the corresponding properties of cuprates. This points uniquely to Bose condensation of hard-core pairs on a lattice as the mechanism that drives the transition.
A model of hard-core bosons on a three-dimensional (3D) lattice has been studied using both quantum Monte Carlo and classical Monte Carlo techniques. We have calculated the transition temperature for Bose-Einstein condensation, the zero-temperature penetration depth and the specific-heat critical amplitude, and have explored the hyperuniversal scaling relationship between these quantities pertaining to the expected 3D XY critical point. As a conclusion we draw a phenomenological analogy between the model studied and extreme type-II superconductors. \textcopyright{} 1996 The American Physical Society.
We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above Tc{\mathit{T}}_{\mathit{c}}Tc​. These features are also mirrored in the shape of the specific-heat peak around Tc{\mathit{T}}_{\mathit{c}}Tc​, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.
We study the three-dimensional (3D) attractive Hubbard model by means of the determinant quantum Monte Carlo method. This model is a prototype for the description of the smooth crossover between BCS superconductivity and Bose-Einstein condensation. By detailed finite-size scaling we extract the finite-temperature phase diagram of the model. In particular, we interpret the observed behavior according to a scenario of two fundamental temperature scales; T∗{T}^{*}T∗ associated with Cooper pair formation and Tc{T}_{c}Tc​ with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high-Tc{T}_{c}Tc​ cuprate superconductors.
Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.
We show that bipolaron formation leads to a d-wave Bose-Einstein condensate in cuprates. It is the bipolaron energy dispersion rather than a particular pairing interaction which is responsible for the d-wave symmetry. The unusual low-temperature dependence of the magnetic field penetration depth in cuprates is explained by the localisation of bosons in the random potential. The temperature dependence of the penetration depth is linear with positive or negative slope depending on the random field profile.
Observed crossover events between different power functions of absolute temperature occurring below about ~1 K in the temperature dependence of the heat capacity or the thermal conductivity of the conventional superconductors are identified as transitions from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2me (with me as mass of the electron) and their high density, the BE-condensation temperature, TBE, of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature TBE turns out to be proportional to the superconducting transition temperature TSC. From the observed TBE-values it is possible to calculate the density of the Cooper pairs. Assuming that the Cooper pairs form a dense gas of bosons, the diameter of the Cooper-pair orbitals turns out to be equal to the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs pairs, only one layer of Cooper-pairs, next to the inner surface of the sample, is sufficient to shield an applied external magnetic field completely.