Abstract We suggest that superconductivity can be traced back to a first-order interaction between the charge carriers which does not necessarily involve second-order electron-phonon coupling. For small molecular model systems it is demonstrated that the formation of Cooper pairs can lead to an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). We suggest that this attenuation of a fermionic quantum constraint is the driving force for the superconducting transition. Whenever the PAP is activated in single-particle hoppings of electrons, the corresponding moves reduce the electronic derealization; they raise the ensemble energy. The stability of a fermionic system is enhanced with decreasing influence of the PAP. Moves of Cooper pairs are not influenced by any quantum constraint of the intersite type. This behaviour differs from the well-known fermionic constraints. The quantum statistics of Cooper pairs is of a mixed type combining a fermionic on-site and a bosonic intersite behaviour. It coincides with the quantum statistics of so-called hard core bosonic ensembles. In the present work Cooper pair formation has been studied for smaller molecular models. The electronic Hamiltonian employed is of the two-parameter Hubbard-type. The solid state phenomenon superconductivity is correlated with the molecular concepts of “antiaromaticity” and “aromaticity”. Arguments are given which support the present interpretation.
Relation between the binding energy of a pair of electrons in Cooper's configuration and the magnitude of the attractive interaction between them is investigated theoretically for a two-dimensional electron gas when the electron pair has (a) zero and (b) finite center of mass momentum (CMM) first (i) in the background of a passive Fermi sea and (ii) with inclusion of the effect of Pauli exclusion principle in the presence of an active Fermi sea, at zero temperature. In the Cooper's approach (Cooper 1956 Phys. Rev. 104 1189) two pairing electrons are considered above the Fermi sea. Due to Pauli exclusion principle, these two electrons are forbidden to go into the states whose energies are less than the Fermi energy. Consequently, the role of the electrons which form the Fermi sea is passive in formation of electron pair (Fujita and Godoy 2001 Theory of High Temperature Superconductivity (Kluwer Academic Publishers)). However, in the case of an active Fermi sea, implying possible presence of multiple pairs of electrons coming out of the Fermi sea, the two electrons will have less available region in the momentum space for pair formation due to the Pauli blocking effect. In both the situations, threshold values of attractive interaction are found to exist to bind the electrons having finite CMM even with respect to the Fermi energy while with arbitrarily small value of attractive interaction they can be bound only in the case of zero CMM and that too in the presence of a passive Fermi sea. However, the presence of an active Fermi sea strongly opposes the pair formation having lower CMM. Furthermore, raising the range of the attractive interaction below and above the Fermi surface makes the pair formation more difficult due to enhanced Pauli blocking in this case. In the case of a passive Fermi sea however, with the increase in the range of the attractive interaction it becomes easier for the electron pairs to be in both Cooper pair state (CP) and true bound state (TB). These results are totally distinct from those obtained by Randeria et al (1989 Phys. Rev. Lett. 62 981, 1990 Phys. Rev. B 41 327) that a fermionic bound state in true vacuum is a necessary and sufficient condition for the Cooper pairing instability in the presence of a passive Fermi sea, independent of attractive interaction strength implying that for a potential which is attractive everywhere in two dimension, a two-body bound state exists for an arbitrarily weak attraction. Our calculations show, in the mean field approximation, that co-existence of TB state and CP state with various CMMs can occur only beyond a critical attractive interaction strength. This could lead to the formation of incoherent pairs even under strong coupling situation, which may hint onto the pseudo gap formation leading to some of the exotic features in the anomalous normal state seen in some of the exotic superconductors.
Exact thermal studies of small (4-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, and, in particular, pairing fluctuations away from half-filling. These exact calculations, carried out in canonical and grand canonical ensembles, monitoring variations in temperature T and magnetic field h, show rich phase diagrams in a $T\ensuremath{-}\ensuremath{\mu}$ space consisting of pairing fluctuations and signatures of condensation. Corresponding electron pairing instabilities are seen when the on-site Coulomb interaction U is smaller than a critical value Uc(T) and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing, and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters, and numerous similarities with experiments on high Tc superconductors are pointed out. In addition, these ideas may be linked to superconducting carbon nanotubes where a purely electronic mechanism could be responsible for superconductivity.
Unification of the Bardeen, Cooper and Schrieffer (BCS) and the Bose‐Einstein condensation (BEC) theories is surveyed in terms of a generalized BEC (GBEC) finite‐temperature statistical formalism. A vital distinction is that Cooper pairs (CPs) are true bosons that may suffer a BEC since they obey BE statistics, in contrast with BCS pairs that are “hard‐core bosons” at best. A second crucial ingredient is the explicit presence of hole‐pairs (2h) alongside the usual electron‐pairs (2e). A third critical element (particularly in 2D where ordinary BEC does not occur) is the linear dispersion relation of CPs in leading order in the center‐of‐mass momentum (CMM) power‐series expansion of the CP energy. The GBEC theory reduces in limiting cases to all five continuum (as opposed to “spin”) statistical theories of superconductivity, from BCS on one extreme to the BEC theory on the other, as well as to the BCS‐Bose “crossover” picture and the 1989 Friedberg‐Lee BEC theory. It accounts for 2e‐ and 2h‐CPs in arbitrary proportions while BCS theory can be deduced from the GBEC theory but allows only equal (50%‐50%) BE condensed‐mixtures of both kinds of CPs. As it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero‐temperature condensation energy for all couplings, it suggests that the BCS condensate is a BE condensate of a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly‐bound zero‐CMM 2e‐ and 2h‐CPs. Without abandoning the electron‐phonon mechanism in moderately weak coupling, and fortuituously insensitive to the BF interactions, the GBEC theory suffices to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01–0.05 empirically found in the so‐called “exotic” superconductors of the Uemura plot, including cuprates, in contrast to the low values of Tc/TF⩽10−3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors.
Many properties of the two-dimensional Hubbard model have been explored for the model parameters appropriate for strongly correlated electronic systems, especially cuprate superconductors.Most of the calculations are done using a well-established dynamical cluster quantum Monte Carlo method.Using this method, we investigate the effect of long-range hoppings on superconductivity with and without the presence of phonons on small clusters.The superconducting transition temperature, T c , is found to generally decrease with a negative next nearest neighbor hopping, t ′ .In the presence of the Holstein phonons, a finite t ′ enhances T c in the under-doped region for the hole-doped system, consistent with band structure calculations and experiment.The validity of the spin-susceptibility-mediated pairing in this model is studied and found to yield symmetries other than d-wave when a finite t ′ is considered.A new numerical algorithm for solving the embedded cluster problems is introduced, and used to calculate the thermodynamic properties of the model on larger clusters, especially those associated with the quantum critical behavior at finite doping.Our results suggest that the quantum critical point (QCP) which separates the Fermi liquid and pseudogap regions, is the second order terminus of the line of first order phase separation transition in the limit when a positive t ′ goes to zero.For small t ′ , the superconducting dome is centered at the QCP, suggesting that charge fluctuations might have a role in the pairing mechanism in this model.I am very thankful to University of Cincinnati for providing me with the opportunity to pursue my education and the support I received during my program.Part of this thesis is a result of my work as a researcher at Louisiana State University.I am also thankful to them for their support.I would like to thank my adviser, Mark Jarrell, who taught me how to be an effective researcher, provided me with the opportunities to interact with other professionals and fully supported me financially for most of the duration of the
Abstract The low-temperature properties of a wide range of many-fermion systems spanning metals, quantum gases and liquids to nuclear matter are well understood within the framework of Landau’s theory of Fermi liquids. The low-energy physics of these systems is governed by interacting fermionic quasiparticles with momenta and energies near a Fermi surface in momentum space. Nonequilibrium properties are described by a kinetic equation for the distribution function for quasiparticles proposed by Landau. Quasiparticle interactions with other quasiparticles, phonons, or impurities lead to internal forces acting on a distribution of nonequilibrium quasiparticles, as well as collision processes that ultimately limit the transport of mass, heat, charge, and magnetization, as well as limiting the coherence times of quasiparticles. For Fermi liquids that are close to a second-order phase transition, e.g., Fermi liquids that undergo a superfluid transition, incipient Cooper pairs—long-lived fluctuations of the ordered phase—provide a new channel for scattering quasiparticles, as well as corrections to internal forces acting on the distribution of nonequilibrium quasiparticles. We develop the theory of quasiparticle transport for Fermi liquids in the vicinity of a BCS-type superfluid transition starting from Keldysh’s field theory for nonequilibrium, strongly interacting fermions. The leading corrections to Fermi-liquid theory for nonequilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. Our theory is applicable to quasiparticle transport in superconductors, nuclear matter, and the low-temperature phases of liquid 3He. As an implementation of the theory we calculate the pairing-fluctuation corrections to the attenuation of zero sound in liquid 3He near the superfluid transition and demonstrate quantitative agreement with experimental results.