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.
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.
We have investigated the ground-state properties of a model system with a strong electron-phonon interaction. It is found that as long as the renormalized intersite electron correlation is attractive, a new type of Cooper pairing will occur whether the renormalized on-site electron correlation is repulsive or attractive. Furthermore, we have shown that a new phonon coherent state, named a two-phonon coherent state, must be introduced to serve as the ground state of the phonon subsystem, so that the ground-state energy of the interacting system can be made a stable minimum and an appropriate condensation energy of the superconducting ground state may be obtained. We have performed numerical calculations for the n=1 case.
We review Cooper pairing starting from its simplest, original 1956 version of two electrons interacting above the Fermi sea of an ideal Fermi gas (IFG). The two-electron interaction assumed extensively (if not exclusively), is the attractive two-parameter Cooper, and then BCS, model interactions. Hole Cooper pairs (CPs) and electron-hole CPs are then included along with the initial electron-CPs in terms of the single-fermion Green functions implied by the Bethe-Salpeter (BS) integral equation in the ladder approximation. A purely-imaginary CP energy "instability" is recovered that is well-documented in the literature at least since the late 1950's. A novel interpretation of this instability is that an unperturbed Hamiltonian different from the IFG one first used by Cooper suffices to obtain meaningful CPs. Instead of the IFG sea, a BCS-correlated Fermi "sea" used in the BS equation interpreted as the associated unperturbed Hamiltonian leads to real CP energies (with small imaginary terms implying damping). We survey how this has been achieved in 1D, 2D and 3D, and give a more detailed treatment in 2D. A vital distinction is that the original and generalized CPs are true bosons in contrast with BCS pairs that are not ordinary bosons but rather "hard-core bosons" as they do not obey strict Bose commutation rules. Another important common element of the original or generalized CPs (particularly in 2D where ordinary Bose-Einstein condensation (BEC) does not occur) is their linear dispersion relation in leading order in the total (or, center-of-mass) momentum power-series expansion of the CP energy. This theory encompasses, in principle, all empirically known superconductors including quasi-2D superconductors such as cuprates and the ET organic compounds, as well as quasi-1D ones such as the organometallic Bechgaard salts and nanotubes.
In cuprate superconductors, superconductivity is consistently accompanied by antiferromagnetism. This raises the question of a potential causal link between superconductivity and antiferromagnetic mechanisms. In this study, we consider the non-local Coulomb interaction and solve the single-particle Green function exactly. The exact solution shows the existence of strong inter-spin correlations in the absence of superexchange, eliminating the directional degrees of freedom for spin quantization in the Hatsugai-Kohmoto (HK) model. Strong Coulomb interactions force the energy band splitting into infinitely equidistant sub-bands weighted by a Poisson distribution, exhibiting boson properties (incoherent pairs of fermions) and non-Fermi liquids. Attractive pairing interactions caused by electron-phonon coupling open a pairing gap at the Fermi surface. Based on the Pauli exclusion principle, paired particles with the same spin quantization direction completely occupy the state below the gap, resulting in pairing insulators, superconducting instability, and especially antiferromagnetism. A pseudogap occurs when the higher split sub-band overlaps in energy with the lowest sub-band. The critical temperature Tc of superconductivity exhibits a multi-dome structure and peaks around the maximum density of states. The maximum Tc depends on splitting sub-bands and particle occupancy, consistent with experiments. This study concludes that the non-local effect preserves the Hubbard and HK models' characteristics while renormalizing the system to antiferromagnetism in pairing insulators and Pauli paramagnetism in weak semimetals.