R. M. Quick

Statistical model of superconductivity in a 2D binary boson–fermion mixture

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, composite-boson Cooper pairs (CPs) in chemical and thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the superconducting singularity temperature is approached from above. The model is derived from {\it first principles} for the BCS model interfermion interaction from three extrema of the system Helmholtz free energy (subject to constant pairable-fermion number) with respect to: a) the pairable-fermion distribution function; b) the number of excited (bosonic) CPs, i.e., with nonzero total momenta--usually ignored in BCS theory--and with the appropriate (linear, as opposed to quadratic) dispersion relation that arises from the Fermi sea; and c) the number of CPs with zero total momenta. Compared with the BCS theory condensate, higher singularity temperatures for the Bose-Einstein condensate are obtained in the binary boson-fermion mixture model which are in rough agreement with empirical critical temperatures for quasi-2D superconductors.

Variational results for the Rabi Hamiltonian

Abstract We present simple two- and three-parameter variational calculations for the Rabi Hamiltonian. The importance of symmetry in the ansatze is stressed. The numerical results indicate that our ansatze provide accurate approximations both to the ground-state energy and wavefunction and to the first excited state if the two-boson energy significantly exceeds the level splitting.

Polaron and bipolaron dispersion curves in one dimension for intermediate coupling

Bipolaron energies are calculated as a function of wave vector by a variational method of Gurari appropriate for weak or intermediate coupling strengths, for a model with electron-phonon interactions independent of phonon wave vector and a short-ranged Coulomb repulsion. It is assumed that the bare electrons have a constant effective mass. A two-parameter trial function is taken for the relative motion of the two electrons in the bipolaron. The energies of the bipolarons are compared with those of two single polarons as a function of wave vector for various parameter values. Results for the effective masses at the zone center are also obtained. Comparison is made with data of other authors for bipolarons in the Hubbard-Holstein model, which differs mainly from the present model in that it has a tight-binding band structure for the bare electrons.

Analytic solution of the Bardeen–Cooper–Schrieffer gap equation in one, two, and three dimensions

Analytic expressions for the Bardeen–Cooper–Schrieffer (BCS) gap of a many‐electron system with the BCS model interaction are obtained in one, two, and three dimensions in the weak coupling limit, but for arbitrary interaction width ν≡ℏωD/EF, 0<ν<∞. Here ℏωD is the maximum energy of a force‐mediating boson, and EF is the Fermi energy (which is fixed by the electronic density). Our results address both phononic (ν≪1) as well as nonphononic (e.g., exciton, magnon, plasmon, etc.) pairing mechanisms where the mediating boson energies are not small compared with EF, provided weak electron–boson coupling prevails. The essential singularity in coupling, sometimes erroneously attributed to the two‐dimensional character of the BCS model interaction with ν≪1, is shown to appear in one, two, and three dimensions before the limit ν→0 is taken.

BCS-bose theory of the superconducting coherence length

Abstract A root-mean square fermion pair radius, defined in terms of an appropriate BCS-Bose pair wave function in momentum space, is obtained analytically in one- and three-dimensions via complex plane integration. Results are compared with the familiar Pippard coherence length, in weak coupling (BCS regime), and with the size of an isolated pair in strong coupling (Bose regime). Inspite of their comparatively small magnitudes, empirical cuprate coherence length data seem to be consistent with a weakly-coupled description within the BCS-Bose picture.

BEC-DRIVEN SUPERCONDUCTIVITY IN THE CUPRATES

We apply to cuprates a three-fluid ideal boson-fermion statistical model of superconductivity in two dimensions (2D) derived from three extrema of the system Helmholtz free energy (subject to constant total fermion-number) for the BCS model interaction between fermions. The same interactions absent in BCS theory are neglected here. As the ensuing bosonic Cooper pairs move not in vacuum but in a Fermi sea we employ the correct linear — as opposed to the commonly-assumed quadratic — dispersion relation in the center-of-mass momentum (CMM). More importantly, pair breakup beyond a certain (very small) CMM is accounted for. Bose–Einstein condensation (BEC) critical temperatures of about 800 K result for moderate coupling with cuprate parameters.

Simple accurate coupled cluster results for the linear E⊗e pseudo-Jahn–Teller effect

Using the coupled cluster method (CCM), we present a simple accurate calculation for the energies of the ground- and first excited states of the linear E⊗e Jahn–Teller and pseudo-Jahn–Teller Hamiltonians. From the solution of a single transcendental equation, we obtain results with a maximal error of 1.2%. These results are notably better than previous results obtained both via the CCM and other many-body approximations.