ON THE EQUIVALENCE OF THE BINDING ENERGY OF A COOPER PAIR AND THE BCS ENERGY GAP: A FRAMEWORK FOR DEALING WITH COMPOSITE SUPERCONDUCTORS

2010 ◽  
Vol 24 (09) ◽  
pp. 1159-1172 ◽  
Author(s):  
G. P. MALIK
Keyword(s):  
Binding Energy ◽  
Cooper Pair ◽  
Energy Gap ◽  
Direct Consequence ◽  
Bcs Theory ◽  
Subsequent Paper ◽  
Hartree Fock ◽  
Composite Superconductors ◽  
The One ◽  
Particle Propagator

Employing the Bethe–Salpeter equation (BSE) and the Matsubara recipe, and invoking both the electron–electron and the hole–hole scattering channels, we establish that the binding energy (W) of a Cooper pair (CP) is real, and equals the BCS energy gap (Δ) for all T ≤ Tc for a one-component superconductor. Given that the BCS theory is a generalization of the Hartree–Fock theory (generalized to allow for particle number fluctuations), the cognescenti would expect this result as a direct consequence of Koopman's theorem, proved for and well-known in the latter theory. However, this theorem is seldom mentioned in the literature on superconductivity; on the contrary, there is the statement in well-known texts that the binding energy of a CP becomes imaginary when the above-stated scattering channels are invoked for their formation. The importance of |W| = |Δ| for high-Tc superconductors is brought out by replacing the one-particle propagator in the BSE by a superpropagator — a field-theoretic construct apt for dealing with composite superconductors (CSs). A set of generalized BCS equations is thus obtained which, with the input of the multiple gaps of a CS, enables one to calculate its Tc uniquely. Applications of these equations will be taken up in a subsequent paper.

GENERALIZED BCS EQUATIONS: APPLICATIONS

2010 ◽  
Vol 24 (19) ◽  
pp. 3701-3712 ◽  
Author(s):  
G. P. MALIK
Keyword(s):  
Cooper Pair ◽  
Energy Gap ◽  
High Temperature Superconductors ◽  
Bcs Theory ◽  
Simple Extension ◽  
Cooper Pairs ◽  
Debye Temperatures ◽  
Unified Study ◽  
Interesting Candidate ◽  
Composite Superconductors

Based on the concepts of a superpropagator, multiple Debye temperatures, and equivalence of the binding energy of a Cooper pair and the BCS energy gap, the set of generalized BCS equations obtained recently via a temperature-generalized Bethe–Salpeter equation is employed for a unified study of the following composite superconductors: MgB 2, Nb 3 Sn , and YBCO. In addition, we study the Nb – Al system in which Cooper pairs as resonances have recently been reported to have been observed. Our approach seems to suggest that a simple extension of the BCS theory that accommodates the concept of Cooper pairs bound via a more than one phonon exchange mechanism may be an interesting candidate for dealing with high-temperature superconductors.

scholarly journals A simple mechanism for unconventional superconductivity in a repulsive fermion model

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
Kevin Slagle ◽  
Yong Baek Kim
Keyword(s):  
Cooper Pair ◽  
Energy Gap ◽  
Tight Binding ◽  
Hard Core ◽  
Particle Energy ◽  
Bcs Theory ◽  
Unconventional Superconductivity ◽  
Fermion Model ◽  
Repulsive Interactions ◽  
Degenerate Perturbation Theory

Motivated by a scarcity of simple and analytically tractable models of superconductivity from strong repulsive interactions, we introduce a simple tight-binding lattice model of fermions with repulsive interactions that exhibits unconventional superconductivity (beyond BCS theory). The model resembles an idealized trilayer. The Cooper pair consists of electrons on opposite sides of the dielectric, which mediates the attraction. In the strong coupling limit, we use degenerate perturbation theory to show that the model reduces to a superconducting hard-core Bose-Hubbard model. Above the superconducting critical temperature, an analog of pseudo-gap physics results where the fermions remain Cooper paired with a large single-particle energy gap.

Structure, Stability and Water Adsorption on Ultra-Thin TiO2 Supported on TiN

2019 ◽  
Author(s):  
Jose Julio Gutierrez Moreno ◽  
Marco Fronzi ◽  
Pierre Lovera ◽  
alan O'Riordan ◽  
Mike J Ford ◽  
...  
Keyword(s):  
Density Functional ◽  
Water Adsorption ◽  
Chemical Potential ◽  
Energy Gap ◽  
Molecular Water ◽  
Structure Stability ◽  
Ambient Conditions ◽  
Rutile Structure ◽  
The Stability ◽  
The One

<p></p><p>Interfacial metal-oxide systems with ultrathin oxide layers are of high interest for their use in catalysis. In this study, we present a density functional theory (DFT) investigation of the structure of ultrathin rutile layers (one and two TiO<sub>2</sub> layers) supported on TiN and the stability of water on these interfacial structures. The rutile layers are stabilized on the TiN surface through the formation of interfacial Ti–O bonds. Charge transfer from the TiN substrate leads to the formation of reduced Ti<sup>3+</sup> cations in TiO<sub>2.</sub> The structure of the one-layer oxide slab is strongly distorted at the interface, while the thicker TiO<sub>2</sub> layer preserves the rutile structure. The energy cost for the formation of a single O vacancy in the one-layer oxide slab is only 0.5 eV with respect to the ideal interface. For the two-layer oxide slab, the introduction of several vacancies in an already non-stoichiometric system becomes progressively more favourable, which indicates the stability of the highly non-stoichiometric interfaces. Isolated water molecules dissociate when adsorbed at the TiO<sub>2</sub> layers. At higher coverages the preference is for molecular water adsorption. Our ab initio thermodynamics calculations show the fully water covered stoichiometric models as the most stable structure at typical ambient conditions. Interfacial models with multiple vacancies are most stable at low (reducing) oxygen chemical potential values. A water monolayer adsorbs dissociatively on the highly distorted 2-layer TiO<sub>1.75</sub>-TiN interface, where the Ti<sup>3+</sup> states lying above the top of the valence band contribute to a significant reduction of the energy gap compared to the stoichiometric TiO<sub>2</sub>-TiN model. Our results provide a guide for the design of novel interfacial systems containing ultrathin TiO<sub>2</sub> with potential application as photocatalytic water splitting devices.</p><p></p>

The Energy Band Structure of Polyacene with Soliton Excitation

1997 ◽  
Vol 11 (11) ◽  
pp. 477-483 ◽  
Author(s):  
Z. J. Li ◽  
H. B. Xu ◽  
K. L. Yao
Keyword(s):  
Band Structure ◽  
Charge Density ◽  
Energy Band ◽  
Energy Gap ◽  
Electronic States ◽  
Energy Band Structure ◽  
Energy Spectra ◽  
Energy Band Gap ◽  
The One ◽  
Soliton Excitation

Starting from the extensional Su–Schrieffer–Heeger model taking into account the effects of interchain coupling, we have studied the energy spectra and electronic states of soliton excitation in polyacene. The dimerized displacement u0 is found to be similar to the case of trans-polyacetylene, and equals to 0.04 Å. The energy-band gap is 0.38 eV, in agreement with the results derived by other authors. Two new bound electronic states have been found in the conduction band and in the valence band, which is different from the one of trans-polyacetylene. There exists two degenerate soliton states in the center of energy gap. Furthermore, the distribution of charge density and spin density have been discussed in detail.

scholarly journals EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER–MULTIELECTRON INTEGRALS

2009 ◽  
Vol 08 (04) ◽  
pp. 597-602 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Charge Densities ◽  
Hartree Fock ◽  
Expansion Formulae ◽  
Multicenter Multielectron Integrals ◽  
Explicitly Correlated ◽  
Explicitly Correlated Methods ◽  
Exponential Type Orbitals ◽  
The One

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETO α = 1,0,-1,-2,…) introduced by the author. Three-center overlap integrals of Ψα appearing in these relations are expressed through the two-center overlap integrals between Ψα-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter–multielectron integrals occurring when the complete orthonormal sets of Ψα-ETO are used as basis functions in the Hartree–Fock–Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter–multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Ψα-orbitals.

THE INNER CRUST OF NEUTRON STARS IN RELATIVISTIC MEAN FIELD APPROACH

2008 ◽  
Vol 17 (09) ◽  
pp. 1765-1773 ◽  
Author(s):  
JIGUANG CAO ◽  
ZHONGYU MA ◽  
NGUYEN VAN GIAI
Keyword(s):  
Boundary Conditions ◽  
Neutron Stars ◽  
Mean Field ◽  
Bcs Theory ◽  
Neutron Density ◽  
Field Approach ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Rmf Model

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

To what question is the Badiouan notion of the subject an answer? On the dialectical elaboration of the concept in his early work

2016 ◽  
Vol 43 (1) ◽  
pp. 96-120
Author(s):  
Jan-Jasper Persijn
Keyword(s):  
Direct Consequence ◽  
The Other ◽  
The Political ◽  
Academic World ◽  
Systematic Account ◽  
Political Field ◽  
Political Implications ◽  
The Subject ◽  
The One ◽  
Work Up

Alain Badiou’s elaboration of a subject faithful to an event is commonly known today in the academic world and beyond. However, his first systematic account of the subject ( Théorie du Sujet) was already published in 1982 and did not mention the ‘event’ at all. Therefore, this article aims at tracing back both the structural and the historical conditions that directed Badiou’s elaboration of the subject in the early work up until the publication of L’Être et l’Événément in 1988. On the one hand, it investigates to what extent the (early) Badiouan subject can be considered an exceptional product of the formalist project of the Cahiers pour l’Analyse as instigated by psychoanalytical discourse (Lacan) and a certain Marxist discourse (Althusser) insofar as both were centered upon a theory of the subject. On the other hand, this article examines the radical political implications of this subject insofar as Badiou has directed his philosophical aims towards the political field as a direct consequence of the events of May ’68.

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