Theoretical Aspects of Superconductivity

Schafeoth, M.R.

doi:10.1016/s0081-1947(08)60704-3

Cited by 20 publications

(6 citation statements)

References 330 publications

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“…The two-particle potential, in the case of (6), is determined by the equation U (2) δγ,αβ (r, r ′ ) = −gδ γα δ δβ δ (r − r ′ ) , (11) which reflects the point nature of the interaction between electrons in the BCS theory. The approximating Bogolyubov Hamiltonian for the model Hamiltonian ( 8)- (11) has the form…”

Section: The Bogolyubov-de Gennes Equationsmentioning

confidence: 99%

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Phonon softening in nanostructured phonon–mediated superconductors (review)

Prischepa

Kushnir

2023

J. Phys.: Condens. Matter

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Various aspects of phonon spectrum changes in nanostructured phonon-mediated superconductors are considered. It is shown how, with the development of experimental techniques and, accordingly, obtaining new results, the understanding of the influence of the surface and nanoscale on the magnitude of the electron-phonon interaction and the critical temperature Tc changed and deepened. The review is organized as follows. After the Introduction, in the first part we give the quick theoretical background for the description of superconductivity within the framework of various formalisms. In the second part we describe the properties of granular thin films paying attention to the impact of grain sizes and methods of deposition on the Tc value. The role of material parameters is underlined and different aspects of the behavior of granular thin films are discussed. In the third section the impact of external sources of modification of the phonon spectra like noble gases and organic molecules are considered. Problems and progress in this area are discussed. The fourth part is dedicated to the phonon modification and related quantum size effects in nanostructured superconductors. In the fifth part we review the results of direct evidence of phonon softening in nanostructured superconductors and in the sixth section we discuss a possible alternative description of the superconducting properties of nanostructured superconductors related to the concept of metamaterials. In the seventh and eighth parts we review the impact of substrates with lattice mismatched parameters and graphene sheets, respectively, on the modification of the phonon spectrum and enhancement of superconductivity in various superconducting thin films. Finally, in the last ninth section we consider the nonequilibrium superconductivity driven by femtosecond pulses of light, which leads to generation of coherent phonons and to a significant increase in the critical temperature in a number of superconducting materials.

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Section: The Bogolyubov-de Gennes Equationsmentioning

confidence: 99%

“…The Fröhlich-Bardeen hypothesis caused quite justified skepticism [9][10][11][12]. First, the validity of the procedure for calculating the energy gap according to the perturbation theory (as well as from the variational principle) turned out to be questionable.…”

Section: Introductionmentioning

confidence: 99%

Phonon softening in nanostructured phonon–mediated superconductors (review)

Prischepa

Kushnir

2023

J. Phys.: Condens. Matter

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“…With the action of the magnetic field on a supercon- ductor is associated the penetration depth  . If the field outside a superconductor is equal to 0 H , its decrease measured inside a sample on a distance z from its surface is represented by the formula [23,24]…”

Section: Penetration Depth In One-dimensional Superconductors and Itsmentioning

confidence: 99%

Low Dimensionality as a Factor Stimulating Formation of the Cooper-Like Pairs Characteristic for Superconductors

Olszewski¹,

Roliński²

2010

JMP

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The electron gas examined in a very thin potential tube exhibits some special kind of the excited pairs making them similar to the Cooper pairs. The coupling energy of the pair can be calculated as an amount of energy required to transform the excitation energy of a coupled pair into the one-electron excitation energy. For an extremely thin potential tube the coupling energy of the pair tends to infinity. The gas energy is unstable with respect to the pair excitation which provides a kind of gap near the Fermi level. A decisive part of the gap energy is due to the electron-electron interaction. The gap is attained on condition the length of a thin potential box exceeds some critical value. In the next step, a coherence length in the gas is obtained. This length, combined with a critical magnetic field representing a transition from a superconducting to a normal state, allows us to calculate the penetration depth of the magnetic field for the singlet and triplet excitations. The penetration depth together with the critical magnetic field and energy gap can provide us with a critical current, as well as critical temperature for the superconducting state

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“…The first factor of 2 in the last line comes precisely from the condition n 0 (T ) = m 0 (T ) while the last two factors of 2 arise from the condition that according to (5) and (6) the magnitudes of f + (ǫ) and f − (ǫ) are the same and equal f . Subtracting (32) from (33) and putting N (ξ) ∼ = N (0), the density of electronic states at the Fermi surface [designated before as…”

Section: Condensation Energymentioning

confidence: 99%

The BCS–Bose crossover theory

Adhikari

Llano

Sevilla

et al. 2007

Physica C: Superconductivity

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We contrast four distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e-and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-T.D. Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h-and 2e-CPs in both BE-condensed and noncondensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h-or 2e-CPs it can do neither. In particular, only half the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures Tc from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the Tcs of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy). 74.20.Mn; 05.30.Fk; 05.30.Jp

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Theoretical Aspects of Superconductivity

Cited by 20 publications

References 330 publications

Phonon softening in nanostructured phonon–mediated superconductors (review)

Phonon softening in nanostructured phonon–mediated superconductors (review)

Low Dimensionality as a Factor Stimulating Formation of the Cooper-Like Pairs Characteristic for Superconductors

The BCS–Bose crossover theory

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