Coulomb repulsion and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>in BCS theory of superconductivity

Zheng, X. H.; Walmsley, D.G.

doi:10.1103/physrevb.71.134512

Cited by 20 publications

(32 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with the N and U-processes being illustrated by the solid and dashed curved arrows in figure 1, respectively, both arrows start from k. Also consider the event arising from the second term in the brackets: which is not normalized unless h N or h U vanishes, consistent with the conclusion in [30][31][32].…”

Section: Discussionsupporting

confidence: 55%

See 1 more Smart Citation

Empirical rule to reconcile Bardeen–Cooper–Schrieffer theory with electron–phonon interaction in normal state

Zheng

Walmsley

2014

Phys. Scr.

View full text Add to dashboard Cite

We introduce a simple empirical rule wherein the pairing interaction in superconductors is cancelled when normal and umklapp phonon scattering coexist. Superconductivity then arises solely from the residual umklapp contribution. As a result the deduced electron-phonon interactions in niobium, tantalum, lead and aluminum become virtually identical in the normal and superconducting states. Transition temperatures calculated under the rule are accurate within a few per cent when compared with experimental data. Features of the Matthias relations are also explained. The high T c so far predicted for metallic hydrogen is probably overly optimistic.

show abstract

Section: Discussionsupporting

confidence: 55%

“…This is a manifestation of the algebraic contradiction within the original BCS theory [30][31][32] that the ground state electronic wavefunction cannot be normalized when normal and umklapp scattering coexist, see appendix.…”

Section: Umklapp Dilemmamentioning

confidence: 99%

Empirical rule to reconcile Bardeen–Cooper–Schrieffer theory with electron–phonon interaction in normal state

Zheng

Walmsley

2014

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Such a potential is known as the Bogoliubov potential. 56,57 This approximation has been used to show extremely counterintuitive behavior of the gap equation and justify a-posteriori another heavily criticized approximation of BCS, neglecting Coulomb repulsion: the BCS mechanism indeed assumes only attraction between electrons, which can be dimmed by Coulomb repulsion, but which never explicitly appears as such (like in the Bogoliubov scenario). The great result of Cooper was that binding occurs at arbitrarily small attraction.…”

Section: Bogoliubov Potentialmentioning

confidence: 98%

Superconductivity with excitons and polaritons: review and extension

Laussy

2012

J. Nanophoton

View full text Add to dashboard Cite

A system where a Bose-Einstein condensate of exciton-polaritons coexists with a Fermi gas of electrons has been recently proposed as promising for realization of roomtemperature superconductivity. In order to find the optimum conditions for exciton and excitonpolariton mediated superconductivity, we studied the attractive mechanism between electrons of a Cooper pair mediated by the exciton and exciton-polariton condensate. We also analyzed the gap equation that follows. We specifically examined microcavities with embedded n-doped quantum wells as well as coupled quantum wells hosting a condensate of spatially indirect excitons, put in contact with a two-dimensional electron gas. An effective potential of interaction between electrons was derived as a function of their exchanged energy ℏω, taking into account the retardation effect that allows two negatively charged carriers to feel an attraction. In the polariton case, the interaction is weakly attractive at long times, followed by a succession of strongly attractive and strongly repulsive windows. Strikingly, this allows high critical temperature solutions of the gap equation. An approximate three-steps potential is used to explain this result that is also obtained numerically. The case of polaritons can be compared with that of excitons, which realize the conventional scenario of high-T c superconductivity where a large coupling strength accounts straightforwardly for the high critical temperatures. Excitons are less advantageous than polaritons but may be simpler systems to realize experimentally. It is concluded that engineering of the interaction in these peculiar Bose-Fermi mixtures is complex and sometimes counter-intuitive, but leaves much freedom for optimization, thereby promising the realization of high-temperature superconductivity in multilayered semiconductor structures.

show abstract

“…It is designed to overcome: (1) conceptual and numerical difficulties of the BCS theory and (2) uncertainty associated with l Ã . It is justified by its highly accurate first principles calculations for superconducting niobium, lead, [41][42][43][44][45][46][47][48] Contents lists available at ScienceDirect Physica C j o u r n a l h o m e p a g e : w w w .…”

Section: Theoretical Approachmentioning

confidence: 99%

“…Some time ago we identified a fundamental conceptual difficulty in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity [1,2]. Independently, in a thorough review of the theory, Hirsch concluded that it ''is fundamentally flawed'' and ''may be destined to be overhauled just as other established scientific theories of the past have been overhauled'' [3].…”

Section: Introductionmentioning

confidence: 96%