Short-distance breakdown of the Higgs mechanism and the robustness of the BCS theory for charged superconductors

Abstract

Through the Higgs mechanism, the long-range Coulomb interaction eliminates the low-energy Goldstone phase mode in superconductors and transfers spectral weight all the way up to the plasma frequency. Here we show that the Higgs mechanism breaks down for length scales shorter than the superconducting coherence length while it stays intact, even at high energies, in the long-wavelength limit. This effect is a consequence of the composite nature of the Higgs field of superconductivity and the broken Lorentz invariance in a solid. Most importantly, the breakdown of the Higgs mechanism inside the superconducting coherence volume is crucial to ensure the stability of the BCS mean-field theory in the weak-coupling limit. We also show that changes in the gap equation due to plasmoninduced fluctuations can lead to significant corrections to the mean-field theory and reveal that changes in the density-fluctuation spectrum of a superconductor are not limited to the vicinity of the gap. arXiv:1711.11382v2 [cond-mat.supr-con]

Superconducting size effect in thin films under electric field: Mean-field self-consistent model

“…Phaseplasmon fluctuation effects in principle can be included in the approach above in a standard way by expanding in Re ∆, Im ∆ and V = −iφ around the mean-field solution. A priori, in view of some existing results, 38,42 however, it's not clear why such corrections would depend strongly on the external electric field.…”

Nonequilibrium susceptibility in photoinduced Floquet states

“…The time-averaged Green functions in Eqs. (52) and (53) are the (m, n) = (0, 0) components of the above equations. Next, we calculate the time-averaged susceptibility, χ q (ω) = ( χ q ) 00 (ω).…”

Role of fluctuations for density-wave instabilities: Failure of the mean-field description

“…We can straightforwardly adopt the formalism developed in the context of superconductivity [18,21] to calculate the leading-order corrections to the zerotemperature mean-field gap equation due to Gaussian fluctuations of the order parameter for density-wave Fig. 3), it is of particular importance for the contributions stemming from the regime of short wavelengths.…”

“…These integrals (see Appendix B for details) are of the same structure as those arising in the context of superconductivity, and hence we can build on the results obtained by previous studies [18,21] in the remainder.…”

“…Experimentally, deviations from mean-field behavior have been observed for density-wave systems in the quantum regime [11][12][13][14]. The aim of this paper is to theoretically clarify to what extent CDW and SDW systems fulfill the second characteristic of the BCS theory, namely a lack of fluctuation corrections as discovered in the case of superconductivity [15][16][17][18][19][20][21]. We find that the result depends on the order-parameter manifold (in particular, the number of components), and on whether longitudinal or transverse fluctuations, i. e., fluctuations of the amplitude or of the phase of the order parameter, dominate.…”