BCS superconductivity in the van Hove scenario in s and d waves

Abstract

The e ect of including a van Hove singularity in the density of state of a renormalized BCS equation in s and d waves and its appropriateness in describing some properties of high-Tc cuprates in the weak-coupling region are studied in two space dimensions. The speci c heat and knight shift as a function of temperature exhibit scaling below the critical temperature in d wave. We also study the jump in the speci c heat at the critical temperature Tc in s and d waves, which can have v alues signi cantly higher than the standard BCS values and which increases with Tc, as experimentally observed in many d-wave high-Tc materials. The experimental results on the speci c heat and knight shift of the Y-123 system are compared with the theoretical predictions.The discovery of high-T c cuprates 1 with many unusual properties both above and below the critical temperature T c presents a serious question on the applicability of the Bardeen-Cooper-Schrie er BCS theory of superconductivity 2 , 3 at high temperatures. The high-T c materials have many u n usual properties, such as, an anomalously large C and 0 =T c and small isotope e ect, where C is the jump in speci c heat at T c and 0 is the zero-temperature BCS gap.Despite much e ort, the normal state of the high-T c cuprates has not been satisfactorily understood yet and there are controversies about the appropriate microscopic Hamiltonian and pairing mechanism 4, 5 . The use of a van Hove singularity vHs in the density of states DOS near or at the Fermi surface makes the standard BCS model more suitable for the high-T c cuprates 6, 7, 8 . The singularity in the density o f states known as the van Hove singularity arises wherever the group velocity v anishes and where there is a locally at region of the frequency as a function of the wavevector k. The critical points where these singularities are observed may be saddle points. In high T c compounds there have been evidences of saddle points which yield a logarithmic divergence. Moreover recent experiments 9, 1 0 h a ve given evidences of an extended saddle point singularity which corresponds to a power law behavior 7 . The use of a vHs in the DOS can simulate di erent non-Fermi liquid type properties of both the normal and superconducting states 6, 7 . Some experiments also suggest a peak in the DOS associated with a vHs near the Fermi level 11, 9 , 1 2 . There have been attempts to explain many anomalous features of the high-T c cuprates using a vHs in the DOS 6, 7 : such as the large values of C and 0 =T c , anomalous isotope e ect, pressure coe cient o f T c , temperature variation of speci c heat C s T and knight shift etc. Virtually, in all these applications an s-wave i n teraction has been employed.However, there are evidences that some of the high-T c cuprates have singlet d-wave Cooper pairs and the gap parameter has d x 2 ,y 2 symmetry in two dimensions 5 . Recent measurements of the penetration depth T 11, 9 , 12 and superconducting speci c heat at different temperatures T 11, 9, 12 and related theoretical analyse...

Inverse scattering approach to coupled higher-order nonlinear Schrödinger equation and N-soliton solutions

“…It is easy to see using the equation of motion that H 1 , H 3 , H 5 are indeed the constants of motion. If we choose the field q, a scalar field then we are able to show that H 1 , H 3 , H 5 reduce to the conserved quantities for the scalar Sasa-Satsuma equation [24].…”

“…It is important to note that the equation (1) is the multifield generalization of the Sasa-Satsuma equation [7]. Interestingly for Sasa-Satsuma (scalar) equation two different 1SS were reported in [7,23,24,25]. One is the convensional sech solution having a single peak and the other is a complex combination of sech function having two peaks.…”

The Walled City of Kowloon and the University of Hong Kong

“…On the other hand, the proximity of a Van Hove singularity (VHS) in the vicinity of the Fermi level, accompanied by a saddle point band structure, presents an alternate avenue to amplify superconductivity. Firstly, the divergence in the density of states, endowing the potential for heightened critical temperatures [23][24][25][26][27] ; and secondly, the provocation of unconventional electron pairing via the anisotropic architecture and the coexistent presence of electrons and holes [28][29][30] . In this work we provide spectroscopic experimental substantiation for the coexistence of flat bands and Van Hove singularity within nitrogen doped lutetium hydride.…”