Superconductivity and the Van Hove Scenario

Abstract

We give a review of the role of the Van Hove singularities in superconductivity. Van Hove singularities (VHs) are a general feature of low-dimensional systems. They appear as divergences of the electronic density of states (DOS). Jacques Friedel and Jacques Labbé were the first to propose this scenario for the A15 compounds. In NbTi, for example, Nb chains give a quasi-1D electronic structure for the d-band, leading to a VHs. They developed this model and explained the high T C and the many structural transformations occurring in these compounds. This model was later applied by Jacques Labbé and Julien Bok to the cuprates and developed by Jacqueline Bouvier and Julien Bok. The high T C superconductors cuprates are quasibidimensional (2D) and thus lead to the existence of Van Hove singularities in the band structure. The presence of VHs near the Fermi level in the cuprates is now well established. In this context we show that many physical properties of these materials can be explained, in particular the high critical temperature T C , the anomalous isotope effect, the superconducting gap and its anisotropy, and the marginal Fermi liquid properties, they studied these properties in the optimum and overdoped regime. These compounds present a topological transition for a critical hole doping p ≈ 0.21 hole per CuO 2 plane.

Systematic study of the superconducting critical temperature in two- and three-dimensional tight-binding models: A possible scenario for superconducting H3S

“…using the density of states from Eq. (14). There is a clear enhancement of T c , especially near the van Hove singularity.…”

“…These ideas were further developed with the discovery of high temperature superconductivity in 1986, and several papers 11,12 subsequently explored some of the consequences of a twodimensional van Hove singularity for superconductivity. Rather than recount a detailed history of the various calculations, we refer the reader to review papers, a comprehensive one in 1997, 13 and a more recent review 14 focussed on the A15 compounds. While the early work focussed on a square-root singularity, most of the work in the last 30 years has almost exclusively utilized a density of states with a logarithmic divergence, motivated by the two-dimensional tight-binding model.…”

Multi-band $s_{++}$ superconductivity in $\textrm{V}_{3}\textrm{Si}$ determined from the response to a controlled disorder

“…At the time of its discovery in 1953 [1], a cubic (A15 structure) V 3 Si compound showed the highest superconducting transition temperature, around 17 K. Despite showing a clear exponential attenuation of all thermodynamic quantities upon cooling towards T = 0, signaling a fully gapped Fermi surface, most of the spectroscopic [2,3], transport [4,5] and thermodynamic measurements [3,[6][7][8] show unconventional behavior or at least unusual features. Naturally, such behavior could be associated with a peculiar electronic band-structure showing Van Hove singularities in the density of states (DOS) close to the Fermi level [3,[9][10][11]. While this certainly plays an important role, now we know that a multi-gap superconductivity is needed as well.…”

“…There is a complication, though. Perhaps due a variation of stoichiometry, atomic disorder or extremely strain-sensitive structure of Van Hove singularities in the vicinity of the Fermi level, V 3 Si samples show a spread of behaviors, especially in the properties related to a two-gap superconductivity [4,8,10,11,24,30,33]. Furthermore, establishing a multi-band nature from thermodynamic measurements is necessary, but insufficient for microscopic understanding of superconductivity, because the order parameter enters thermodynamic quantities in the even powers and so the gaps of the same or opposite signs on different bands give the same result [7,27,34,35].…”

Applying experimental constraints to a one-dimensional model for BiS2 superconductivity

“…This has led to renewed interest in the Ruthenate compound Sr 2 RuO 4 , discovered in 1994 7 , which is one of the few candidates to realizing pwave-type SC 8,9 , another candidate being the organic superconductor (TMTSF) 2 PF 6 . It should also be emphasized that, as was the case for intermetallics with A15 structure (like Nb 3 Sn or V 3 Si) 10 , the Ruthenates display 'hidden' quasi-onedimensional (quasi-1d) SC 11 (while organic superconductors are explicitly 1d). Finally, we also mention SC in doped semiconductors, studied since before the 60s 12 , with the interest greatly increasing after the discovery of SC in Boron-doped Diamond with T c = 4 K 13 .…”