van Hove Singularities and Strong Electron-Phonon Coupling: Superconductivity and H₃S

van Hove singularities (vHs) have long been implicated in high temperature suuperconductivity. In A15 superconductors, with T_c up to 23K, Labe and coworkers proposed and studied a 1D vHs associated iwth the transition metal chains. In the cuprates, Newns et al introduced the role of the 2D vHs associated with the square lattice tight binding model. For H₃S we have emphasized [3] the importance of vHs and the concept of spectral smearing due to strong electron-phonon coupling. vHs cause peaks and fine structure in the electronic density of states, whichiis the root of their interest. vHs "mirroring" has lately been proposed [4]as the mechanism behind the weak AFM emerging at low temperature in TiAu, which has a sharper and higher DOS peak than does H₃S. Why is it magnetic rather than superconducting? The formalism for the smearing effect has been around a while,[5] with application to A15 compounds. vHs cause another complication, because electron velocities become less that phonon velocities near the vHs, violating the Midgal theorem premise of Eliashberg theory; this aspect was addressed by Drozhov[6] who found non-quasiparticle behavior near the vHs, but many questions remain. This talk will discuss the various aspects of vHs primarily in 3D materials, with special focus on H₃S. Recent work has been done in collaboration iwth Yundi Quan.

[1] J. Labbe et al., PRL 19, 1039 (1967).
[2] D. M. Newns et al., PRL 69, 1264 (1992).
[3] Y. Quan and W. E. Pickett, PRB 93, 104526 (2016).
[4] W. F. Goh and W. E. Pickett, PRB 85, 205124 (2017); EPL 116, 27004 (2016).
[5] W. E. Pickett, PRL 48, 1548 (1982); PRB 26, 1186 (1982).
[6] Yu. P. Drozhov, Phys. Stat. Sol. (b), 98, 781 (1980).