Illuminating the Bragg intersections as roots of Dirac nodal lines and high-order van Hove singularities

Abstract

We theoretically reexamine nearly uniform electron models with weak crystalline potentials. In particular, we theorize the modulation of the plane-wave branches at linear regions where multiple Bragg planes intersect. Any such linear intersections involve three or more plane-wave branches diffracted by the periodic potential. Small interbranch interactions can yield various crossing and anticrossing singularities with promised breakdown of the quadratic approximation, extending alongside the intersection lines. Most of the intersections run in low-symmetric paths in the Brillouin zone and therefore we cannot completely characterize their electronic states with standard band-structure plotting methods. The present theory reveals a general mechanism in nearly uniform systems to induce the Dirac nodal lines and van Hove singularities with broken quadratic band approximation in three dimensions, which may host a variety of anomalous low-energy electronic properties. We apply the theory to a recently discovered high-temperature superconductor H3S to interpret the enigmatic density-of-state (DOS) peaking therein. The results show how and the continuous saddle points–the source of the peaked DOS–emerge, as well as reveal the companion Dirac nodal lines hidden in the conduction bands. Published by the American Physical Society 2024