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 inter-branch 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 H$_{3}$S to interpret the enigmatic density-of-state (DOS) peaking therein. The results show how and {\it why there} 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.