Topologically unavoidable points and lines of crossings in the band structure of solids

Rules are developed for a new kind of topologically unavoidable branch crossing in the band structure of solids. It is proved that there exists a great variety of four-branch energy bands in crystalline solids of the orthorhombic system in which the crossings are necessitated by symmetry and topology. These crossings are different from conventional degeneracies that follow from space group symmetry alone, and they can take place on either points or lines in the Brillouin zone. (author)