Conversion rules for Weyl points and nodal lines in topological media

Understand

According to a widely-held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together.

• In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue.
• Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision.
• Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states.