"Hinge" surface states in Weyl semimetals

Topological insulators have anomalous surface states due to the bulk-edge correspondence. In recent years, a higher-order topological insulator (HOTI) has been proposed. It is insulating both in the bulk and in the surface. However, it has anomalous gapless hinge states at the hinges, which are intersections of two surfaces. One interesting question here is whether we can define a gapless counterpart of the HOTI, i.e. a "higher-order" topological semimetal. As a step to answer this question, we study an intermediate Weyl semimetal phase between a normal insulator phase and an inversion-symmetric HOTI phase [1]. We investigate its hinge states and clarify how the hinge states develop from the Fermi-arc surface states, which are well-known anomalous surface states in Weyl semimetals. By using tight-binding models, we demonstrate that in some cases, gapless hinge states in topological semimetals are separated in the momentum space from gapless surface/bulk states. On the other hand, they may merge into gapless surface/bulk states in some cases.
[1]E. Khalaf, H.C. Po, A. Vishwanath, H. Watanabe, arXiv:1711.11589 (2017).