Quadrupole Quantized Hinge Arcs in Crystalline Dirac Semimetals

Topological semimetals, from graphene in 2D to Weyl semimetals in 3D, have been shown to display topological surface states on boundaries with one fewer dimension than that of the bulk. In this talk, I present the discovery of the first 3D semimetal with topological surface states in two fewer dimensions than its bulk, such that it displays arcs on its 1D hinges connecting the projections of its bulk 3D Dirac points. Using the recently developed multipole generalization of topological electric moments, I use nested Wilson loops to show that 2D slices of this semimetal can be modeled using hybridized spinful s and d orbitals in a magnetic layer group, and are topologically equivalent to recently presented spinless, flux-based models of insulators with quantized quadrupole moments. I then demonstrate that “hinge-arc” Dirac semimetals can be realized with or without time-reversal symmetry, and discuss the prospects for realizing topological hinge arcs in previously synthesized crystals.