Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs

Abstract

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit 1D higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an $s-d$-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw-Rebbi formulation of QIs and HOFA states. Employing $abinitio$ calculations, we demonstrate HOFAs in both the room- ($\alpha$) and intermediate-temperature (${\alpha }^{\prime \prime }$) phases of Cd${}_3$As${}_2$, KMgBi, and rutile-structure (${\beta }^{\prime }$-) PtO${}_2$.

Post Final Version, 12 + 73 pages, 5 + 26 figures. Revtex version updated, minor formatting changes. Sign error corrected in Eq. (D16) and Figs. 8 and 10 replotted with updated parameters, results and conclusions unaffected by this correction. Nested Wilson loop code with example scripts and documentation freely available at https://github.com/kuansenlin/nested_and_spin_resolved_Wilson_loop

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