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

## TL;DR

This paper reveals that strong and fragile topological Dirac semimetals host universal higher-order Fermi arcs as direct consequences of their bulk Dirac points, establishing a topological bulk-boundary correspondence.

## Contribution

It introduces a layered spinful model of quadrupole insulators and develops a nested Jackiw-Rebbi formulation to predict and analyze higher-order Fermi arcs in Dirac semimetals.

## Key findings

- HOFAs are demonstrated in Cd3As2, KMgBi, and PtO2 via ab initio calculations.
- HOFAs coexist with surface states in topological Dirac semimetals.
- The study establishes a bulk-boundary correspondence for Dirac semimetals.

## 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 $ab\ initio$ calculations, we demonstrate HOFAs in both the room- ($\alpha$) and intermediate-temperature ($\alpha''$) phases of Cd$_{3}$As$_2$, KMgBi, and rutile-structure ($\beta'$-) PtO$_2$.