Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Benjamin J Wieder,Leslie M Schoop,Barry Bradlyn,Zhijun Wang,Jennifer Cano,B Andrei Bernevig,Xi Dai

doi:10.1038/s41467-020-14443-5

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 one-dimensional (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- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure ( beta ^{prime} -) PtO2.

Highlights

Topological nature of the higher-order Fermi-arc (HOFA) states by performing several extensive calculations that bridge the significant gap between previously established theoretical concepts and the candidate real-material HOFA Dirac semimetals identified in this work
We use TQC22 to formulate a new, spinful model of a quadrupole insulators (QIs) derived from s–d-orbital hybridization in a magnetic layer group, and show that it is topologically equivalent to the spinless model with staggered magnetic flux proposed in ref. 23
We prove using band representations a Corner 2D Bulk Edge c b

Summary

Methods

All tight-binding, surface state, hinge state, and Wilson loop calculations were performed using the standard implementation of the open-source PYTHTB Python package. Nested Wilson loop calculations were performed using an extension of PYTHTB that is documented in ref. First-principles calculations were performed using the projector augmented wave method as implemented in the Vienna Ab initio Simulation Package. The hinge states of α′′-Cd3As2, KMgBi, and β′-PtO2 were obtained by mapping the bands closest to the Fermi energy to tight-binding models and calculating the Green’s function along a single 1D hinge of a slab that was infinite along the crystal axis parallel to the hinge and respectively finite and semi-infinite along the two perpendicular axes. Further details of our first-principles and hinge Green’s function calculations are provided in Supplementary Note 13

Results

Discussion

Conclusion