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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…
Three-dimensional Dirac semimetals (DSMs) have been shown to exhibit one-dimensional hinge modes which are termed the higher-order hinge Fermi-arc (HOFA) states. They are the topological consequences of Dirac points. Superconducting states…
In recent years, there has been a surge of interest in exploring higher-order topology and their semi-metallic counterparts, particularly in the context of Dirac, Weyl, and nodal line semimetals, termed as higher-order Dirac semimetal…
Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with four-fold rotation symmetry have been shown to exhibit a higher order bulk-hinge correspondence: they display "higher order Fermi arcs," which are…
Usually the quantum spin Hall states are expected to possess gapless, helical edge modes. Are there clean, non-interacting, quantum spin Hall states without gapless, edge modes? We show the generic, $n$-fold-symmetric, momentum planes of…
In this article we study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs). Our focus is on $C_4$-symmetric non-Hermitian systems where we investigate inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) symmetric models of…
Recently, higher-order topological matter and 3D quantum Hall effects have attracted great attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed in Weyl semimetals is characterized by the one-sided hinge states, which do…
Topological Dirac semimetals are a class of semimetals that host symmetry-protected Dirac points near the Fermi level, which arise due to a band inversion of the conduction and valence bands. In this work, we study the less explored class…
Higher-order topological insulators and semimetals, which generalize the conventional bulk-boundary correspondence, have attracted extensive research interest. Among them, higher-order Weyl semimetals feature two-fold linear crossing points…
The zero gap surface states of a 3D-topological insulator host Dirac fermions with spin locked to the momentum. The gap-less Dirac fermions exhibit electronic behaviour different from those predicted in conventional materials. While…
KZnBi was discovered recently as a new three-dimensional Dirac semimetal with a pair of bulk Dirac fermions in contrast to the $\mathbb{Z}_2$ trivial insulator reported earlier. In order to address this discrepancy, we have performed…
We study with first-principles methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological…
We theoretically demonstrate hybrid-order topology in a two-dimensional nonsymmorphic antiferromagnet. Utilizing a generic antiferromagnetic Dirac model with a symmetry-allowed, momentum-dependent spin-density-wave (SDW) mass, we show that…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional…
A Berry phase of odd multiples of $\pi$ inferred from quantum oscillations (QOs) has often been treated as evidence for nontrivial reciprocal space topology. However, disentangling the Berry phase values from the Zeeman effect and the…
The discovery of topological semimetal phase in three-dimensional (3D) systems is a new breakthrough in topological material research. Dirac nodal-line semimetal is one of the three topological semimetal phases discovered so far; it is…
We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, that we dub a $2nd$ order Weyl node, that can be identified as a transition in…
We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II semimetallic candidates \emph{M}Al$_3$ (where, \emph{M} = V, Nb and Ta). The angular-dependence of their Fermi surface (FS) cross-sectional areas reveals a remarkably…
The field of topological electronic materials has seen rapid growth in recent years, in particular with the increasing number of weakly interacting systems predicted and observed to host topologically non-trivial bands. Given the broad…
We demonstrate theoretically the coexistence of Dirac semimetal and topological insulator phases in InSb/$\alpha$-Sn conventional semiconductor superlattices, based on advanced first-principles calculations combined with low-energy $k\cdot…