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Topological semimetals, known for their intriguing properties arising from band degeneracies, have garnered significant attention. However, the discovery of a material realization and the detailed characterization of spinless Dirac…
We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband structure is developed that applies to a range…
Condensed matter systems can host quasiparticle excitations that are analogues to elementary particles such as Majorana, Weyl, and Dirac fermions. Recent advances in band theory have expanded the classification of fermions in crystals, and…
Emergent quasiparticles with a Dirac dispersion in condensed matter systems can be described by the Dirac equation for relativistic electrons, in analogy with Dirac particles in high-energy physics. For example, electrons with a Dirac…
In this review we discuss a wide range of topological properties of electron quasiparticles in Dirac and Weyl semimetals. Their nontrivial topology is quantified by a monopole-like Berry curvature in the vicinity of Weyl nodes, as well as…
Noncollinear and noncoplanar spin textures in solids manifest themselves not only in their peculiar magnetism but also in unusual electronic and transport properties. We here report our theoretical studies of a noncoplanar order on a simple…
Electrons in materials with linear dispersion behave as massless Weyl- or Dirac-quasiparticles, and continue to intrigue physicists due to their close resemblance to elusive ultra-relativistic particles as well as their potential for future…
Electronic properties of two-dimensional allotropes of carbon, such as graphene and its bilayer, multi-layer epitaxial graphene, few-layer Bernal-stacked graphene, as well as of three-dimensional bulk graphite are reviewed from the…
Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic…
Two-dimensional (2D) Dirac states with linear band dispersion have attracted enormous interest since the discovery of graphene. However, to date, 2D Dirac semimetals are still very rare due to the fact that 2D Dirac states are generally…
The Dirac equation for relativistic electron waves is the parent model for Weyl and Majorana fermions as well as topological insulators. Simulation of Dirac physics in three-dimensional photonic crystals, though fundamentally important for…
We propose that the noncentrosymmetric LiGaGe-type hexagonal $ABC$ crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. The symmetry-protected Dirac points arise due to a band…
The recent discoveries of Dirac fermions in graphene and on the surface of topological insulators have ignited worldwide interest in physics and materials science. A Weyl semimetal is an unusual crystal where electrons also behave as…
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
The surface states of Weyl semi-metals (SM's) consist of disjointed Fermi-arcs. This unusual surface-Fermiology provides a fingerprint of the topological features of the bulk Weyl-phase. Using a combination of semiclassical and numerical…
Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black…
We study the electronic properties of strongly spin-orbit coupled electrons on the elastic pyrochlore lattice. Akin to the Peierls transition in one-dimensional systems, the coupling of the lattice to the electronic degrees of freedom can…
We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $\theta=45^\circ$ and a pair of hexagonal lattices with…
Three-dimensional Dirac semimetals, a three-dimensional analogue of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry.…
Weyl and Dirac (semi)metals in three dimensions have robust gapless electronic band structures. Their massless single-body energy spectra are protected by symmetries such as lattice translation, (screw) rotation and time reversal. In this…