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The metallic surface states of a topological insulator support helical Dirac fermions protected by topology with their spin locked perpendicular to their momentum. They can acquire mass through magnetic doping or through hybridization of…
Topological semimetals with several types of three-dimensional (3D) fermion of electrons, such as Dirac fermions, Weyl fermions, Dirac nodal lines and triply degenerate nodal points have been theoretically predicted and then experimentally…
We show that a class of compounds with $I$4/$mcm$ crystalline symmetry hosts three-dimensional semi-Dirac fermions. Unlike the known two-dimensional semi-Dirac points, the degeneracy of these three-dimensional semi-Dirac points is not…
Graphene as a two-dimensional (2D) topological Dirac semimetal has attracted much attention for its outstanding properties and potential applications. However, three-dimensional (3D) topological semimetals for carbon materials are still…
Magnetic order in van der Waals magnets can strongly influence their lattice dynamics, yet how this interaction manifests across different phonon length scales remains unclear. Optical phonons probe bond-scale exchange modulation and…
The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, electronic correlations have so far been little investigated in Weyl…
Dirac and Weyl materials refer to a class of solid materials which host low-energy quasiparticle excitations that can be described by the Dirac and Weyl equations in relativistic quantum mechanics. Starting with the advent of graphene as…
We review recent theoretical and experimental developments in magnetic Weyl semimetals, focusing on the electromagnetic responses emerging from the interplay of their electronic band topology and magnetism. We begin by introducing the…
We use a symmetry approach to construct a systematic derivative expansion of the low energy effective Hamiltonian modifying the continuum Dirac description of graphene in the presence of non-uniform elastic deformations. We extract all…
In magnetic pyrochlore materials, the interplay of spin-orbit coupling, electronic correlations, and geometrical frustration gives rise to exotic quantum phases, including topological semimetals and spin ice. While these phases have been…
The electron-electron Coulomb interaction in Dirac-Weyl semimetals harbours a novel paradigm of correlation effects that hybridizes diverse realms of solid-state physics with their relativistic counterpart. Driving spontaneous mass…
Dirac materials respond to lattice deformations as if the electrons were coupled to gauge fields. We derive the elastic gauge fields in the hyperhoneycomb lattice, a three dimensional (3D) structure with trigonally connected sites. In its…
The recent discovery of Weyl fermions in solids enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. They are constituted of pairs of Weyl points with two-fold band degeneracy, which…
The rich structure of solid state physics provides us with Dirac materials the effective theory of which enjoys the Lorentz symmetry. In non-symmorphic lattices, the Lorentz symmetry will be deformed in a way that the null energy-momentum…
We theoretically study low energy electric transport in a junction consisting of a Weyl semimetal and a metallic superconductor. The characteristic features of the differential conductance depend on the relative directions between the…
Very recently, the standard description of electrons in strained graphene has been completed by the explicit inclusion of the lattice deformation. Here, the effect of these lattice corrections is taken into account to find the mechanical…
Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several…
In two-dimensional crystals that lack symmetry under reflections on the horizontal plane of the lattice (non-$\sigma_{\rm h}$-symmetric), electrons can couple to flexural modes (ZA phonons) at first order. We show that in materials of this…
Weyl semimetals typically appear in systems in which either time-reversal (T) or inversion (P}) symmetry are broken. Here we show that in the presence of gauge potentials these topological states of matter can also arise in fermionic…
Recent theoretical and experimental attemps have been successful in finding magnetic Weyl semimetal phases, which show both nodal-point structure in the electronic bands and magnetic orders. Beyond uniform ferromagnetic or antiferromagnetic…