Related papers: Trapped Modes and Steered Dirac Cones in Platonic …
This study is devoted to the profound implications of tilted Dirac cones on the quantum transport properties of two-dimensional (2D) Dirac materials. These materials, characterized by their linear conic energy dispersions in the vicinity of…
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion…
Dirac-like band crossings are paradigms in condensed matter systems to emulate high-energy physics phenomena. They are associated with two aspects: gap and tilting. The ability to design sign-changing gap gives rise to band topology,…
Existence and stability of Dirac points in the dispersion relation of operators periodic with respect to the hexagonal lattice is investigated for different sets of additional symmetries. The following symmetries are considered: rotation by…
Topological characteristics of energy bands, such as Dirac/Weyl nodes, have attracted substantial interest in condensed matter systems as well as in classical wave systems. Among these energy bands, the type-II Dirac point is a nodal…
We investigate linear and nonlinear evolution dynamics of light beams propagating along a dislocated edge-centered square lattice. The band structure and Brillouin zones of this novel lattice are analyzed analytically and numerically.…
We study the transport properties of Dirac fermions in a graphene-based double-barrier structure composed of two tilted-cone regions separated by a central pristine graphene region. Using the transfer matrix method, we systematically…
The Dirac fermion with linear dispersion in the kagom\'e lattice governs the low-energy physics of different valleys at two inequivalent corners of hexagonal Brillouin zone. The effective Hamiltonian based on the cyclic permutation symmetry…
Galvanised by the emergent fields of metamaterials and topological wave physics, there is currently much interest in controlling wave propagation along structured arrays, and interfacial waves between geometrically different crystal…
It is recent that the emergence of topological insulators in condensed matter physics has inspired analogous wave phenomena in mechanical systems, mostly in the setting of discrete lattice models. Here we report a numerical and experimental…
It is well known that a single Dirac cone at high-symmetry point (HSP) of a Brillouin zone, akin to the one in graphenes' band structure, can not appear as the only quasiparticle at the Fermi level in two-dimensional (2D), non-magnetic…
We explore a new class of topologically stable zero energy modes which are protected by coexisting chiral and spatial symmetries. If a chiral symmetric Hamiltonian has an additional spatial symmetry such as reflection, inversion and…
We investigate the spectrum and the dispersion relation of the Schr\"odinger operator with point scatterers on a triangular lattice and a honeycomb lattice. We prove that the low-level dispersion bands have conic singularities near Dirac…
At magic twisted angles, Dirac cones in twisted bilayer graphene (TBG) can evolve into flat bands, serving as a critical playground for the study of strongly correlated physics. When chiral symmetry is introduced, rigorous mathematical…
In electronic topological Dirac semimetals the conduction and valence bands touch at discrete points in the Brillouin zone and form Dirac cones. They are robust against spin-orbit interaction (SOI) and protected by crystal symmetries. They…
We argue that spin and valley-polarized metallic phases recently observed in graphene bilayers and trilayers support chiral edge modes that allow spin waves to propagate ballistically along system boundaries without backscattering. The…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
Massless Dirac fermions in an electric field propagate along the field lines without backscattering, due to the combination of spin-momentum locking and spin conservation. This phenomenon, known as "Klein tunneling", may be lost if the…
We reconsider the problem of surface states spectrum in type One Dirac metals. We find that the surface states, despite being gapped, always form branches terminating at Dirac points. Furthermore, we consider evolution of the surface states…
We show theoretically that, in the limit of weak dispersion, one-dimensional (1D) binary centrosymmetric photonic crystals can support topological edge modes in all photonic band gaps. By analyzing their bulk band topology, these "harmonic"…