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Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law…
Two-dimensional and three-dimensional massless Dirac fermions can form a sequence of quasibound states with an attractive charged impurity. These quasibound states exhibit a discrete scaling symmetry, i.e., the energy ratio between two…
Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not…
Mass is commonly regarded as an intrinsic property of matter, but modern physics reveals particle masses to have complex origins, such as the Higgs mechanism in high-energy physics. In crystal lattices such as graphene, relativistic Dirac…
Interaction driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite making its…
Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators [1, 2]. At a Dirac point, two energy bands…
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,…
We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nano-wires. We modelled the non-uniform nano-wires as junction between two cylindrical nano-wires…
We study the topological properties of magnon excitations in three-dimensional antiferromagnets, where the ground state configuration is invariant under time-reversal followed by space-inversion ($PT$-symmetry). We prove that Dirac points…
Band crossings observed in a wide range of condensed matter systems are recognized as a key to understand low-energy fermionic excitations that behave as massless Dirac particles. Despite rapid progress in this field, the exploration of…
We address the issue whether it is possible to generate Majorana bound states at the magnetic-superconducting interface in two-dimensional topological insulators with hidden Dirac points in the spectrum. In this case, the Dirac point of…
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…
The recent discovery of Dirac semimetals represents a new achievement in our fundamental understanding of topological states of matter. Due to their topological surface states, high mobility, and exotic properties associated with bulk Dirac…
Electrons in a Dirac semimetals possess linear dispersion in all three spatial dimensions, and form part of a developing platform of novel quantum materials. Bi$_{1-x}$Sb$_x$ supports a three-dimensional Dirac cone at the Sb-induced band…
Nodal-line semimetals with magnetic orders have been theoretically predicted and experimentally observed in only few compounds. We theoretically explore the electronic structure in bulk and boundary of such a magnetic nodal-line state by…
Planar topological superconductors with power-law-decaying pairing display different kinds of topological phase transitions where quasiparticles dubbed nonlocal-massive Dirac fermions emerge. These exotic particles form through long-range…
Dirac materials have unique transport properties, partly due to the presence of surface states. A new type of Dirac materials, protected by non-symmorphic symmetries was recently proposed by Young and Kane [1]. By breaking of time reversal…
In two-dimensional Dirac semimetals, massless Dirac fermions can form a series of Efimov-like quasibound states in an attractive Coulomb potential. In an applied magnetic field, these quasibound states can become bound states around the…
While "Dirac cone" dispersions can only be meaningfully defined in two dimensional (2D) systems, the notion of a Dirac point can be extended to three dimensional (3D) classical wave systems. We show that a simple cubic photonic crystal…
Motivated by the results of recent transport and optical conductivity studies, we propose a semi-infinite two-dimensional lattice model for interacting massive Dirac electrons in the pressurized organic conductor…