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We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electron-electron interaction, split into two (levels) associated with a "bond ordering" formation having a "Kekule…
We review the theoretical and experimental results connected with the electron states in two-dimensional Dirac systems paying a special attention to the atomic collapse in graphene. Two-electron bound states of a Coulomb impurity are…
The $\pi$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a…
Two-dimensional electrons in graphene are known to behave as massless fermions with Dirac-Weyl type linear dispersion near the Dirac crossing points. We have investigated the collective excitations of this system in the presence or absence…
We theoretically study the stability of three dimensional Dirac semimetals against short-range electron-electron interaction and quenched time-reversal symmetric disorder (but excluding mass disorder). First we focus on the clean…
The conductance of metallic graphene nanoribbons (GNRs) with single defects and weak disorder at their edges is investigated in a tight-binding model. We find that a single edge defect will induce quasi-localized states and consequently…
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature…
The paper presents the author view on spin-rooted properties of graphene supported by numerous experimental and calculation evidences. Dirac fermions of crystalline graphene and local spins of graphene molecules are suggested to meet a…
Graphene -a recently discovered one-atom-thick layer of graphite- constitutes a new model system in condensed matter physics, because it is the first material in which charge carriers behave as massless chiral relativistic particles. The…
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…
Electrons and holes in clean, charge-neutral graphene behave like a strongly coupled relativistic liquid. The thermo-electric transport properties of the interacting Dirac quasiparticles are rather special, being constrained by an emergent…
As a canonical response to the applied magnetic field, the electronic states of a metal are fundamentally reorganized into Landau levels. In Dirac metals, Landau levels can be expected without magnetic fields, provided that an inhomogeneous…
We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. In the clean system, the density of states vanishes quadratically at the Dirac point. Disorder is known to be perturbatively irrelevant, and…
The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended…
Magic-angle twisted bilayer graphene (TBG) exhibits a captivating phase diagram as a function of doping, featuring superconductivity and a variety of insulating and magnetic states. The bands host Dirac fermions with a reduced Fermi…
We consider the effects of weak quenched fermionic disorder on the quantum-phase transition between the Dirac semimetal and charge density wave (CDW) insulator in two spatial dimensions. The symmetry breaking transition is described by the…
We analyze numerically ensembles of tight-binding Hamiltonians describing highly-symmetric graphene nanoflakes with weak diagonal disorder induced by random electrostatic potential landscapes. When increasing the disorder strength,…
The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport…
Itinerant electrons in a two-dimensional Kagome lattice form a Dirac semi-metal, similar to graphene. When lattice and spin symmetries are broken by various periodic perturbations this semi-metal is shown to spawn interesting non-magnetic…
Massless Dirac fermions occur as low-energy modes in several quasi-two-dimensional condensed matter systems such as graphene, the surface of bulk topological insulators, and in layered organic semiconductors. When the rotational symmetry in…