Related papers: Quantum confinement in Dirac-like nanostructures
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
The non-trivial topology of the three-dimensional (3D) topological insulator (TI) dictates the appearance of gapless Dirac surface states. Intriguingly, when a 3D TI is made into a nanowire, a gap opens at the Dirac point due to the quantum…
In topological quantum materials the conduction and valence bands are connected at points (Dirac/Weyl semimetals) or along lines (Line Node semimetals) in the momentum space. Numbers of studies demonstrated that several materials are indeed…
The relativistic nature of Dirac electrons and holes in graphene profoundly affects the way they interact with impurities. Signatures of the relativistic behavior have been observed recently in scanning tunneling measurements on individual…
We recall Dirac's early proposals to develop a description of quantum phenomena in terms of a non-commutative algebra in which he suggested a way to construct what he called `quantum trajectories'. Generalising these ideas, we show how they…
We present calculations of electronic quantum transport in graphene nanoribbons with adsorbed H, F, OH and O, based on a tight binding model derived from extended Huckel theory. The relaxed atomic geometries of the adsorbates and graphene…
The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. Topological insulators…
Quantum transition probabilities and quantum entanglement for two-qubit states of a four level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a…
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range…
We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic…
The model of a classical particle with the weak linear AAD potential is subjected to path integral quantization. The light cone constraints and peculiar properies of its internal variables permit to use in calculations commutative dynamics…
We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system…
Starting from the QCD Lagrangian and taking into account both perturbative and nonperturbative effects, we use the method of vacuum correlators to derive the Dirac equation (rigorously for the Coulomb interaction and heuristically for the…
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scaterring and the Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector…
We discuss the relation of the Kerr-Newman spinning particle to the Dirac electron and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the Kerr-Newman geometry. As a…
We first review the application of Dirac's method to the dynamics of a classical particle constrained to a circle and its subsequent quantization. Then, we extend the analysis to a particle constrained to move on an ellipse. Particularly,…
The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…
The three dimensional (3D) Dirac semimetal, which has been predicted theoretically, is a new electronic state of matter. It can be viewed as 3D generalization of graphene, with a unique electronic structure in which conduction and valence…