Related papers: Zero-energy states of massive Dirac equation in ma…
Quantum electrodynamics predicts that heavy atoms ($Z > Z_c \approx 170$) will undergo the process of atomic collapse where electrons sink into the positron continuum and a new family of so-called collapsing states emerges. The relativistic…
We study the interaction of electrons in graphene with the quantized electromagnetic field in the presence of an applied uniform electric field using the Dirac model of graphene. Electronic states are represented by exact solutions of the…
A number of physical processes occurring in a flat one-dimensional graphene structure under the action of strong time-dependent electric fields are considered. It is assumed that the Dirac model can be applied to the graphene as a subsystem…
We consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In…
We discuss free Dirac fermions rotating uniformly inside a cylindrical cavity in the presence of background magnetic field parallel to the cylinder axis. We show that in addition to the known bulk states the system contains massive edge…
We study the planar magnetic textures in an insulating magnetic film coupled to the Dirac surface state of a topological insulator. It is shown that the radial vortex with winding number $w=\pm1$ leads to the confinement of Dirac states,…
Massless Dirac fermions in graphene at charge neutrality form a strongly interacting system in which both charged and neutral (energy) modes play an important role. These modes are essentially decoupled in the absence of a magnetic field,…
A close study is made of the static structure factor for graphene in a magnetic field at integer filling factors nu, with focus on revealing possible signatures of "relativistic" quantum field theory in the low-energy physics of graphene.…
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…
The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed.
We find a new type of topological vortex solution in the $U(1)_Z \times U(1)_A$ Chern Simons gauge theory in the presence of a $U(1)_A$ magnetic field background. In this theory $U(1)_Z$ is broken spontaneously by the $U(1)_A$ magnetic…
The low energy quasiparticle dispersion of various narrow gap and gapless semiconductors are respectively described by three dimensional massive and massless Dirac fermions. The three dimensional Dirac spinor structure admits a…
The Dirac approach to include magnetic charge in Maxwell's equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical…
Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a…
We consider $(2+1)$ dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states and the Dirac Hamiltonians are…
In this article we discuss generalized harmonic confinement of massless Dirac fermions in (2+1) dimensions using smooth finite magnetic fields. It is shown that these types of magnetic fields lead to conditional confinement, that is…
The induced current density, corresponding to the massless Dirac equation in (2+1) dimensions in a magnetic flux tube of small radius is considered. This problem is important for graphene. In the case, when an electron can not penetrate the…
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum…
The second-order Dirac equation (DE) and its velocity operator of graphene electrons in an electromagnetic field are obtained according to tight-binding k.p method. With extra terms included, they demonstrate the motion of graphene…
In Dirac's hole theory the vacuum state is generally believed to be the state of minimum energy. It will be shown that this is not, in fact, the case and that there must exist states in hole theory with less energy than the vacuum state. It…