Related papers: A Relativistic One Dimensional Band Model with Pos…
Mutual dependencies of mass and orbital moment increase for rotating bodies of various configurations (a string with uniform mass distribution, a string with squared mass distribution or a sphere with uniform mass distribution, double…
We present a detailed study of a generalised one-dimensional Kronig-Penney model using $\delta\text{-}\delta'$ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite…
We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size $N$…
We study the effects of random positional disorder in the transmission of waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical expression for the localization length and relate it to the transmission coefficient for…
For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The…
We consider a model for a one-dimensional photonic crystal formed by a succession of Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate the band structure and reflectance of this structure as a function of…
In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the left-handed and right-handed projection operators. Next, we explicitly…
System of Dirac fermions with random-varying mass is studied in detail. We reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random telegraphic mass…
In the framework of the band theory, we consider two tight-binding models of insulators. The first one, proposed recently by Taraskin et al, is a translationally invariant system, built out of two independent non-overlapping bands of…
In this work, we demonstrate an alternative method of deriving an isotropic energy band model using a one-dimensional definition of the effective mass and experimentally observed dependence of mass on energy. We extend the effective mass…
A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov-Kimball model. For the half-filled band, the single-particle density matrix $\uprho (x,y)$ in the ground state and in…
In this work, a one-dimensional model of crystalline solids based on the Dirac comb limit of the Kronig-Penney model is considered. From the wave functions of the valence electrons, we calculate a statistical measure of complexity and the…
Locally periodic rods, which show approximate invariance with respect to translations, are constructed by joining $N$ unit cells. The spectrum then shows a band spectrum. We then break the local periodicity by including one or more defects…
We present a systematic method of creating type-III Dirac cones from degenerate directionally flat bands. Here, the directionally flat band means a completely dispersionless band only in a certain direction. The key strategy is to retain…
The Dirac equation is extended for a relativistic electron in an orthorhombically-anisotropic conduction band. Its covariance is established with general proper and improper Lorentz transformations. In the non-relativistic limit, the…
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a…
The existence of flat bands is generally thought to be physically possible only for dimensions larger than one. However, by exciting a system with different orthogonal states this condition can be reformulated. In this work, we demonstrate…
Two forms of relativistic density functional are derived from Dirac equation. Based on their structure analysis model of split electron is proposed. In this model electric charge and mass of electron behave like two point-like particles. It…
We study low-energy properties of the random displacement model, a random Schr\"odinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are…
We show that four narrow zigzag dice lattice ribbons, which have the minimal widths among their separate categories, constitute a unique collection of systems to study physics related to one-dimensional Dirac cones and flat bands. In zero…