Related papers: Embedding on to a one-dimensional crystal
Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a…
Previously reported formulation for electrons on curved periodic surfaces is used to analyze the band structure of an electron bound on the gyroid surface (the only triply-periodic minimal surface that has screw axes). We find that an…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
Accurate analytic approximations are developed for the band gap boundaries and surface waves of a 1D photonic crystal, making use of the semiclassical theory recently developed by the authors: [Phys. Rev. E {69} (2004) 016612 and {70}…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
We study the homogenization of a Schrodinger equation in a periodic medium with a time dependent potential. This is a model for semiconductors excited by an external electromagnetic wave. We prove that, for a suitable choice of oscillating…
In this article we consider the one-dimensional Schrodinger operator L(Q) with a Hermitian periodic m by m matrix potential Q. We investigate the bands and gaps of the spectrum and prove that the main part of the positive real axis is…
Exact and general results on the electronic states in one dimensional crystals bounded at tau and tau+L - where L=Na, N is a positive integer and a is the potential period - are presented. Corresponding to each energy band of Bloch wave,…
We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrodinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size…
We describe a broad class of bounded non-periodic potentials in one-dimensional stationary quantum mechanics having the same spectral properties as periodic potentials. The spectrum of the corresponding Schroedinger operator consists of a…
We study an impurity in a one-dimensional potential consisting of a harmonic and a periodic part using both the time-evolving block decimation (TEBD) algorithm and a variational ansatz. Attractive and repulsive contact interactions with a…
We consider a spatially periodic (cosine) potential as a model for a crystalline solid that interacts with a harmonically oscillating external electric field. This problem is periodic both in space and time and can be solved analytically…
The zero-range potentials of the radial Schrodinger equation are investigated from a point of Darboux transformations scheme. The dressing procedure is realized as a sequence of Darboux transformations in a way similar to that used to…
The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
We introduce a general first-principles methodology for computing electronic structure in a finite uniform magnetic field which allows for an arbitrary rational magnetic flux and nonlocal pseudopotentials, at a comparable time complexity of…
In the effective-mass approximation, the step-like crystal potential of a wurtzite semiconductor heterostucture should be supplemented by Dirac delta-function heterointerface terms. They stem from the difference in the Bloch functions of…
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…
A general method is presented to unfold band structures of first-principles super-cell calculations with proper spectral weight, allowing easier visualization of the electronic structure and the degree of broken translational symmetry. The…
The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of…