Behavior of Andreev states for topological phase transition

Theoretical and Mathematical Physics - We consider three one-dimensional superconducting structures: 1) the one with $$p$$ -wave superconductivity; 2) the main experimental model of a nanowire with...     

Width of electron-transparency windows at structural geometric resonance in a planar nanostructure

Structural geometric resonance of low-energy electrons is considered for nanostructures consisting of three crystalline films. The width of electron-transparency windows is shown to increase with increasing interfilm potential induced by the dipole charge of the outer films.     

Decay law for a quasistationary state of the Schrödinger operator for a crystal film

For the Schrödinger operator in a cell corresponding to a crystal film pattern, eigenvalues may exist in the continuous spectrum and become resonances under perturbations. We prove that the corresponding decay law in a nonstationary approach is exponential for a nondegenerate (in some cases, degenerate) eigenvalue.     

Resonance multiplicity of a perturbed periodic Schrödinger operator

We consider the perturbation of a periodic Schrödinger operator by a potential that is periodic in the variables x₁ and x₂ and exponentially decreases as |x₃|→∞. Near the zero surface of the derivative of the eigenvalue of the periodic operator in a cell with respect to the third quasi-momentum component, we obtain relations between the resonance multiplicity and the order of the pole of the quantities characterizing the scattering. As a rule, the forward scattering amplitude vanishes on this surface.     

Schrödinger Operator Levels for a Crystal Film with a Nonlocal Potential

For a crystal film, we consider the Schrödinger operator defined on Bloch functions (with respect to two variables) in a cell. The potential is the sum of two small terms: a function decreasing with respect to the third variable and an operator of rank one. We prove the existence of two levels (eigenvalues or resonances) near the parameter value E=0 and obtain their asymptotic behavior.     

Majorana States Near an Impurity in the Kitaev Infinite and Semi-Infinite Model

Theoretical and Mathematical Physics - For an infinite Kitaev chain with an impurity described by a deltalike potential, we analytically prove that two overlapping Majorana bound states in a...     

Electron scattering at the domain wall

We study the transmission and reflection coefficients for the Hamiltonian of a spin-polarized electron passing through the domain wall in a ferromagnetic quantum wire. We prove that total reflection occurs for energies λ ∈ (−α, α) (−α is the boundary of the essential spectrum) for both sufficiently small and sufficiently large λ, which agrees with the ballistic magnetoresistance effect in ferromagnetic nanocontacts. For energies λ > α, almost total reflection becomes almost total transmission, and both effects occur without a spin flip.     

Specific features of low-energy electron scattering by thin films of cubic crystals

The specific features of the electron states in thin films of cubic crystals are considered in the energy range above the vacuum zero of the crystal potential. It is demonstrated that bands of bound states embedded in the energy continuum can exist along particular directions of the two-dimensional Brillouin zone. These bands can substantially affect the intensity of low-energy electron scattering.     

On the schrödinger equation for a flat film with an asymptotically periodic grating

For a potential asymptotically periodic in x ₁ , x ₂ and decreasing at |x ₃ | , the Schrödinger equation is solved and some properties of the solutions are described.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 133–144, January, 1996.     

Solutions of the Schrödinger equation in the case of a semiinfinite crystal

It is shown that bounded solutions of Bloch type with respect to the variablesx ₁,x ₂ for a Schrödinger equation in which the potential is periodic in the half-space {x ₃0} and decreases exponentially asx ₃– can be approximated by the solutions of the Schrödinger equation for a thick film when the number of its layers tends to infinity. Under certain conditions, this makes it possible to find the number of linearly independent solutions of such kind.Physicotechnical Institute, Urals Scientific Center, Russian Academy of Sciences, Sverdlovsk. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 38–47, January, 1994.