Related papers: Two Interacting Electrons in a Disorder Potential:…
We study a system in which the quantum dynamics of electrons depend on the particle density in their neighborhood. For any on-site repulsive interaction, we show that the exact two-body and three-body ground states are bound states. We also…
The problem of two electrons in a square billiard interacting via a finite-range repulsive Yukawa potential and subjected to a constant magnetic field is considered. We compute the energy spectrum for both singlet and triplet states, and…
A number of novel two-dimensional materials and nanostructures demonstrate complex single-electron energy dispersion, which is called the mexican-hat dispersion. In this paper, we analyze interaction of a pair of electrons with such an…
Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…
We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define…
This paper is written as a brief introduction for beginning graduate students. The picture of electron waves moving in a cristalline potential and interacting weakly with each other and with cristalline vibrations suffices to explain the…
We report results of a numerical study of non-interacting electrons moving in a random potential in two dimensions in the presence of a weak perpendicular magnetic field. We study the topological properties of the electronic eigenstates…
We have studied the non-ohmic effects in the conductivity of a two-dimensional system which undergoes the crossover from weak to strong localization with decreasing electron concentration. When the electrons are removed from equilibrium…
In this paper we consider pairs of interacting electrons moving in a simple quantum wire, namely the half-line. In particular, we extend the results obtained in [arXiv:1708.03753] by allowing for contact interactions of the Lieb-Liniger…
The influence of disorder and interaction on the ground state polarization of the two-dimensional (2D) correlated electron gas is studied by numerical investigations of unrestricted Hartree-Fock equations. The ferromagnetic ground state is…
We investigate a one-dimensional wire of interacting electrons connected to semi-infinite leads in the absence and in the presence of a backscattering potential. An incident electron on the clean wire is perfectly transmitted into spatially…
We investigate the effect of electron-electron interactions on proximity-induced $s$-wave superconductivity in one-dimensional nanowires. We treat the interactions on a self-consistent mean-field level, and find an analytic expression for…
Using Single Electron Capacitance Spectroscopy, we study electron additions in quantum dots containing two potential minima separated by a shallow barrier. Analysis of addition spectra in magnetic field allows us to distinguish whether…
Electrons in condensed matter may transition into a variety of broken-symmetry phase states due to electron-electron interactions. Applying diverse mean-field approximations to the interaction term is arguably the simplest way to identify…
We consider the change in electron localization due to the presence of electron-electron repulsion in the \HA model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an…
We study the effect of electron-electron interaction on a two dimensional (2D) disordered lattice. For the case of two electrons the analytical estimates are presented showing a transition from localized to delocalized states in a way…
The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, non-local cluster self-energy ($\Sigma_c[{\cal \tilde{G}}](i,j\neq…
We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length $\lambda_2$ on disorder and interaction strength is investigated. Our results…
The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at $E_c = \epsilon_{a,b}$ of two possible values of the chemical potential in case of…
Electron localization is the tendency of an electron in a many-body system to exclude other electrons from its vicinity. Using a new natural measure of localization based on the exact manyelectron wavefunction, we find that localization can…