Related papers: A Spatial Localizer for Electrons in Insulators
We present a simple and general method for construction of localized orbitals to describe electronic structure of extended periodic metals and insulators as well as confined systems. Spatial decay of these orbitals is found to exhibit…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show…
A new quantum algebraic description of relativistic electrons, built on a conformal dynamical symmetry (SO(4,2)), has recently been proposed to treat localization in space-time. It is shown here that localization of an electron may be…
Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with…
We study localized two- and three-dimensional Langmuir solitons in the framework of model based on generalized nonlinear Schr\"odinger equation that accounts for local and nonlocal contributions to electron-electron nonlinearity. General…
The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
While band insulators are usually described in wavevector space in terms of fully filled bands, they are sometimes also described in terms of a complementary Wannier picture in which electrons occupy localized, atom-like orbitals. Under…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative…
Calculations for two electrons in an elliptic quantum dot, using symmetry breaking at the unrestricted Hartree-Fock level and subsequent restoration of the broken parity via projection techniques, show that the electrons can localize and…
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the…
Analysis of experimental data shows that the metal--insulator transition is possible in materials composed of atoms of only metallic elements. Such a transition may occur in spite of the high concentration of valence electrons. It requires…
The 2D system of electron confined to the lowest Landau level is described using a representation of the density matrix depending both on electron and hole coordinates. Condensation of the electron system into a fractional quantum Hall…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
We report new accurate mesasurements of the mobility of excess electrons in high density Helium gas in extended ranges of temperature $[(26\leq T\leq 77) K ]$ and density $[ (0.05\leq N\leq 12.0) {atoms} \cdot {nm}^{-3}]$ to ascertain the…
A two-dimensional electron gas in a high magnetic field displays macroscopically degenerate Landau levels, which can be split into Hofstadter subbands by means of a weak periodic potential. By carefully engineering such a potential, one can…
A theory for an electron affinity of ionic clusters is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. An interaction of an electron with longitudinal optical phonons in…