Quantum hall effects in two-dimensional electron systems: a global approach

Up to almost the last two decades all the experimental results concerning the quantum Hall effect (QHE), i.e. the observation of plateaux at integer or fractional (FQHE) values of the constant h/e2, were related to quantum-wells in semiconductor heterostructures. However, more recently, a renewed interest in revisiting these phenomena has arisen thanks to the observation of entirely similar effects in graphene and topological insulators. In this paper we show an approach encompassing all these QHEs using the same theoretical frame, entailing both Hall effect plateaux and Shubnikov-de Haas oscillations. Moreover, the model also enables the analysis of both phenomena as a function not only of the magnetic field but the gate voltage as well. More specifically, in the light of the approach, the FQHE in any two-dimensional electron system appears to be an effect of the breaking of the degeneration of every Landau level, n, as a result of the electrostatic interaction involved, and being characterized by the set of three integer numbers (n, p, q), where p and q have clear physical meanings too.

How to Calculate Condensed Matter Electronic Structure Based on Multi-Electron Atom Semi-Classical Model

Atoms are proved to be semi-classical electronic systems in the sense of closeness of their exact quantum electron energy spectrum with that calculated within semi-classical approximation. Introduced semi-classical model of atom represents the wave functions of bounded in atom electrons in form of hydrogen-like atomic orbitals with explicitly defined effective charge numbers. The hydrogen-like electron orbitals of constituting condensed matter atoms are used to calculate the matrix elements of the secular equation determining the condensed matter electronic structure in the linear-combination-of-atomic-orbitals (LCAO) approach. Preliminary test calculations are conducted for boron B atom and diboron B2 molecule electron systems.

Hydrogen and Lithium Bonds—Lewis Acid Units Possessing Multi-Center Covalent Bonds

MP2/aug-cc-pVTZ calculations were carried out on complexes wherein the proton or the lithium cation is located between π-electron systems, or between π-electron and σ-electron units. The acetylene or its fluorine and lithium derivatives act as the Lewis base π-electron species similarly to molecular hydrogen, which acts as the electron donor via its σ-electrons. These complexes may be classified as linked by π-H∙∙∙π/σ hydrogen bonds and π-Li∙∙∙π/σ lithium bonds. The properties of these interactions are discussed, and particularly the Lewis acid units are analyzed, because multi-center π-H or π-Li covalent bonds may occur in these systems. Various theoretical approaches were applied here to analyze the above-mentioned interactions—the Quantum Theory of Atoms in Molecules (QTAIM), the Symmetry-Adapted Perturbation Theory (SAPT) and the Non-Covalent Interaction (NCI) method.