Formal derivation of the Laughlin function and its generalization for other topological phases of FQHE

Using the braid symmetry we demonstrate the derivation of the Laughlin function for the main hierarchy 1/q of FQHE in the lowest Landau level of two-dimensional electron system with a mathematical rigour. This proves that the derivation of Laughlin function unavoidably requires some topological elements and cannot be completed within a local quantum mechanics, i.e., without global topological constraints imposed. The method shows the way for the generalization of this function onto other fractions from the general quantum Hall hierarchy. A generalization of the Laughlin function is here formulated.

Спонтанный спиновый магнетизм донорных электронов проводимости гибридизированных состояний кристалла, образованных системой примесных атомов 3d-элементов низкой концентрации (<1 at.%)

The given work is devoted to the experimental proof of existing the spontaneous spin polarization of the donor electron system of 3d-transition element impurity atoms of low concentration (<1 at.%) in a mercury selenide crystal. For this purpose there have been measured the dependences of the magnetization on the magnetic field strength. As a result of the analysis of the obtained dependences, there were extracted the impurity contributions, which are described by the magnetization curves typical of the ferromagnets, and by the magnetic parameters conforming to the spontaneous magnetism of the systems under study, which are unambiguously related to the donor conduction electrons of the outer d-shells of impurity atoms. By its nature, according to the developed theoretical concepts, the spontaneous spin polarization manifests itself in exchange interaction, taking place in hybridizing the electronic states of the impurity atom and the conduction band ones of the crystal.

Двумерные электроны низкой плотности в магнитном поле

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered.

Reparametrization of the Colle–Salvetti formula

We investigate the Colle–Salvetti (CS) formula, the basis of the Lee, Yang and Parr (LYP) correlation functional used in approximate density functional theory. The CS formula is reparametrized using high-accuracy Hartree–Fock (HF) wavefunctions to determine the accuracy of the formula to calculate anions. Fitting to the hydride ion or the two-electron system just prior to electron detachment at the HF level of theory does not, in general, improve the calculated correlation energies using the parameters derived from the CS/LYP method. An analysis of the CS parameters used in the popular LYP functional demonstrates the ingenuity and perhaps fortuitousness of the original formulation by CS.

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.