We investigate the Read-Rezayi parafermion state of correlated electrons at the fractional Landau level filling ν=3/5. It is a Jack polynomial generated by contact four-body repulsion. We show by exact diagonalization that it is also emerges from a suitable short-range two-body interaction. We find that it closely matches Coulomb ground state in the second Landau level of non-relativistic fermions, and thus possibly describes the ν=13/5 (and, by conjugation, ν=12/5) fractional quantum Hall effect in GaAs.
Correlations in partially filled electron and composite fermion Landau levels are studied numerically. Insight into the nature of the correlations is obtained by using model pair pseudopotentials. Energy spectra of a model short-range three-body repulsion are calculated. Moore-Read ground state at the half-filling and its quasielectron, quasihole, magnetoroton, and pair-breaking excitations are all identified. The quasielectron/quasihole excitations are described by a composite fermion model for Laughlin-correlated electron pairs. Comparison of energy spectra and wavefunction overlaps obtained for different pseudopotentials suggests that finite-size effects can be important in numerical diagonalization studies on a sphere.
Pair-distribution functions g(r) of the Laughlin quasielectrons are calculated in the fractional quantum Hall states at electron filling factorsν=4/11 and 3/8. They all have a shoulder at a medium range, supporting the idea of quasielectron cluster formation. The intra- and inter-cluster contributions to g(r) are identified. The average cluster sizes are estimated; pairs and triplets of quasielectrons are suggested atν=4/11 and 3/8, respectively.
From the analysis of their interaction pseudopotentials, it is argued that (at certain filling factors) Laughlin quasiparticles can form pairs. It is further proposed that such pairs could have Laughlin correlations with one another and form condensed states of a new type. The sequence of fractions corresponding to these states includes all new fractions observed recently in experiment (e.g.,ν=5/13, 3/8, or 4/11).
We investigate properties of strongly correlated, spinless electrons confined within given Landau level at filling factor ν = 1/3. Our analysis is based on the formalism of the Jack polynomials. Selected Jack polynomial wave functions are compared with ground states of the Coulomb interaction Hamiltonians, in different materials and the Landau levels, obtained by exact diagonalization. We show that certain Jack wave functions can be used as a description of fractional quantum Hall states.
We study spin polarization of the ν_e=4/11 fractional quantum Hall state corresponding to the ν=1/3 filling of the second composite fermion Landau level, and predict a spin phase transition in realistic systems.
We study spin polarization of the ν_e=4/11 fractional quantum Hall state corresponding to the ν=1/3 filling of the second composite fermion Landau level, and predict a spin phase transition in realistic systems.
Two- and three-body correlation functions (number of pairs or triplets vs. relative angular momentum) of electrons or Laughlin quasielectrons (i.e., composite fermions in their first excited Landau level) are studied numerically in several fractional quantum Hall liquids. It is shown directly that theν_e=4/11 liquid (corresponding to aν=1/3 filling of composite fermions in their first excited Landau level) is a paired state of quasielectrons, hence interpreted as a condensate of "second-generation" quasiholes of Moore-Readν=1/2 state of composite fermions.
In the Weyl semimetals, a recently discovered class of bulk materials, inverted band gap closes in the first Brillouin zone at topologically protected points of degeneracy called the Weyl nodes. By using the Chern number formalism it is possible to assign to each of the nodes an integer topological charge Q. While around typical Weyl points the energy disperses linearly in all three directions, double-Weyl nodes (with |Q|=2) exhibit quadratic dispersion in two directions and linear in the third one. We use a simple 2-band tight-binding lattice model to investigate the dispersion of the Landau levels in the presence of quantizing magnetic field in the vicinity of a double-Weyl node. In the long wavelength limit we obtain analytically the expected presence of two chiral levels. In addition, we find numerous level crossings between the non-chiral Landau levels and the chiral ones, a feature which is distinct from the single node case. Calculations for a finite-size sample, both with periodic and hard-wall boundary conditions (the latter corresponding to slab geometry), show that the two chiral levels hybridize in the conduction band with the two lowest non-chiral Landau levels. In the case of slab geometry these four levels are responsible for the formation of a protected surface state.
Using exact numerical diagonalization we have studied correlated many-electron ground states in a partially filled second Landau level. We consider filling fractions ν = 1/2 and 2/5, for which incompressible quantum liquids with non-Abelian anion statistics have been proposed. Our calculations include finite layer width, Landau level mixing and arbitrary deformation of the interaction pseudopotential. Computed energies, gaps, and correlation functions support the non-Abelian ground states at both ν = 1/2 ("Pfaffian") and ν = 2/5 ("parafermion" state).
A simple model of disorder in fractional quantum Hall systems is combined with the standard exact diagonalisation technique. Electron-density-dependent gaps at filling factors 1/3,2/3,2/5, and 3/5 measured by activated transport can then be fitted with a single reasonable value of d which has the meaning of the separation of ionized donors from the quasi-2D electron gas.
We calculate topological contributions to the spin Hall and spin Nernst effects due to intrinsic spin-orbit interaction in a single-layer graphene. To describe electronic spectrum of the graphene we have assumed the k·p model as well as the full tight-binding Hamiltonian. The corresponding contributions to the spin Hall and spin Nernst effects have been determined using the linear response theory and Green function formalism.
Realistic calculations of photoluminescence spectra for a 20 nm quantum well at a filling factorν=1/3 are presented. The new states formed from charged excitons (trions) by correlation with the surrounding electrons are identified. These "quasiexcitons" differ from usual excitons and trions by having fractionally charged constituents. Their binding energies and emission intensities depend on the involved trion, leading to discontinuity in photoluminescence.
We seek for an oscillating center solution of the wave function satisfying the Schrödinger equation for a nonrelativistic charge particle in an arbitrary external field, where the oscillating center of physical system is a motion governing by a guidance formula of the classical mechanics and at the same time, the physical system obeys the rule of quantum mechanics. In terms of our approach, one enables to know how quantum process may actually come about. The results are applied to analyze the Landau level. We explain successfully that the orbit of oscillator center for the Landau level is circle.
The quantum Hall ferromagnets at the half-filling of a pair of degenerate electron or composite fermion Landau levels are studied by exact numerical diagonalization. The results obtained using open and closed geometries (rectangular - with periodic boundary conditions and spherical) are compared. The ferro- and paramagnetic ground states are identified in finite-size energy spectra, and the pair-correlation functions are used in search of the domain structure at half-polarization.
We review results of our modeling of excitons and excitonic trions confined in vertically stacked InGaAs/GaAs self-assembled quantum dots. Electrons and holes in double quantum dots are much more significantly correlated than in a single dot. For that reason our modeling was based on simple confinement potentials that allow for an exact diagonalization of the resulting two- and three-particle Hamiltonians with a precise account for the relative electron and hole localization along the stack. We studied the optical signatures of the coupling in context of the photoluminescence experiments performed in the external electric field. The calculations predicted prior to the experiment the mechanism of the exciton and negative trion dissociation by electron removal from the dot occupied by the hole. We discuss the competition between the tunnel and the electrostatic interdot couplings. Effects of the non-perfect alignment of the dots as well as stacks containing more than two dots are also discussed.
We used a theory of thermo-hydrodynamics in quantum Hall system observed on a two-dimensional system in high magnetic fields at low temperatures, to investigate the electron temperature in the linear response regime. The variation of electron temperature exhibits an antisymmetric distribution of the incompressible strips. According to this result, we obtain effects of the electron temperature on the current density distribution using a Thomas-Fermi-Poisson approximation. We observe that incompressible strips change with increasing and/or decreasing the electron temperature with regard to the lattice temperature.
We focus on a certain aspect of trial wave function approach in the fractional quantum Hall effect. We analyze the role of partition orderings and discuss the possible numerical search for the partition determining the subspace of the Hilbert space containing a particular quantum Hall wave function. This research is inspired by analogical properties of certain polynomials which are the object of interest of the symmetric function theory, especially the Jack polynomials (related to the so-called "Jack states"). Presented method may be used in the search of candidate trial wave functions. We also justify (in certain cases) diagonalization of the Coulomb repulsion Hamiltonian restricted to certain subspaces. We focus on the states at filling factor ν=1/3 in the lowest and second Landau level.
Spin Hall effect in a two-dimensional electron gas with uniform and random components of the Rashba spin-orbit interaction is considered theoretically. Relaxation time due to scattering on Rashba fluctuations is also calculated. It is shown that the presence of a uniform component of Rashba coupling not only modifies relaxation time, but also suppresses the contribution to the spin Hall conductivity due to random Rashba field.
The quantum Hall effect is a set of phenomena observed at low temperature in a two-dimensional electron gas subject to a strong perpendicular magnetic field. It manifests itself as a quantization of the nondiagonal elements (ρ_{xy}) of the resistivity tensor accompanied by simultaneous vanishingρ_{xx} for ranges of the magnetic field. For the integer quantum Hall effectρ_{xy}= h/νe^2, where h is the Planck constant, e - charge of an electron andν is an integer, while for the fractional quantum Hall effectν is a simple fraction. In spite of similar phenomenology deep and profound differences exist between these two effects. In the lecture the precision of the Hall quantization in the integer quantum Hall effect and briefly new types of quantum fluids observed in the fractional quantum Hall effect are discussed. Some recent theoretical and experimental discoveries connected with quantum Hall liquids are also mentioned.
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