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.
Fractional quantum Hall effect is a remarkable behaviour of correlated electrons, observed exclusively in two dimensions, at low temperatures, and in strong magnetic fields. The most prominent fractional quantum Hall state occurs at Landau level filling factor ν = 1/3 and it is described by the famous Laughlin wave function, which (apart from the trivial Gaussian factor) is an example of Jack polynomial. Fermionic Jack polynomials also describe another pair of candidate fractional quantum Hall states: Moore-Read and Read-Rezayi states, believed to form at the ν = 1/2 and 3/5 fillings of the second Landau level, respectively. Bosonic Jacks on the other hand are candidates for certain correlated states of cold atoms. We examine here a continuous family of fermionic Jack polynomials whose special case is the Laughlin state as approximate wave functions for the 1/3 fractional quantum Hall effect.
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 argue that in a strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of 2π. By unraveling consequences of the nontrivial topology of the charge gauge U(2) group, we found that the pinning of the chemical potential and the zero-temperature divergence of charge compressibility define a novel "hidden" quantum criticality on verge of the Mott transition governed by the protectorate of stable topological numbers rather than the Landau paradigm of the symmetry breaking.
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.
The breakdown of the dissipationless conductance in the integer and fractional quantum Hall effect regime is reviewed. The temperature dependence of the critical current and of the critical magnetic field at breakdown bears a striking resemblance to the phase diagram of the phenomenological two-fluid Gorter-Casimir model for superconductivity. In addition, a remarkably simple scaling law exists between different filling factors.
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).
The mean field composite fermion picture successfully predicts low lying states of fractional quantum Hall systems. This success cannot be attributed to a cancellation between the Coulomb and Chern-Simons interactions beyond the mean field and solely depends on the short-range of the Coulomb pseudopotential in the lowest Landau level. The class of pseudopotentials for which the mean field composite fermion picture can be applied is defined. The success or failure of the mean field composite fermion picture in various systems (electrons in excited Landau levels, Laughlin quasiparticles, charged magnetoexcitons) is explained.
The spin-rotationally invariant SU(2)×U(1) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated. We argue that in strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of 2π. Furthermore, it is shown that U(1) and SU(2) gauge fields play a similar role as phonons in the BCS theory: they act as the the "glue" for fermion pairing.
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.
It is shown that a time-reversal invariant topological superconductivity can be realized in a quasi-one-dimensional structure, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when s-wave intra-wire and d-wave inter-wire pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. The time-reversal topological superconductor belongs to DIII class of symmetry with a Z₂ invariant.
We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite fermions remains stable against a pairing transition in the lowest two Landau levels. However, it undergoes spontaneous depolarization, which is unprotected owing to the lack of single-particle pseudospin splitting. These results suggest the absence of the Pfaffian phase in graphene.
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.
The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-T_c cuprates. The theory includes the effects of the relevant energy scales with the emphasis on the Coulomb interaction $U$ governed by the electromagnetic U(1) compact group. The results are obtained for the layered t-t'-t_⊥-U-J system of strongly correlated electrons relevant for cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time", labelled by a topological winding numbers, governed by gauge flux changes by an integer multiple of 2π, are essential configurations of the phase field dual to the charge. The impact of these topological excitations is calculated for the phase diagram, which displays the "hidden" quantum critical point on verge of the Mott transition that is given by a divergence of the charge compressibility.
Density of states and absorption spectrum of narrow quantum wells containing a small number of free electrons and subject to a high magnetic field are calculated numerically. The effect of an additional, second electron on the photoexcited electron-hole pair is analyzed. In density of states, the exciton-electron interaction fills the gaps between the Landau levels and yields additional discrete peaks corresponding to bound trions. In absorption, interaction with the additional free electron has no effect on the position or intensity of the main sequence of excitonic peaks. However, it gives rise to additional weaker trion peaks, both in the lowest and higher Landau levels.
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.
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