37 research outputs found
Search for electron liquids with non-Abelian quasiparticles
We use exact numerical diagonalization in the search of fractional quantum
Hall states with non-Abelian quasiparticle statistics. For the (most promising)
states in a partially filled second Landau level, the search is narrowed to the
range of filling factors . In this range, the analysis of
energy spectra and correlation functions, calculated including finite width and
Landau level mixing, supports the prominent non-Abelian candidates at
(paired Moore--Read "pfafian" state) and 12/5 (clustered
Read--Rezayi "parafermion" state). Outside of this range, the noninteracting
composite fermion model with four attached flux quanta is validated, yielding
the family of quantum liquids with fractional, but Abelian statistics. The
borderline state is shown to be adiabatically connected to the
Laughlin liquid, but its short-range correlations are significantly different.Comment: 9 pages, 8 figure
Three-body correlations and finite-size effects in the Moore--Read states on a sphere
Two- and three-body correlations in partially filled degenerate fermion
shells are studied numerically for various interactions between the particles.
Three distinct correlation regimes are defined, depending on the short-range
behavior of the pair pseudopotential. For pseudopotentials similar to those of
electrons in the first excited Landau level, correlations at half-filling have
a simple three-body form consisting of the maximum avoidance of the triplet
state with the smallest relative angular momentum R_3=3. In analogy to the
superharmonic criterion for Laughlin two-body correlations, their occurrence is
related to the form of the three-body pseudopotential at short range. The
spectra of a model three-body repulsion are calculated, and the zero-energy
Moore--Read ground state, its +-e/4-charged quasiparticles, and the
magnetoroton and pair-breaking bands are all identified. The quasiparticles are
correctly described by a composite fermion model appropriate for Halperin's
p-type pairing with Laughlin correlations between the pairs. However, the
Moore--Read ground state, and specially its excitations, have small overlaps
with the corresponding Coulomb eigenstates when calculated on a sphere. The
reason lies in surface curvature which affects the form of pair pseudopotential
for which the "R_3>3" three-body correlations occur. In finite systems, such
pseudopotential must be slightly superharmonic at short range (different from
Coulomb pseudopotential). However, the connection with the three-body
pseudopotential is less size-dependent, suggesting that the Moore--Read state
and its excitations are a more accurate description for experimental nu=5/2
states than could be expected from previous calculations.Comment: 12 pages, 12 figures, submitted to PR
Interaction and dynamical binding of spin waves or excitons in quantum Hall systems
Interaction between spin waves (or excitons) moving in the lowest Landau
level is studied using numerical diagonalization. Becuse of complicated
statistics obeyed by these composite particles, their effective interaction is
completely different from the dipole-dipole interaction predicted in the model
of independent (bosonic) waves. In particular, spin waves moving in the same
direction attract one another which leads to their dynamical binding. The
interaction pseudopotentials V_[up,up](k) and V_[up,down](k) for two spin waves
with equal wavevectors k and moving in the same or opposite directions have
been calculated and shown to obey power laws V(k) ~ k^alpha at small k. A high
value of alpha_[up,up]~4 explains the occurrence of linear bands in the spin
excitation spectra of quantum Hall droplets.Comment: 6 pages, 4 figures, submitted to PR
Fractional Quantum Hall States of Clustered Composite Fermions
The energy spectra and wavefunctions of up to 14 interacting quasielectrons
(QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are
investigated using exact numerical diagonalization. It is shown that at
sufficiently high density the QE's form pairs or larger clusters. This
behavior, opposite to Laughlin correlations, invalidates the (sometimes
invoked) reapplication of the composite fermion picture to the individual QE's.
The series of finite-size incompressible ground states are identified at the QE
filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings
nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4,
1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states
were recently discovered experimentally. Detailed analysis indicates that QE or
QH correlations in these states are different from those of well-known FQH
electron states (e.g., Laughlin or Moore-Read states), leaving the origin of
their incompressibility uncertain. Halperin's idea of Laughlin states of QP
pairs is also explored, but is does not seem adequate.Comment: 14 pages, 9 figures; revision: 1 new figure, some new references,
some new data, title chang
Energy, interaction, and photoluminescence of spin-reversed quasielectrons in fractional quantum Hall systems
The energy and photoluminescence spectra of a two-dimensional electron gas in
the fractional quantum Hall regime are studied. The single-particle properties
of reversed-spin quasielectrons (QE's) as well as the
pseudopotentials of their interaction with one another and with Laughlin
quasielectrons (QE's) and quasiholes (QH's) are calculated. Based on the
short-range character of the QE--QE and QE--QE
repulsion, the partially unpolarized incompressible states at the filling
factors and are postulated within Haldane's
hierarchy scheme. To describe photoluminescence, the family of bound
QE states of a valence hole and QE's are
predicted in analogy to the found earlier fractionally charged excitons
QE. The binding energy and optical selection rules for both families are
compared. The QE is found radiative in contrast to the dark QE,
and the QE is found non-radiative in contrast to the bright
QE.Comment: 9 pages, 6 figure
Negatively Charged Excitons and Photoluminescence in Asymmetric Quantum Well
We study photoluminescence (PL) of charged excitons () in narrow
asymmetric quantum wells in high magnetic fields B. The binding of all
states strongly depends on the separation of electron and hole layers.
The most sensitive is the ``bright'' singlet, whose binding energy decreases
quickly with increasing even at relatively small B. As a result, the
value of B at which the singlet--triplet crossing occurs in the spectrum
also depends on and decreases from 35 T in a symmetric 10 nm GaAs well
to 16 T for nm. Since the critical values of at which
different states unbind are surprisingly small compared to the well
width, the observation of strongly bound states in an experimental PL
spectrum implies virtually no layer displacement in the sample. This casts
doubt on the interpretation of PL spectra of heterojunctions in terms of
recombination
Energy spectra of fractional quantum Hall systems in the presence of a valence hole
The energy spectrum of a two-dimensional electron gas (2DEG) in the
fractional quantum Hall regime interacting with an optically injected valence
band hole is studied as a function of the filling factor and the
separation between the electron and hole layers. The response of the 2DEG
to the hole changes abruptly at of the order of the magnetic length
. At , the hole binds electrons to form neutral () or
charged () excitons, and the photoluminescence (PL) spectrum probes the
lifetimes and binding energies of these states rather than the original
correlations of the 2DEG. The ``dressed exciton'' picture (in which the
interaction between an exciton and the 2DEG was proposed to merely enhance the
exciton mass) is questioned. Instead, the low energy states are explained in
terms of Laughlin correlations between the constituent fermions (electrons and
's) and the formation of two-component incompressible fluid states in the
electron--hole plasma. At , the hole binds up to two Laughlin
quasielectrons (QE) of the 2DEG to form fractionally charged excitons
QE. The previously found ``anyon exciton'' QE is shown to be
unstable at any value of . The critical dependence of the stability of
different QE complexes on the presence of QE's in the 2DEG leads to the
observed discontinuity of the PL spectrum at or .Comment: 16 pages, 14 figures, submitted to PR
Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes
The pseudopotentials describing the interactions of quasiparticles in
fractional quantum Hall (FQH) states are studied. Rules for the identification
of incompressible quantum fluid ground states are found, based upon the form of
the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where
n and p are integers, appear to be the only incompressible states in the
thermodynamic limit, although other FQH hierarchy states occur for finite size
systems. This explains the success of the composite Fermion picture.Comment: RevTeX, 10 pages, 7 EPS figures, submitted fo Phys.Rev.
Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids
The exact diagonalization technique is used to study many-particle properties
of interacting electrons with spin, confined in a two-dimensional harmonic
potential. The single-particle basis is limited to the lowest Landau level. The
results are analyzed as a function of the total angular momentum of the system.
Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5 etc.
the system is fully polarized. The lowest energy states exhibit spin-waves,
domains, and localization, depending on the angular momentum. Vortices exist
only at excited polarized states. The high angular momentum limit shows
localization of electrons and separation of the charge and spin excitations.Comment: 14 pages 18 figure