10 research outputs found
Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect
Motivated by the discovery of extremely low energy collective modes in the
fractional quantum Hall effect (Kang, Pinczuk {\em et al.}), with energies
below the Zeeman energy, we study theoretically the spin reversed excitations
for fractional quantum Hall states at and 3/7 and find qualitatively
different behavior than for . We find that a low-energy,
charge-neutral "spin roton," associated with spin reversed excitations that
involve a change in the composite-fermion Landau level index, has energy in
reasonable agreement with experiment.Comment: Postscript figures included. Accepted in Phys. Rev. B (Rapid
Communication
Exchange Instabilities in Semiconductor Double Quantum Well Systems
We consider various exchange-driven electronic instabilities in semiconductor
double-layer systems in the absence of any external magnetic field. We
establish that there is no exchange-driven bilayer to monolayer charge transfer
instability in the double-layer systems. We show that, within the unrestricted
Hartree-Fock approximation, the low density stable phase (even in the absence
of any interlayer tunneling) is a quantum ``pseudospin rotated'' spontaneous
interlayer phase coherent spin-polarized symmetric state rather than the
classical Ising-like charge-transfer phase. The U(1) symmetry of the double
quantum well system is broken spontaneously at this low density quantum phase
transition, and the layer density develops quantum fluctuations even in the
absence of any interlayer tunneling. The phase diagram for the double quantum
well system is calculated in the carrier density--layer separation space, and
the possibility of experimentally observing various quantum phases is
discussed. The situation in the presence of an external electric field is
investigated in some detail using the
spin-polarized-local-density-approximation-based self-consistent technique and
good agreement with existing experimental results is obtained.Comment: 24 pages, figures included. Also available at
http://www-cmg.physics.umd.edu/~lzheng/preprint/ct.uu/ . Revised final
version to appear in PR
Structures for Interacting Composite Fermions: Stripes, Bubbles, and Fractional Quantum Hall Effect
Much of the present day qualitative phenomenology of the fractional quantum
Hall effect can be understood by neglecting the interactions between composite
fermions altogether. For example the fractional quantum Hall effect at
corresponds to filled composite-fermion Landau levels,and
the compressible state at to the Fermi sea of composite fermions.
Away from these filling factors, the residual interactions between composite
fermions will determine the nature of the ground state. In this article, a
model is constructed for the residual interaction between composite fermions,
and various possible states are considered in a variational approach. Our study
suggests formation of composite-fermion stripes, bubble crystals, as well as
fractional quantum Hall states for appropriate situations.Comment: 16 pages, 7 figure
Hamiltonian Description of Composite Fermions: Calculation of Gaps
We analytically calculate gaps for the 1/3, 2/5, and 3/7 polarized and
partially polarized Fractional Quantum Hall states based on the Hamiltonian
Chern-Simons theory we have developed. For a class of potentials that are soft
at high momenta (due to the finite thickness of the sample) we find good
agreement with numerical and experimental results.Comment: 4 pages, 2 eps figures. One reference added, some typos (one in
equation 7) corrected, and minor notational modification
Excitation gaps in fractional quantum Hall states: An exact diagonalization study
We compute energy gaps for spin-polarized fractional quantum Hall states in
the lowest Landau level at filling fractions nu=1/3, 2/5,3/7 and 4/9 using
exact diagonalization of systems with up to 16 particles and extrapolation to
the infinite system-size limit. The gaps calculated for a pure Coulomb
interaction and ignoring finite width effects, disorder and LL mixing agree
with predictions of composite fermion theory provided the logarithmic
corrections to the effective mass are included. This is in contrast with
previous estimates, which, as we show, overestimated the gaps at nu=2/5 and 3/7
by around 15%. We also study the reduction of the gaps as a result of the
non-zero width of the 2D layer. We show that these effects are accurately
accounted for using either Gaussian or z*Gaussian' (zG) trial wavefunctions,
which we show are significantly better variational wavefunctions than the
Fang-Howard wavefunction. For quantum well parameters typical of
heterostructure samples, we find gap reductions of around 20%. The experimental
gaps, after accounting heuristically for disorder,are still around 40% smaller
than the computed gaps. However, for the case of tetracene layers
inmetal-insulator-semiconductor (MIS) devices we find that the measured
activation gaps are close to those we compute. We discuss possible reasons why
the difference between computed and measured activation gaps is larger in GaAs
heterostructures than in MIS devices. Finally, we present new calculations
using systems with up to 18 electrons of the gap at nu=5/2 including width
corrections.Comment: 18 pages, 17 figure
Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself
based on the fermionic Chern-Simons approach, has recently been quite
successful in calculating gaps in Fractional Quantum Hall states, and in
predicting approximate scaling relations between the gaps of different
fractions. I now apply this formalism towards computing magnetoexciton
dispersions (including spin-flip dispersions) in the , 2/5, and 3/7
gapped fractions, and find approximate agreement with numerical results. I also
analyse the evolution of these dispersions with increasing sample thickness,
modelled by a potential soft at high momenta. New results are obtained for
instabilities as a function of thickness for 2/5 and 3/7, and it is shown that
the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state,
cannot be described as a simple quantum ferromagnet.Comment: 18 pages, 18 encapsulated ps figure
Realistic Calculations of Correlated Incompressible Electronic States in GaAs--Al_{x}Ga_{1-x}As Heterostructures and Quantum Wells
We perform an exact spherical geometry finite-size diagonalization
calculation for the fractional quantum Hall ground state in three different
experimentally relevant GaAs-Al_{x}Ga_{1-x}As systems: a wide parabolic quantum
well, a narrow square quantum well, and a heterostructure. For each system we
obtain the Coulomb pseudopotential parameters entering the exact
diagonalization calculation by using the realistic subband wave function from a
self-consistent electronic structure calculation within the local density
approximation (LDA) for a range of electron densities. We compare our realistic
LDA pseudopotential parameters with those from widely used simpler model
approximations in order to estimate the accuracies of the latter. We also
calculate the overlap between the exact numerical ground state and the
analytical Laughlin state as well as the excitation gap as a function of
density. For the three physical systems we consider the calculated overlap is
found to be large in the experimental electron density range. We compare our
calculated excitation gap energy to the experimentally obtained activated
transport energy gaps after subtracting out the effect of level broadening due
to collisions. The agreement between our calculated excitation gaps and the
experimental measurements is excellent.Comment: 24 pages, RevTex, 20 figure