158 research outputs found
Magnetic phenomena at and near nu =1/2 and 1/4: theory, experiment and interpretation
I show that the hamiltonian theory of Composite Fermions (CF) is capable of
yielding a unified description in fair agreement with recent experiments on
polarization P and relaxation rate 1/T_1 in quantum Hall states at filling nu =
p/(2ps+1), at and near nu = 1/2 and 1/4, at zero and nonzero temperatures. I
show how rotational invariance and two dimensionality can make the underlying
interacting theory behave like a free one in a limited context.Comment: Latex 4 pages, 2 figure
Rotating fermions in two dimensions: Thomas Fermi approach
Properties of confined mesoscopic systems have been extensively studied
numerically over recent years. We discuss an analytical approach to the study
of finite rotating fermionic systems in two dimension. We first construct the
energy functional for a finite fermionic system within the Thomas-Fermi
approximation in two dimensions. We show that for specific interactions the
problem may be exactly solved. We derive analytical expressions for the
density, the critical size as well as the ground state energy of such systems
in a given angular momentum sector.Comment: Latex 15 pages, 3 ps. figures. Poster in SCES-Y2K, held at SAHA
Institute of Nuclear Physics,Calcutta,October (2000
Finite Temperature Magnetism in Fractional Quantum Hall Systems: Composite Fermion Hartree-Fock and Beyond
Using the Hamiltonian formulation of Composite Fermions developed recently,
the temperature dependence of the spin polarization is computed for the
translationally invariant fractional quantum Hall states at and
in two steps. In the first step, the effect of particle-hole
excitations on the spin polarization is computed in a Composite Fermion
Hartree-Fock approximation. The computed magnetization for lies above
the experimental results for intermediate temperatures indicating the
importance of long wavelength spin fluctuations which are not correctly treated
in Hartree-Fock. In the second step, spin fluctuations beyond Hartree-Fock are
included for by mapping the problem on to the coarse-grained
continuum quantum ferromagnet. The parameters of the effective continuum
quantum ferromagnet description are extracted from the preceding Hartree-Fock
analysis. After the inclusion of spin fluctuations in a large-N approach, the
results for the finite-temperature spin polarization are in quite good
agreement with the experiments.Comment: 10 pages, 8 eps figures. Two references adde
Scaling Relations for Gaps in Fractional Quantum Hall States
The microscopic approach of Murthy and Shankar, which has recently been used
to calculate the transport gaps of quantum Hall states with fractions
p/(2ps+1), also implies scaling relations between gaps within a single sequence
(fixed s) as well as between gaps of corresponding states in different
sequences. This work tests these relations for a system of electrons in the
lowest Landau level interacting with a model potential cutoff at high momenta
due to sample thickness
Hamiltonian Theory of the Composite Fermion Wigner Crystal
Experimental results indicating the existence of the high magnetic field
Wigner Crystal have been available for a number of years. While variational
wavefunctions have demonstrated the instability of the Laughlin liquid to a
Wigner Crystal at sufficiently small filling, calculations of the excitation
gaps have been hampered by the strong correlations. Recently a new Hamiltonian
formulation of the fractional quantum Hall problem has been developed. In this
work we extend the Hamiltonian approach to include states of nonuniform
density, and use it to compute the excitation gaps of the Wigner Crystal
states. We find that the Wigner Crystal states near are
quantitatively well described as crystals of Composite Fermions with four
vortices attached. Predictions for gaps and the shear modulus of the crystal
are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table
Hamiltonian theory of gaps, masses and polarization in quantum Hall states: full disclosure
I furnish details of the hamiltonian theory of the FQHE developed with Murthy
for the infrared, which I subsequently extended to all distances and apply it
to Jain fractions \nu = p/(2ps + 1). The explicit operator description in terms
of the CF allows one to answer quantitative and qualitative issues, some of
which cannot even be posed otherwise. I compute activation gaps for several
potentials, exhibit their particle hole symmetry, the profiles of charge
density in states with a quasiparticles or hole, (all in closed form) and
compare to results from trial wavefunctions and exact diagonalization. The
Hartree-Fock approximation is used since much of the nonperturbative physics is
built in at tree level. I compare the gaps to experiment and comment on the
rough equality of normalized masses near half and quarter filling. I compute
the critical fields at which the Hall system will jump from one quantized value
of polarization to another, and the polarization and relaxation rates for half
filling as a function of temperature and propose a Korringa like law. After
providing some plausibility arguments, I explore the possibility of describing
several magnetic phenomena in dirty systems with an effective potential, by
extracting a free parameter describing the potential from one data point and
then using it to predict all the others from that sample. This works to the
accuracy typical of this theory (10 -20 percent). I explain why the CF behaves
like free particle in some magnetic experiments when it is not, what exactly
the CF is made of, what one means by its dipole moment, and how the comparison
of theory to experiment must be modified to fit the peculiarities of the
quantized Hall problem
Hamiltonian Description of Composite Fermions: Aftermath
The Lowest Landau Level (LLL), long distance theory of Composite Fermions
(CF) developed by Murthy and myself is minimally extended to all distances,
guided by very general principles. The resulting theory is mathematically
consistent, and physically appealing: we clearly see the electron and the
vortices binding to form the CF. The meaning of the constraints, their role in
ensuring compressibility of dipolar objects at , and the
observability of dipoles are clarified.Comment: Revised for publication in PRL, 4 - epsilon page
Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
Using a fermionic renormalization group approach we analyse a model where the
electrons diffusing on a quantum dot interact via Fermi-liquid interactions.
Describing the single-particle states by Random Matrix Theory, we find that
interactions can induce phase transitions (or crossovers for finite systems) to
regimes where fluctuations and collective effects dominate at low energies.
Implications for experiments and numerical work on quantum dots are discussed.Comment: 4 pages, 1 figure; version to appear in Phys Rev Letter
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