28 research outputs found
Fermi edge singularity in a non-equilibrium system
We report exact results for the Fermi Edge Singularity in the absorption
spectrum of an out-of-equilibrium tunnel junction. We consider two metals with
chemical potential difference V separated by a tunneling barrier containing a
defect, which exists in one of two states. When it is in its excited state,
tunneling through the otherwise impermeable barrier is possible. We find that
the lineshape not only depends on the total scattering phase shift as in the
equilibrium case but also on the difference in the phase of the reflection
amplitudes on the two sides of the barrier. The out-of-equilibrium spectrum
extends below the original threshold as energy can be provided by the power
source driving current across the barrier. Our results have a surprisingly
simple interpretation in terms of known results for the equilibrium case but
with (in general complex-valued) combinations of elements of the scattering
matrix replacing the equilibrium phase shifts.Comment: 4 page
Unpolarized quasielectrons and the spin polarization at filling fractions between 1/3 and 2/5
We prove that for a hard core interaction the ground state spin polarization
in the low Zeeman energy limit is given by for filling fractions in
the range . The same result holds for a Coulomb
potential except for marginally small magnetic fields. At the magnetic fields
unpolarized quasielectrons can manifest themselves by a characteristic
peak in the I-V characteristics for tunneling between two
ferromagnets.Comment: 8 pages, Latex. accepted for publication in Phys.Rev.
Effective Mass of the Four Flux Composite Fermion at
We have measured the effective mass () of the four flux composite
fermion at Landau level filling factor (CF), using the
activation energy gaps at the fractional quantum Hall effect (FQHE) states
= 2/7, 3/11, and 4/15 and the temperature dependence of the Shubnikov-de
Haas (SdH) oscillations around . We find that the energy gaps show a
linear dependence on the effective magnetic field (), and from this linear dependence we obtain and
a disorder broadening 1 K for a sample of density /cm. The deduced from the temperature dependence of
the SdH effect shows large differences for and . For
, . It scales as with the mass
derived from the data around and shows an increase in as , resembling the findings around . For ,
increases rapidly with increasing and can be described by . This anomalous dependence on is
precursory to the formation of the insulating phase at still lower filling.Comment: 5 pages, 3 figure
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
Scaling Law for a Magnetic Impurity Model with Two-Body Hybridization
We consider a magnetic impurity coupled to the hybridizing and screening
channels of a conduction band. The model is solved in the framework of poor
man's scaling and Cardy's generalized theories. We point out that it is
important to include a two-body hybridization if the scaling theory is to be
valid for the band width larger than . We map out the boundary of the
Fermi-non-Fermi liquid phase transition as a function of the model parameters.Comment: 14 pages, latex, 1 figure included
The excitonic collapse of higher Landau level fractional quantum Hall effect
The scarcity of the fractional quantum Hall effect in higher Landau levels is
a most intriguing fact when contrasted with its great abundance in the lowest
Landau level. This paper shows that a suppression of the hard core repulsion in
going from the lowest Landau level to higher Landau levels leads to a collapse
of the energy of the neutral excitation, destabilizing all fractional states in
the third and higher Landau levels, and almost all in the second Landau level.
The remaining fractions are in agreement with those observed experimentally.Comment: 5 pages, 3 figures. To appear in Phys. Rev. B Rapid Communicatio
Hamiltonian Theory of the FQHE: Conserving Approximation for Incompressible Fractions
A microscopic Hamiltonian theory of the FQHE developed by Shankar and the
present author based on the fermionic Chern-Simons approach has recently been
quite successful in calculating gaps and finite tempertature properties in
Fractional Quantum Hall states. Initially proposed as a small- theory, it
was subsequently extended by Shankar to form an algebraically consistent theory
for all in the lowest Landau level. Such a theory is amenable to a
conserving approximation in which the constraints have vanishing correlators
and decouple from physical response functions. Properties of the incompressible
fractions are explored in this conserving approximation, including the
magnetoexciton dispersions and the evolution of the small- structure factor
as \nu\to\half. Finally, a formalism capable of dealing with a nonuniform
ground state charge density is developed and used to show how the correct
fractional value of the quasiparticle charge emerges from the theory.Comment: 15 pages, 2 eps figure
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: 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