7,128 research outputs found
Specific heat and validity of quasiparticle approximation in the half-filled Landau level
We calculate the specific heat of composite fermion system in the half-filled
Landau level. Two different methods are used to examine validity of the
quasiparticle approximation when the two-body interaction is given by (). The singular part of the specific heat
is calculated from the free energy of the gauge field, which is compared with
the specific heat calculated from the quasiparticle approximation via the
singular self-energy correction due to the gauge field fluctuations. It turns
out that two results are in general different and they coincide only for the
case of the Coulomb interaction (). This result supports the fact
that the quasiparticle approximation is valid only for the case of the Coulomb
interaction. It is emphasized that this result is obtained by looking at a
gauge-invariant quantity -- the specific heat.Comment: 8 pages, Revte
Influence of gauge-field fluctuations on composite fermions near the half-filled state
Taking into account the transverse gauge field fluctuations, which interact
with composite fermions, we examine the finite temperature compressibility of
the fermions as a function of an effective magnetic field ( is the density of electrons) near the half-filled state. It is
shown that, after including the lowest order gauge field correction, the
compressibility goes as for , where . Here we assume that the interaction between
the fermions is given by , where is a dependent constant. This result can be
interpreted as a divergent correction to the activation energy gap and is
consistent with the divergent renormalization of the effective mass of the
composite fermions.Comment: Plain Tex, 24 pages, 5 figures available upon reques
Quasi-particle behavior of composite fermions in the half-filled Landau level
We calculate the effect of infrared fluctuations of the Chern-Simons gauge
field on the single-particle Green's function of composite fermions in the
half-filled Landau level via higher-dimensional bosonization on a curved Fermi
surface. We find that composite fermions remain well-defined quasi-particles,
with an effective mass given by the mean-field value, but with anomalously
large damping and a spectral function that contains considerable weight away
from the quasi-particle peak.Comment: reference added; accepted for publication in Phys. Rev. Let
Quantum Boltzmann equation of composite fermions interacting with a gauge field
We derive the quantum Boltzmann equation (QBE) of composite fermions at/near
the state using the non-equilibrium Green's function technique. The
lowest order perturbative correction to the self-energy due to the strong gauge
field fluctuations suggests that there is no well defined
Landau-quasi-particle. Therefore, we cannot assume the existence of the
Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an
alternative formulation, we derive the QBE for the generalized Fermi surface
displacement which corresponds to the local variation of the chemical potential
in momentum space. {}From this QBE, one can understand in a unified fashion the
Fermi-liquid behaviors of the density-density and the current-current
correlation functions at (in the long wave length and the low
frequency limits) and the singular behavior of the energy gap obtained from the
finite temperature activation behavior of the compressibility near .
Implications of these results to the recent experiments are also discussed.Comment: 44 pages, Plain Tex, 5 figures (ps files) available upon reques
Effective Mass of Composite Fermions and Fermionic Chern-Simons Theory in Temporal Gauge
The definitions of the effective mass of the composite fermion are discussed
for the half-filled Landau level problem. In a recent work, Shankar and Murthy
show a finite effective mass of the composite fermion by a canonical
transformation while the perturbative calculation gives the logarithmic
divergence of the effective mass at the Fermi surface. We will emphasize that
the different definition of the effective mass has the different physical
processes. The finite one could be defined for any momentum of the composite
fermion while the divergence only appears at the Fermi surface. We work with
the standard Halperin-Lee-Read model but in the temporal gauge. The advantage
of this gauge to be employed is that the finite effective mass could be
calculated in the Hartree-Fock approximation. Furthermore, it is precisely
equal to the result that Shankar and Murthy obtained which is well-fit with the
numerical calculation from the ground state energy analysis and a
semi-classical estimation. However, if we consider the random phase
approximation, one sees that the divergence of the effective mass of the
quasiparticle at the Fermi surface emerges again no matter that we work on the
temporal or Coulomb gauges. We develop an effective theory where the finite
effective mass serves as a `bare' effective mass and show that the same
divergence of the RPA effective mass. On the other hand, the correct behavior
of the response functions in the small band mass limit could be seen clearly in
the temporal gauge since there is a self-interaction among the magnetoplasmons.Comment: 27 pages,6 eps figure
Gauge (non-)invariant Green functions of Dirac fermions coupled to gauge fields
We develop a unified approach to both infrared and ultraviolet asymptotics of
the fermion Green functions in the condensed matter systems that allow for an
effective description in the framework of the Quantum Electrodynamics. By
applying a path integral representation to the previously suggested form of the
physical electron propagator we demonstrate that in the massless case this
gauge invariant function features a "stronger-than-a-pole" branch-cut
singularity instead of the conjectured Luttinger-like behavior. The obtained
results alert one to the possibility that construction of physically relevant
amplitudes in the effective gauge theories might prove more complex than
previously thought
Gauge-invariant response functions of fermions coupled to a gauge field
We study a model of fermions interacting with a gauge field and calculate
gauge-invariant two-particle Green's functions or response functions. The
leading singular contributions from the self-energy correction are found to be
cancelled by those from the vertex correction for small and . As a
result, the remaining contributions are not singular enough to change the
leading order results of the random phase approximation. It is also shown that
the gauge field propagator is not renormalized up to two-loop order. We examine
the resulting gauge-invariant two-particle Green's functions for small and
, but for all ratios of and we conclude that they can
be described by Fermi liquid forms without a diverging effective mass.Comment: Plain Tex, 35 pages, 5 figures available upon request, Revised
Version (Expanded discussion), To be published in Physical Review B 50,
(1994) (December 15 issue
Low energy properties of M-state tunneling systems in metals: New candidates for non-Fermi-liquid systems
We construct a generalized multiplicative renormalization group
transformation to study the low energy dynamics of a heavy particle tunneling
among different positions and interacting with independent conduction
electron channels. Using a -expansion we show that this M-level scales
towards a fixed point equivalent to the channel
Coqblin-Schrieffer model. Solving numerically the scaling equations we find
that a realistic M-level system scales close to this fixed point (FP) and its
Kondo temperature is in the experimentally observable range .Comment: 11 Latex pages, to appear in Phys. Rev. Lett, Figures available from
the author by reques
Theory of Fermion Liquids
We develop a general theory of fermion liquids in spatial dimensions greater
than one. The principal method, bosonization, is applied to the cases of short
and long range longitudinal interactions, and to transverse gauge interactions.
All the correlation functions of the system may be obtained with the use of a
generating functional. Short-range and Coulomb interactions do not destroy the
Landau Fermi fixed point. Novel fixed points are found, however, in the cases
of a super-long range longitudinal interaction in two dimensions and transverse
gauge interactions in two and three spatial dimensions. We consider in some
detail the 2+1-dimensional problem of a Chern-Simons gauge action combined with
a longitudinal two-body interaction which
controls the density, and hence gauge, fluctuations. For we find that
the gauge interaction is irrelevant and the Landau fixed point is stable, while
for the interaction is relevant and the fixed point cannot be accessed
by bosonization. Of special importance is the case (Coulomb
interaction) which describes the Halperin-Lee-Read theory of the half-filled
Landau level. We obtain the full quasiparticle propagator which is of a
marginal Fermi liquid form. Using Ward Identities, we show that neither the
inclusion of nonlinear terms in the fermion dispersion, nor vertex corrections,
alters our results: the fixed point is accessible by bosonization. As the
two-point fermion Green's function is not gauge invariant, we also investigate
the gauge-invariant density response function. Near momentum , in
addition to the Kohn anomaly we find singular behavior. In Appendices we
present a numerical calculation of the spectral function for a Fermi liquid
with Landau parameter . We also show how Kohn's theorem isComment: Minor corrections and clarifications, and additional references. 30
pages, RevTex 3.0, 3 figures in uuencoded postscript files
The Screening Cloud in the k-Channel Kondo Model: Perturbative and Large-k Results
We demonstrate the existence of a large Kondo screening cloud in the
k-channel Kondo model using both renormalization group improved perturbation
theory and the large-k limit. We study position (r) dependent spin Green's
functions in both static and equal time cases. The equal-time Green's function
provides a natural definition of the screening cloud profile, in which the
large Kondo scale appears. At large distances it consists of both a slowly
varying piece and a piece which oscillates at twice the Fermi wave-vector. This
function is calculated at all r in the large-k limit. Static Green's functions
(Knight shift or susceptibility) consist only of a term oscillating at 2kF, and
appear to factorize into a function of r times a function of T for rT << vF, in
agreement with NMR experiments. Most of the integrated susceptibility comes
from the impurity-impurity part with conduction electron contributions
suppressed by powers of the bare Kondo coupling. The single-channel and
overscreened multi-channel cases are rather similar although anomalous
power-laws occur in the latter case at large r and low T due to irrelevant
operator corrections.Comment: 22 Revtex pages, 12 figure
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