194 research outputs found
Regular networks of Luttinger liquids
We consider arrays of Luttinger liquids, where each node is described by a
unitary scattering matrix. In the limit of small electron-electron interaction,
we study the evolution of these scattering matrices as the high-energy single
particle states are gradually integrated out. Interestingly, we obtain the same
renormalization group equations as those derived by Lal, Rao, and Sen, for a
system composed of a single node coupled to several semi-infinite 1D wires. The
main difference between the single node geometry and a regular lattice is that
in the latter case, the single particle spectrum is organized into periodic
energy bands, so that the renormalization procedure has to stop when the last
totally occupied band has been eliminated. We therefore predict a strongly
renormalized Luttinger liquid behavior for generic filling factors, which
should exhibit power-law suppression of the conductivity at low temperatures
E_{F}/(k_{F}a) >
1. Some fully insulating ground-states are expected only for a discrete set of
integer filling factors for the electronic system. A detailed discussion of the
scattering matrix flow and its implication for the low energy band structure is
given on the example of a square lattice.Comment: 16 pages, 7 figure
Observation of Resonant Tunneling in Silicon Inversion Layers
Measurements of the temperature and carrier-density dependence of the strongly localized conductance of short silicon inversion layers are reported. At the lowest temperatures we observe well-isolated, large conductance peaks whose width and temperature dependence are only consistent with resonant tunneling and are inconsistent with Mott hopping. Several new features are observed which we believe may be the result of Coulomb interactions
Theory of Incompressible States in a Narrow Channel
We report on the properties of a system of interacting electrons in a narrow
channel in the quantum Hall effect regime. It is shown that an increase in the
strength of the Coulomb interaction causes abrupt changes in the width of the
charge-density profile of translationally invariant states. We derive a phase
diagram which includes many of the stable odd-denominator states as well as a
novel fractional quantum Hall state at lowest half-filled Landau level. The
collective mode evaluated at the half-filled case is strikingly similar to that
for an odd-denominator fractional quantum Hall state.Comment: 4 pages, REVTEX, and 4 .ps file
Disorder suppression and precise conductance quantization in constrictions of PbTe quantum wells
Conductance quantization was measured in submicron constrictions of PbTe,
patterned into narrow,12 nm wide quantum wells deposited between
PbEuTe barriers. Because the quantum confinement imposed by
the barriers is much stronger than the lateral one, the one-dimensional
electron energy level structure is very similar to that usually met in
constrictions of AlGaAs/GaAs heterostructures. However, in contrast to any
other system studied so far, we observe precise conductance quantization in
units, {\it despite of significant amount of charged defects in the
vicinity of the constriction}. We show that such extraordinary results is a
consequence of the paraelectric properties of PbTe, namely, the suppression of
long-range tails of the Coulomb potentials due to the huge dielectric constant.Comment: 7 pages, 6 figures, submitted to Phys. Rev.
Finite Size Analysis of Luttinger Liquids with a source of 2k_f Scattering
Numerical analysis of the spectrum of large finite size Luttinger liquids
(g<1) in the presence of a single source of 2k_f scattering has been made
possible thanks to an effective integration of high degrees of freedom.
Presence of irrelevant operators and their manifestation in transport are
issues treated independently. We confirm the existence of two irrelevant
operators: particle hopping and charge oscillations, with regions of dominance
separated by g=1/2. Temperature dependence of conductance is shown to be
dominated by hopping alone. Frequency dependence is affected by both irrelevant
operators.Comment: 4 pages, LaTex (RevTex), 3 PostScript figures appende
Renormalization group study of the conductances of interacting quantum wire systems with different geometries
We examine the effect of interactions between the electrons on the
conductances of some systems of quantum wires with different geometries. The
systems include a wire with a stub in the middle, a wire containing a ring
which can enclose a magnetic flux, and a system of four wires which are
connected in the middle through a fifth wire. Each of the wires is taken to be
a weakly interacting Tomonaga-Luttinger liquid, and scattering matrices are
introduced at all the junctions. Using a renormalization group method developed
recently for studying the flow of scattering matrices for interacting systems
in one dimension, we compute the conductances of these systems as functions of
the temperature and the wire lengths. We present results for all three regimes
of interest, namely, high, intermediate and low temperature. These correspond
respectively to the thermal coherence length being smaller than, comparable to
and larger than the smallest wire length in the different systems, i.e., the
length of the stub or each arm of the ring or the fifth wire. The
renormalization group procedure and the formulae used to compute the
conductances are different in the three regimes. We present a
phenomenologically motivated formalism for studying the conductances in the
intermediate regime where there is only partial coherence. At low temperatures,
we study the line shapes of the conductances versus the electron energy near
some of the resonances; the widths of the resonances go to zero with decreasing
temperature. Our results show that the conductances of various systems of
experimental interest depend on the temperature and lengths in a non-trivial
way when interactions are taken into account.Comment: Revtex, 17 pages including 15 figure
Characterization of one-dimensional quantum channels in InAs/AlSb
We report the magnetoresistance characteristics of one-dimensional electrons
confined in a single InAs quantum well sandwiched between AlSb barriers. As a
result of a novel nanofabrication scheme that utilizes a 3nm-shallow wet
chemical etching to define the electrostatic lateral confinement, the system is
found to possess three important properties: specular boundary scattering, a
strong lateral confinement potential, and a conducting channel width that is
approximately the lithography width. Ballistic transport phenomena, including
the quenching of the Hall resistance, the last Hall plateau, and a strong
negative bend resistance, are observed at 4K in cross junctions with sharp
corners. In a ring geometry, we have observed Aharonov-Bohm interference that
exhibits characteristics different from those of the GaAs counterpart due to
the ballistic nature of electron transport and the narrowness of the conducting
channel width.Comment: pdf-file, 8 figures, to be published in Phys. Rev.
Giant Oscillations of Acoustoelectric Current in a Quantum Channel
A theory of d.c. electric current induced in a quantum channel by a
propagating surface acoustic wave (acoustoelectric current) is worked out. The
first observation of the acoustoelectric current in such a situation was
reported by J. M. Shilton et al., Journ. Phys. C (to be published). The authors
observed a very specific behavior of the acoustoelectric current in a
quasi-one-dimensional channel defined in a GaAs-AlGaAs heterostructure by a
split-gate depletion -- giant oscillations as a function of the gate voltage.
Such a behavior was qualitatively explained by an interplay between the
energy-momentum conservation law for the electrons in the upper transverse mode
with a finite temperature splitting of the Fermi level. In the present paper, a
more detailed theory is developed, and important limiting cases are considered.Comment: 7 pages, 2 Postscript figures, RevTeX 3.
Resonance Patterns of an Antidot Cluster: From Classical to Quantum Ballistics
We explain the experimentally observed Aharonov-Bohm (AB) resonance patterns
of an antidot cluster by means of quantum and classical simulations and Feynman
path integral theory. We demonstrate that the observed behavior of the AB
period signals the crossover from a low B regime which can be understood in
terms of electrons following classical orbits to an inherently quantum high B
regime where this classical picture and semiclassical theories based on it do
not apply.Comment: 5 pages revtex + 2 postscript figure
Kondo Effect in a Luttinger Liquid: Exact Results from Conformal Field Theory
We report on exact results for the low-temperature thermodynamics of a
spin- magnetic impurity coupled to a one-dimensional interacting
electron system. By using boundary conformal field theory, we show that there
are only two types of critical behaviors consistent with the symmetries of the
problem: {\em either} a local Fermi liquid, {\em or} a theory with an anomalous
response identical to that recently proposed by Furusaki and Nagaosa.
Suppression of back scattering off the impurity leads to the same critical
properties as for the two-channel Kondo effect.Comment: 9 pages, REVTeX, uses amsfonts, accepted for publication in Phys.
Rev. Let
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