116 research outputs found
Edge and Bulk of the Fractional Quantum Hall Liquids
An effective Chern-Simons theory for the Abelian quantum Hall states with
edges is proposed to study the edge and bulk properties in a unified fashion.
We impose a condition that the currents do not flow outside the sample. With
this boundary condition, the action remains gauge invariant and the edge modes
are naturally derived. We find that the integer coupling matrix should
satisfy the condition (: filling of Landau
levels, : the number of gauge fields ) for the quantum Hall liquids. Then
the Hall conductance is always quantized irrespective of the detailed dynamics
or the randomness at the edge.Comment: 13 pages, REVTEX, one figure appended as a postscript fil
Impurity scattering and transport of fractional Quantum Hall edge state
We study the effects of impurity scattering on the low energy edge state
dynamic s for a broad class of quantum Hall fluids at filling factor , for integer and even integer . When is positive all
of the edge modes are expected to move in the same direction, whereas for
negative one mode moves in a direction opposite to the other modes.
Using a chiral-Luttinger model to describe the edge channels, we show that for
an ideal edge when is negative, a non-quantized and non-universal Hall
conductance is predicted. The non-quantized conductance is associated with an
absence of equilibration between the edge channels. To explain the robust
experimental Hall quantization, it is thus necessary to incorporate impurity
scattering into the model, to allow for edge equilibration. A perturbative
analysis reveals that edge impurity scattering is relevant and will modify the
low energy edge dynamics. We describe a non-perturbative solution for the
random channel edge, which reveals the existence of a new
disorder-dominated phase, characterized by a stable zero temperature
renormalization group fixed point. The phase consists of a single propagating
charge mode, which gives a quantized Hall conductance, and neutral modes.
The neutral modes all propagate at the same speed, and manifest an exact SU(n)
symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral
modes decay with a finite rate which varies as at low temperatures.
Various experimental predictions and implications which follow from the exact
solution are described in detail, focusing on tunneling experiments through
point contacts.Comment: 19 pages (two column), 5 post script figures appended, 3.0 REVTE
Current and charge distributions of the fractional quantum Hall liquids with edges
An effective Chern-Simons theory for the quantum Hall states with edges is
studied by treating the edge and bulk properties in a unified fashion. An exact
steady-state solution is obtained for a half-plane geometry using the
Wiener-Hopf method. For a Hall bar with finite width, it is proved that the
charge and current distributions do not have a diverging singularity. It is
shown that there exists only a single mode even for the hierarchical states,
and the mode is not localized exponentially near the edges. Thus this result
differs from the edge picture in which electrons are treated as strictly one
dimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil
Spin swap gate in the presence of qubit inhomogeneity in a double quantum dot
We study theoretically the effects of qubit inhomogeneity on the quantum
logic gate of qubit swap, which is an integral part of the operations of a
quantum computer. Our focus here is to construct a robust pulse sequence for
swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum
dot trapped electron spins and the finite-time ramp-up of exchange coupling in
a double dot. We first present a geometric explanation of spin swap operation,
mapping the two-qubit operation onto a single-qubit rotation. We then show that
in this geometric picture a square-pulse-sequence can be easily designed to
perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate
how finite ramp-up times for the exchange coupling negatively affect the
performance of the swap gate sequence, and show how to correct the problems
numerically.Comment: published versio
An NMR-based nanostructure switch for quantum logic
We propose a nanostructure switch based on nuclear magnetic resonance (NMR)
which offers reliable quantum gate operation, an essential ingredient for
building a quantum computer. The nuclear resonance is controlled by the magic
number transitions of a few-electron quantum dot in an external magnetic field.Comment: 4 pages, 2 separate PostScript figures. Minor changes included. One
reference adde
Bulk Versus Edge in the Quantum Hall Effect
The manifestation of the bulk quantum Hall effect on edge is the chiral
anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge
approach'' of quantum Hall effect. In that approach, \sxy should not be taken
as the conductance derived from the space-local current-current correlation
function of the pure one-dimensional edge problem.Comment: 4 pages, RevTex, 1 postscript figur
Universal structure of the edge states of the fractional quantum Hall states
We present an effective theory for the bulk fractional quantum Hall states on
the Jain sequences on closed surfaces and show that it has a universal form
whose structure does not change from fraction to fraction. The structure of
this effective theory follows from the condition of global consistency of the
flux attachment transformation on closed surfaces. We derive the theory of the
edge states on a disk that follows naturally from this globally consistent
theory on a torus. We find that, for a fully polarized two-dimensional electron
gas, the edge states for all the Jain filling fractions have
only one propagating edge field that carries both energy and charge, and two
non-propagating edge fields of topological origin that are responsible for the
statistics of the excitations. Explicit results are derived for the electron
and quasiparticle operators and for their propagators at the edge. We show that
these operators create states with the correct charge and statistics. It is
found that the tunneling density of states for all the Jain states scales with
frequency as .Comment: 10 page
Quantum cellular automata quantum computing with endohedral fullerenes
We present a scheme to perform universal quantum computation using global
addressing techniques as applied to a physical system of endohedrally doped
fullerenes. The system consists of an ABAB linear array of Group V endohedrally
doped fullerenes. Each molecule spin site consists of a nuclear spin coupled
via a Hyperfine interaction to an electron spin. The electron spin of each
molecule is in a quartet ground state . Neighboring molecular electron
spins are coupled via a magnetic dipole interaction. We find that an
all-electron construction of a quantum cellular automata is frustrated due to
the degeneracy of the electronic transitions. However, we can construct a
quantum celluar automata quantum computing architecture using these molecules
by encoding the quantum information on the nuclear spins while using the
electron spins as a local bus. We deduce the NMR and ESR pulses required to
execute the basic cellular automata operation and obtain a rough figure of
merit for the the number of gate operations per decoherence time. We find that
this figure of merit compares well with other physical quantum computer
proposals. We argue that the proposed architecture meets well the first four
DiVincenzo criteria and we outline various routes towards meeting the fifth
criteria: qubit readout.Comment: 16 pages, Latex, 5 figures, See http://planck.thphys.may.ie/QIPDDF/
submitted to Phys. Rev.
Direct observation by resonant tunneling of the B^+ level in a delta-doped silicon barrier
We observe a resonance in the conductance of silicon tunneling devices with a
delta-doped barrier. The position of the resonance indicates that it arises
from tunneling through the B^+ state of the boron atoms of the delta-layer.
Since the emitter Fermi level in our devices is a field-independent reference
energy, we are able to directly observe the diamagnetic shift of the B^+ level.
This is contrary to the situation in magneto-optical spectroscopy, where the
shift is absorbed in the measured ionization energy.Comment: submitted to PR
Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
We present an effective Chern-Simons theory for the bulk fully polarized
fractional quantum Hall (FQH) hierarchical states constructed as daughters of
general states of the Jain series, {\it i. e.} as FQH states of the
quasi-particles or quasi-holes of Jain states. We discuss the stability of
these new states and present two reasonable stability criteria. We discuss the
theory of their edge states which follows naturally from this bulk theory. We
construct the operators that create elementary excitations, and discuss the
scaling behavior of the tunneling conductance in different situations. Under
the assumption that the edge states of these fully polarized hierarchical
states are unreconstructed and unresolved, we find that the differential
conductance for tunneling of electrons from a Fermi liquid into {\em any}
hierarchical Jain FQH states has the scaling behavior with the
universal exponent , where is the filling fraction of the
hierarchical state. Finally, we explore alternative ways of constructing FQH
states with the same filling fractions as partially polarized states, and
conclude that this is not possible within our approach.Comment: 10 pages, 50 references, no figures; formerly known as "Composite
Fermions: The Next Generation(s)" (title changed by the PRB thought police).
This version has more references and a discussion of the stability of the new
states. Published version. One erroneous reference is correcte
- …