213 research outputs found
Measuring the phonon-assisted spectral function by using a non-quilibrium three-terminal single-molecular device
The electron transport through a three-terminal single-molecular transistor
(SMT) is theoretically studied. We find that the differential conductance of
the third and weakly coupled terminal versus its voltage matches well with the
spectral function versus the energy when certain conditions are met.
Particularly, this excellent matching is maintained even for complicated
structure of the phonon-assisted side peaks. Thus, this device offers an
experimental approach to explore the shape of the phonon-assisted spectral
function in detail. In addition we discuss the conditions of a perfect
matching. The results show that at low temperatures the matching survives
regardless of the bias and the energy levels of the SMT. However, at high
temperatures, the matching is destroyed.Comment: 9 pages, 5 figure
One-dimensional quantum channel in a graphene line defect
Using a tight-binding model, we study a line defect in graphene where a bulk
energy gap is opened by sublattice symmetry breaking. It is found that
sublattice symmetry breaking may induce many configurations that correspond to
different band spectra. In particular, a gapless state is observed for a
configuration which hold a mirror symmetry with respect to the line defect. We
find that this gapless state originates from the line defect and is independent
of the width of the graphene ribbon, the location of the line defect, and the
potentials in the edges of the ribbon. In particular, the gapless state can be
controlled by the gate voltage embedded below the line defect. Finally, this
result is supported with conductance calculations. This study shows how a
quantum channel could be constructed using a line defect, and how the quantum
channel can be controlled by tuning the gate voltage embedded below the line
defect.Comment: 8 pages, 10 figure
Provable Sample-Efficient Sparse Phase Retrieval Initialized by Truncated Power Method
We study the sparse phase retrieval problem, recovering an -sparse
length- signal from magnitude-only measurements. Two-stage non-convex
approaches have drawn much attention in recent studies for this problem.
Despite non-convexity, many two-stage algorithms provably converge to the
underlying solution linearly when appropriately initialized. However, in terms
of sample complexity, the bottleneck of those algorithms often comes from the
initialization stage. Although the refinement stage usually needs only
measurements, the widely used spectral initialization in
the initialization stage requires measurements to produce
a desired initial guess, which causes the total sample complexity order-wisely
more than necessary. To reduce the number of measurements, we propose a
truncated power method to replace the spectral initialization for non-convex
sparse phase retrieval algorithms. We prove that
measurements, where is the stable sparsity of the underlying signal,
are sufficient to produce a desired initial guess. When the underlying signal
contains only very few significant components, the sample complexity of the
proposed algorithm is and optimal. Numerical experiments
illustrate that the proposed method is more sample-efficient than
state-of-the-art algorithms
Disorder and metal-insulator transitions in Weyl semimetals
The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has
Weyl nodes in bulk excitations and Fermi arcs surface states. We study the
effects of disorder and localization in WSMs and find three exotic phase
transitions. (I) Two Weyl nodes near the Brillouin zone boundary can be
annihilated pairwise by disorder scattering, resulting in the opening of a
topologically nontrivial gap and a transition from a WSM to a three-dimensional
(3D) quantum anomalous Hall state. (II) When the two Weyl nodes are well
separated in momentum space, the emergent bulk extended states can give rise to
a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (III)
Two Weyl nodes can emerge near the zone center when an insulating gap closes
with increasing disorder, enabling a direct transition from a normal band
insulator to a WSM. We determine the phase diagram by numerically computing the
localization length and the Hall conductivity, and propose that the exotic
phase transitions can be realized on a photonic lattice.Comment: 7 pages with appendix, 6 figure
Disorder induced field effect transistor in bilayer and trilayer graphene
We propose use of disorder to produce a field effect transistor (FET) in
biased bilayer and trilayer graphene. Modulation of the bias voltage can
produce large variations in the conductance when the disorder's effects are
confined to only one of the graphene layers. This effect is based on the bias
voltage's ability to select which of the graphene layers carries current, and
is not tied to the presence of a gap in the density of states. In particular,
we demonstrate this effect in models of gapless ABA-stacked trilayer graphene,
gapped ABC-stacked trilayer graphene, and gapped bilayer graphene.Comment: 21 pages, 7 figure
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