64,219 research outputs found
Degenerate states of narrow semiconductor rings in the presence of spin orbit coupling: Role of time-reversal and large gauge transformations
The electron Hamiltonian of narrow semiconductor rings with the Rashba and
Dresselhaus spin orbit terms is invariant under time-reversal operation
followed by a large gauge transformation. We find that all the eigenstates are
doubly degenerate when integer or half-integer quantum fluxes thread the
quantum ring. The wavefunctions of a degenerate pair are related to each other
by the symmetry operation. These results are valid even in the presence of a
disorder potential. When the Zeeman term is present only some of these
degenerate levels anticross
Comment on ``Effective Mass and g-Factor of Four Flux Quanta Composite Fermions"
In a recent Letter, Yeh et al.[Phys. Rev. Lett. 82, 592 (1999)] have shown
beautiful experimental results which indicate that the composite fermions with
four flux quanta (CF) behave as fermions with mass and spin just like those
with two flux quanta. They observed the collapse of the fractional quantum Hall
gaps when the following condition is satisfied with some integer ,
, where and
are the g-factor and the cyclotron frequency of the CF,
respectively. However, in their picture the gap at the Fermi energy remains
always finite even if the above condition is satisfied, thus the reason of the
collapse was left as a mystery. In this comment it is shown that part of the
mystery is resolved by considering the electron-hole symmetry properly.Comment: 2 pages, RevTeX. Minor chang
Comment on ``Evidence for Anisotropic State of Two-Dimensional Electrons in High Landau Levels''
In a recent letter M. Lilly et al [PRL 82, 394 (1999)] have shown that a
highly anisotropic state can arise in certain two dimensional electron systems.
In the large square samples studied, resistances measured in the two
perpendicular directions are found to have a ratio that may be 60 or larger at
low temperature and at certain magnetic fields. In Hall bar measurements, the
anisotropy ratio is found to be much smaller (roughly 5). In this comment we
resolve this discrepancy by noting that the anisotropy of the underlying sheet
resistivities is correctly represented by Hall bar resistance measurements but
shows up exponentially enhanced in resistance measurements on square samples
due to simple geometric effects. We note, however, that the origin of this
underlying resistivity anisotropy remains unknown, and is not addressed here.Comment: 1 page, minor calculational error repaire
Finite Conductivity in Mesoscopic Hall Bars of Inverted InAs/GaSb Quantum Wells
We have studied experimentally the low temperature conductivity of mesoscopic
size InAs/GaSb quantum well Hall bar devices in the inverted regime. Using a
pair of electrostatic gates we were able to move the Fermi level into the
electron-hole hybridization state, and observe a mini gap. Temperature
dependence of the conductivity in the gap shows residual conductivity, which
can be consistently explained by the contributions from the free as well as the
hybridized carriers in the presence of impurity scattering, as proposed by
Naveh and Laikhtman [Euro. Phys. Lett., 55, 545-551 (2001)]. Experimental
implications for the stability of proposed helical edge states will be
discussed.Comment: 5 pages, 4 figure
Counting Labelled Trees with Given Indegree Sequence
For a labelled tree on the vertex set , define the
direction of each edge to be if . The indegree sequence of
can be considered as a partition . The enumeration of
trees with a given indegree sequence arises in counting secant planes of curves
in projective spaces. Recently Ethan Cotterill conjectured a formula for the
number of trees on with indegree sequence corresponding to a partition
. In this paper we give two proofs of Cotterill's conjecture: one is
`semi-combinatorial" based on induction, the other is a bijective proof.Comment: 10 page
Microwave photoresistance of a high-mobility two-dimensional electron gas in a triangular antidot lattice
The microwave (MW) photoresistance has been measured on a high-mobility
two-dimensional electron gas patterned with a shallow triangular antidot
lattice, where both the MW-induced resistance oscillations (MIRO) and
magnetoplasmon (MP) resonance are observed superposing on sharp commensurate
geometrical resonance (GR). Analysis shows that the MIRO, MP, and GR are
decoupled from each other in these experiments.Comment: 5 pages, 4 figures, paper accepted by PR
Counting Humps in Motzkin paths
In this paper we study the number of humps (peaks) in Dyck, Motzkin and
Schr\"{o}der paths. Recently A. Regev noticed that the number of peaks in all
Dyck paths of order is one half of the number of super Dyck paths of order
. He also computed the number of humps in Motzkin paths and found a similar
relation, and asked for bijective proofs. We give a bijection and prove these
results. Using this bijection we also give a new proof that the number of Dyck
paths of order with peaks is the Narayana number. By double counting
super Schr\"{o}der paths, we also get an identity involving products of
binomial coefficients.Comment: 8 pages, 2 Figure
Measurement of brood patch temperature of British passerines using an infrared thermometer
Capsule An infrared ear thermometer can be easily used to measure brood patch temperature in passerines caught on the nest or in mist-nets
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