4,586 research outputs found
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
In contrast to the homogeneous case, we show that there are compact
cohomogeneity one manifolds, that do not support invariant metrics of
non-negative sectional curvature. In fact we exhibit infinite families of such
manifolds including the exotic Kervaire spheres. Such examples exist for any
codimension of the singular orbits except for the case where both are equal to
two, where existence of non-negatively curved metrics is known.Comment: 10 page
Orientation and symmetries of Alexandrov spaces with applications in positive curvature
We develop two new tools for use in Alexandrov geometry: a theory of ramified
orientable double covers and a particularly useful version of the Slice Theorem
for actions of compact Lie groups. These tools are applied to the
classification of compact, positively curved Alexandrov spaces with maximal
symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice
Theorem, correcting omissions in the previous versio
Critical Current 0- Transition in Designed Josephson Quantum Dot Junctions
We report on quantum dot based Josephson junctions designed specifically for
measuring the supercurrent. From high-accuracy fitting of the current-voltage
characteristics we determine the full magnitude of the supercurrent (critical
current). Strong gate modulation of the critical current is observed through
several consecutive Coulomb blockade oscillations. The critical current crosses
zero close to, but not at, resonance due to the so-called 0- transition in
agreement with a simple theoretical model.Comment: 5 pages, 4 figures, (Supplementary information available at
http://www.fys.ku.dk/~hij/public/nl_supp.pdf
Coupling of shells in a carbon nanotube quantum dot
We systematically study the coupling of longitudinal modes (shells) in a
carbon nanotube quantum dot. Inelastic cotunneling spectroscopy is used to
probe the excitation spectrum in parallel, perpendicular and rotating magnetic
fields. The data is compared to a theoretical model including coupling between
shells, induced by atomically sharp disorder in the nanotube. The calculated
excitation spectra show good correspondence with experimental data.Comment: 8 pages, 4 figure
The asymmetrical anthropocene: resilience and the limits of posthumanism
In this article we critique resilience’s oft-celebrated overcoming of modern liberal frameworks. We bring work on resilience in geography and cognate fields into conversation with explorations of the ‘asymmetrical Anthropocene’, an emerging body of thought which emphasizes human-nonhuman relational asymmetry. Despite their resonances, there has been little engagement between these two responses to the human/world binary. This is important for changing the terms of the policy debate: engaging resilience through the asymmetrical Anthropocene framing shines a different light upon policy discourses of adaptative management, locating resilience as a continuation of modernity’s anthropocentric will-to-govern. From this vantage point, resilience is problematic, neglecting the powers of nonhuman worlds that are not accessible or appropriable for governmental use. However, this is not necessarily grounds for pessimism. To conclude, we argue that human political agency is even more vital in an indeterminate world
Single wall carbon nanotube double quantum dot
We report on two top-gate defined, coupled quantum dots in a semiconducting
single wall carbon nanotube, constituting a tunable double quantum dot system.
The single wall carbon nanotubes are contacted by titanium electrodes, and
gated by three narrow top-gate electrodes as well as a back-gate. We show that
a bias spectroscopy plot on just one of the two quantum dots can be used to
extract the addition energy of both quantum dots. Furthermore, honeycomb charge
stability diagrams are analyzed by an electrostatic capacitor model that
includes cross capacitances, and we extract the coupling energy of the double
quantum dot.Comment: Published in Applied Physics Letters 4 December 2006.
http://link.aip.org/link/?APL/89/23211
Magnetic-Field Dependence of Tunnel Couplings in Carbon Nanotube Quantum Dots
By means of sequential and cotunneling spectroscopy, we study the tunnel
couplings between metallic leads and individual levels in a carbon nanotube
quantum dot. The levels are ordered in shells consisting of two doublets with
strong- and weak-tunnel couplings, leading to gate-dependent level
renormalization. By comparison to a one- and two-shell model, this is shown to
be a consequence of disorder-induced valley mixing in the nanotube. Moreover, a
parallel magnetic field is shown to reduce this mixing and thus suppress the
effects of tunnel renormalization.Comment: 5 pages, 3 figures; revised version as publishe
Singlet-Triplet Physics and Shell Filling in Carbon Nanotube Double Quantum Dots
An artifcial two-atomic molecule, also called a double quantum dot (DQD), is
an ideal system for exploring few electron physics. Spin-entanglement between
just two electrons can be explored in such systems where singlet and triplet
states are accessible. These two spin-states can be regarded as the two states
in a quantum two-state system, a so-called singlet-triplet qubit. A very
attractive material for realizing spin based qubits is the carbon nanotube
(CNT), because it is expected to have a very long spin coherence time. Here we
show the existence of a gate-tunable singlet-triplet qubit in a CNT DQD. We
show that the CNT DQD has clear shell structures of both four and eight
electrons, with the singlet-triplet qubit present in the four-electron shells.
We furthermore observe inelastic cotunneling via the singlet and triplet
states, which we use to probe the splitting between singlet and triplet, in
good agreement with theory.Comment: Supplement available at:
http://www.fys.ku.dk/~hij/public/singlet-triple_supp.pd
Quantum transport in carbon nanotubes
Carbon nanotubes are a versatile material in which many aspects of condensed
matter physics come together. Recent discoveries, enabled by sophisticated
fabrication, have uncovered new phenomena that completely change our
understanding of transport in these devices, especially the role of the spin
and valley degrees of freedom. This review describes the modern understanding
of transport through nanotube devices.
Unlike conventional semiconductors, electrons in nanotubes have two angular
momentum quantum numbers, arising from spin and from valley freedom. We focus
on the interplay between the two. In single quantum dots defined in short
lengths of nanotube, the energy levels associated with each degree of freedom,
and the spin-orbit coupling between them, are revealed by Coulomb blockade
spectroscopy. In double quantum dots, the combination of quantum numbers
modifies the selection rules of Pauli blockade. This can be exploited to read
out spin and valley qubits, and to measure the decay of these states through
coupling to nuclear spins and phonons. A second unique property of carbon
nanotubes is that the combination of valley freedom and electron-electron
interactions in one dimension strongly modifies their transport behaviour.
Interaction between electrons inside and outside a quantum dot is manifested in
SU(4) Kondo behavior and level renormalization. Interaction within a dot leads
to Wigner molecules and more complex correlated states.
This review takes an experimental perspective informed by recent advances in
theory. As well as the well-understood overall picture, we also state clearly
open questions for the field. These advances position nanotubes as a leading
system for the study of spin and valley physics in one dimension where
electronic disorder and hyperfine interaction can both be reduced to a very low
level.Comment: In press at Reviews of Modern Physics. 68 pages, 55 figure
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