Swiss cheese sets are compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Such sets have provided numerous counterexamples in the theory of uniform algebras. In this paper, we introduce a topological
space whose elements are what we call abstract Swiss cheeses. Working within this topological space, we show how to prove the existence of classical Swiss cheese sets (as discussed in a paper of Feinstein and Heath from 2010) with various desired properties. We first give a new proof of the Feinstein-Heath classicalisation theorem. We then consider when it is possible to classicalise a Swiss cheese while leaving disks which lie outside a given region unchanged. We also consider sets obtained by deleting a sequence of open disks from a closed annulus, and we obtain an analogue of the Feinstein-Heath theorem for these sets. We then discuss regularity for certain uniform algebras. We conclude with an application of these techniques to obtain a classical Swiss cheese set which has the same properties as a non-classical example of OFarrell (1979).
The new paradigm of heterostructures based on two-dimensional (2D) atomic crystals has already led to the observation of exciting physical phenomena and creation of novel devices. The possibility of combining layers of different 2D materials in one s
tack allows unprecedented control over the electronic and optical properties of the resulting material. Still, the current method of mechanical transfer of individual 2D crystals, though allowing exceptional control over the quality of such structures and interfaces, is not scalable. Here we show that such heterostructures can be assembled from chemically exfoliated 2D crystals, allowing for low-cost and scalable methods to be used in the device fabrication.
Semiconductor quantum dots provide a two-dimensional analogy for real atoms and show promise for the implementation of scalable quantum computers. Here, we investigate the charge configurations in a silicon metal-oxide-semiconductor double quantum do
t tunnel coupled to a single reservoir of electrons. By operating the system in the few-electron regime, the stability diagram shows hysteretic tunnelling events that depend on the history of the dots charge occupancy. We present a model which accounts for the observed hysteretic behaviour by extending the established description for transport in double dots coupled to two reservoirs. We demonstrate that this type of device operates like a single-electron memory latch.
The valley-orbit coupling in a few-electron Si quantum dot is expected to be a function of its occupation number N. We study the spectrum of multivalley Si quantum dots for 2 <= N <= 4, showing that, counterintuitively, electron-electron interaction
effects on the valley-orbit coupling are negligible. For N=2 they are suppressed by valley interference, for N=3 they vanish due to spinor overlaps, and for N = 4 they cancel between different pairs of electrons. To corroborate our theoretical findings, we examine the experimental energy spectrum of a few-electron metal-oxide-semiconductor quantum dot. The measured spin-valley state filling sequence in a magnetic field reveals that the valley-orbit coupling is definitively unaffected by the occupation number.
We observe interfacial ferromagnetism in superlattices of the paramagnetic metal LaNiO3 and the antiferromagnetic insulator CaMnO3. LaNiO3 exhibits a thickness dependent metal-insulator transition and we find the emergence of ferromagnetism to be coi
ncident with the conducting state of LaNiO3. That is, only superlattices in which the LaNiO3 layers are metallic exhibit ferromagnetism. Using several magnetic probes, we have determined that the ferromagnetism arises in a single unit cell of CaMnO3 at the interface. Together these results suggest that ferromagnetism can be attributed to a double exchange interaction among Mn ions mediated by the adjacent itinerant metal.
Although silicon is a promising material for quantum computation, the degeneracy of the conduction band minima (valleys) must be lifted with a splitting sufficient to ensure formation of well-defined and long-lived spin qubits. Here we demonstrate th
at valley separation can be accurately tuned via electrostatic gate control in a metal-oxide-semiconductor quantum dot, providing splittings spanning 0.3 - 0.8 meV. The splitting varies linearly with applied electric field, with a ratio in agreement with atomistic tight-binding predictions. We demonstrate single-shot spin readout and measure the spin relaxation for different valley configurations and dot occupancies, finding one-electron lifetimes exceeding 2 seconds. Spin relaxation occurs via phonon emission due to spin-orbit coupling between the valley states, a process not previously anticipated for silicon quantum dots. An analytical theory describes the magnetic field dependence of the relaxation rate, including the presence of a dramatic rate enhancement (or hot-spot) when Zeeman and valley splittings coincide.
Understanding interactions between orbital and valley quantum states in silicon nanodevices is crucial in assessing the prospects of spin-based qubits. We study the energy spectra of a few-electron silicon metal-oxide-semiconductor quantum dot using
dynamic charge sensing and pulsed-voltage spectroscopy. The occupancy of the quantum dot is probed down to the single-electron level using a nearby single-electron transistor as a charge sensor. The energy of the first orbital excited state is found to decrease rapidly as the electron occupancy increases from N=1 to 4. By monitoring the sequential spin filling of the dot we extract a valley splitting of ~230 {mu}eV, irrespective of electron number. This indicates that favorable conditions for qubit operation are in place in the few-electron regime.
The nature of the magnetism brought about by Fe adatoms on the surface of the topological insulator Bi2Se3 was examined in terms of density functional calculations. The Fe adatoms exhibit strong easy-axis magnetic anisotropy in the dilute adsorption
limit due to the topological surface states (TSS). The spin exchange J between the Fe adatoms follows a Ruderman-Kittel-Kasuya-Yosida (RKKY) behavior with substantial anisotropy, and the Dzyaloshinskii-Moriya (DM) interaction between them is quite strong with |D/J|~0.3 under the mediation by the TSS, and can be further raised to ~0.6 by an external electric field. The apparent single-ion anisotropy of a Fe adatom is indispensable in determining the spin orientation.
We report charge sensing measurements of a silicon metal-oxide-semiconductor quantum dot using a single-electron transistor as a charge sensor with dynamic feedback control. Using digitallycontrolled feedback, the sensor exhibits sensitive and robust
detection of the charge state of the quantum dot, even in the presence of charge drifts and random charge rearrangements. The sensor enables the occupancy of the quantum dot to be probed down to the single electron level.
State-to-state differential cross sections (DCSs) for rotationally inelastic scattering of H2O by H2 have been measured at 71.2 meV (574 cm-1) and 44.8 meV (361 cm-1) collision energy using crossed molecular beams combined with velocity map imaging.
A molecular beam containing variable compositions of the (J = 0, 1, 2) rotational states of hydrogen collides with a molecular beam of argon seeded with water vapor that is cooled by supersonic expansion to its lowest para or ortho rotational levels (JKaKc= 000 and 101, respectively). Angular speed distributions of fully specified rotationally excited final states are obtained using velocity map imaging. Relative integral cross sections are obtained by integrating the DCSs taken with the same experimental conditions. Experimental state-specific DCSs are compared with predictions from fully quantum scattering calculations on the most complete H2O-H2 potential energy surface. Comparison of relative total cross sections and state-specific DCSs show excellent agreement with theory in almost all details
