Symmetry, delocalization, and molecular conductance

Molecules bonded between two metal contacts form the simplest possible molecular devices. Coupled by the molecule, the left and right contact-based states form symmetric and antisymmetric pairs near the Fermi level. We relate the size of the resulting energy splitting DeltaE to the symmetry and degree of delocalization of the coupling molecular orbital. Qualitative trends in molecular conductances are then estimated from the variations in DeltaE. We examine benzenedithiol and other molecules of interest in transport. (C) 2005 American Institute of Physics.

Broken symmetry and pseudogaps in ropes of carbon nanotubes

Since the discovery of carbon nanotubes, it has been speculated that these materials should behave like nanoscale wires with unusual electronic properties and exceptional strength. Recently, 'ropes' of close-packed single-wall nanotubes have been synthesized in high yield. The tubes in these ropes are mainly of the (10,10) type3, which is predicted to be metallic. Experiments on individual nanotubes and ropes indicate that these systems indeed have transport properties that qualify them to be viewed as nanoscale quantum wires at low temperature. It has been expected that the close-packing of individual nanotubes into ropes does not change their electronic properties significantly. Here, however, we present first-principles calculations which show that a broken symmetry of the (10,10) tube caused by interactions between tubes in a rope induces a pseudogap of about 0.1 eV at the Fermi level. This pseudogap strongly modifies many of the fundamental electronic properties: we predict a semimetal-like temperature dependence of the electrical conductivity and a finite gap in the infrared absorption spectrum. The existence of both electron and hole charge carriers will lead to qualitatively different thermopower and Hall-effect behaviours from those expected for a normal metal.

Broken symmetry and pseudogaps in ropes of carbon nanotubes

We investigate the influence of tube-tube interactions in ropes of (10,10) carbon nanotubes, and find that these effects induce a pseudogap in the density of state (DOS) of the rope of width 0.1 eV at the Fermi level. In an isolated (n,n) carbon nanotube there are two bands that cross in a linear fashion at the Fermi level, making the nanotube metallic with a DOS that is constant in a 1.5 eV wide window around the Fermi energy. The presence of the neighbouring tubes causes these two bands to repel, opening up a band gap that can be as large as 0.3 eV. The small dispersion in the plane perpendicular to the rope smears out this gap for a rope with a large cross-sectional area, and we see a pseudogap at the Fermi energy in the DOS where the DOS falls to one third of its value for the isolated tube. This phenomenon should affect many properties of the behavior of ropes of (n,n) nanotubes, which should display a more semimetallic character than expected in transport and doping experiments, with the existence of both hole and electron carriers leading to qualitatively different thermopower and Hall-effect behaviors from those expected for a normal metal. Band repulsion like this can be expected to occur for any tube perturbed by a sufficiently strong interaction, for example, from contact with a surface or with other tubes.

Complete Sudoku - extra rules for more symmetry

We propose some extra rules to add to the well-known Sudoku puzzle and present an argument to justify their inclusion. The rules mean that puzzles can be created with fewer cells completed initially yet which still have only one solution. We have created a Web-based program which can be used to generate and solve both standard and extended (Complete) puzzles.

Presentism and ontological symmetry

In this paper, I argue that there is an inconsistency between two presentist doctrines: that of ontological symmetry and asymmetry of fixity. The former refers to the presentist belief that the past and future are equally unreal. The latter refers to the A-Theoretic intuition that the past is closed or actual, and the future is open or potential. My position in this paper is that the presentist is unable to account for the temporal asymmetry that is so fundamentally a part of her theory. In Section I, I briefly outline a recent defence of presentism due to Craig, and argue that a flaw in this defence highlights the tension between the presentist's doctrines of ontological symmetry and asymmetry of fixity. In Section II, I undertake an investigation, on the presentist's behalf, in order to determine whether she is capable of reconciling these two doctrines. In the course of the investigation, I consider different asymmetries, other than that of ontology, which might be said fundamentally to constitute temporal asymmetry, and the asymmetry of fixity in particular. In Section III, I also consider whether the presentist is able to avail herself of some of the standard B-Theoretic accounts of the asymmetry of fixity, and argue that she cannot. Finally, I conclude that temporal asymmetry cannot be accounted for (or explained) other than through the postulation of an ontological asymmetry.

Lorentz TEM investigation of the switching behavior in artificial spin ice building blocks

Frustration – the inability to simultaneously satisfy all interactions – occurs in a wide range of systems including neural networks, water ice and magnetic systems. An example of the latter is the so called spin-ice in pyrochlore materials [1] which have attracted a lot of interest not least due to the emergence of magnetic monopole defects when the ‘ice rules’ governing the local ordering breaks down [2]. However it is not possible to directly measure the frustrated property – the direction of the magnetic moments – in such spin ice systems with current experimental techniques. This problem can be solved by instead studying artificial spin-ice systems where the molecular magnetic moments are replaced by nanoscale ferromagnetic islands [3-8]. Two different arrangements of the ferromagnetic islands have been shown to exhibit spin ice behaviour: a square lattice maintaining four moments at each vertex [3,8] and the Kagome lattice which has only three moments per vertex but equivalent interactions between them [4-7]. Magnetic monopole defects have been observed in both types of lattices [7-8]. One of the challenges when studying these artificial spin-ice systems is that it is difficult to arrive at the fully demagnetised ground-state [6-8].
Here we present a study of the switching behaviour of building blocks of the Kagome lattice influenced by the termination of the lattice. Ferromagnetic islands of nominal size 1000 nm by 100 nm were fabricated in five island blocks using electron-beam lithography and lift-off techniques of evaporated 18 nm Permalloy (Ni80Fe20) films. Each block consists of a central island with four arms terminated by a different number and placement of ‘injection pads’, see Figure 1. The islands are single domain and magnetised along their long axis. The structures were grown on a 50 nm thick electron transparent silicon nitride membrane to allow TEM observation, which was back-coated with a 5 nm film of Au to prevent charge build-up during the TEM experiments.
To study the switching behaviour the sample was subjected to a magnetic field strong enough to magnetise all the blocks in one direction, see Figure 1. Each block obeys the Kagome lattice ‘ice-rules’ of “2-in, 1-out” or “1-in, 2-out” in this fully magnetised state. Fresnel mode Lorentz TEM images of the sample were then recorded as a magnetic field of increasing magnitude was applied in the opposite direction. While the Fresnel mode is normally used to image magnetic domain structures [9] for these types of samples it is possible to deduce the direction of the magnetisation from the Lorentz contrast [5]. All images were recorded at the same over-focus judged to give good Lorentz contrast.
The magnetisation was found to switch at different magnitudes of the applied field for nominally identical blocks. However, trends could still be identified: all the blocks with any injection pads, regardless of placement and number, switched the direction of the magnetisation of their central island at significantly smaller magnitudes of the applied magnetic field than the blocks without injection pads. It can therefore be concluded that the addition of an injection pad lowers the energy barrier to switching the connected island, acting as a nucleation site for monopole defects. In these five island blocks the defects immediately propagate through to the other side, but in a larger lattice the monopoles could potentially become trapped at a vertex and observed [10].
References

[1] M J Harris et al, Phys Rev Lett 79 (1997) p.2554.
[2] C Castelnovo, R Moessner and S L Sondhi, Nature 451 (2008) p. 42.
[3] R F Wang et al, Nature 439 (2006) 303.
[4] M Tanaka et al, Phys Rev B 73 (2006) 052411.
[5] Y Qi, T Brintlinger and J Cumings, Phys Rev B 77 (2008) 094418.
[6] E Mengotti et al, Phys Rev B 78 (2008) 144402.
[7] S Ladak et al, Nature Phys 6 (2010) 359.
[8] C Phatak et al, Phys Rev B 83 (2011) 174431.
[9] J N Chapman, J Phys D 17 (1984) 623.
[10] The authors gratefully acknowledge funding from the EPSRC under grant number EP/D063329/1.

MALTS: A Tool to Simulate Lorentz Transmission Electron Microscopy From Micromagnetic Simulations

Here we describe the development of the MALTS software which is a generalized tool that simulates Lorentz Transmission Electron Microscopy (LTEM) contrast of magnetic nanostructures. Complex magnetic nanostructures typically have multiple stable domain structures. MALTS works in conjunction with the open access micromagnetic software Object Oriented Micromagnetic Framework or MuMax. Magnetically stable trial magnetization states of the object of interest are input into MALTS and simulated LTEM images are output. MALTS computes the magnetic and electric phases accrued by the transmitted electrons via the Aharonov-Bohm expressions. Transfer and envelope functions are used to simulate the progression of the electron wave through the microscope lenses. The final contrast image due to these effects is determined by Fourier Optics. Similar approaches have been used previously for simulations of specific cases of LTEM contrast. The novelty here is the integration with micromagnetic codes via a simple user interface enabling the computation of the contrast from any structure. The output from MALTS is in good agreement with both experimental data and published LTEM simulations. A widely-available generalized code for the analysis of Lorentz contrast is a much needed step towards the use of LTEM as a standardized laboratory technique.

Design of a cavity backed spiral antenna with improved pattern symmetry

In this paper we investigate the azimuthal pattern symmetry of an Archimedean spiral antenna which is designed to operate over the frequency range 3-10 GHz. The performance of the spiral in free space is compared with a structure that is backed by a perfect electric conductor with a separation distance of ?/4 at the operating frequencies. The latter arrangement exhibits a higher gain, however it is observed that the radiation patterns are less symmetrical about boresight and this performance degradation increases with frequency. The predicted 3 dB beamwidth difference is shown to vary between 14° (3 GHz) and 51° (10 GHz). An improved antenna design is described which reduces the pattern asymmetry to ˜ 2° at 10 GHz. The reduction in modal contamination is obtained by inserting slots carefully arranged in a radial pattern to disrupt the surface currents that flow on the ground plane of the antenna