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We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining transition, Luescher's gradient flow, and the cooling flow to set the scale. Of those, the cooling flow turns out to be computationally most efficient. We explore systematic errors due to use of three different energy observables and two distinct reference values for the flow time, the latter obtained by matching initial scaling behavior of some energy observables to that of the deconfining transition. Another important source of systematic errors are distinct fitting forms for the approach to the continuum limit. Besides relying in the conventional way on ratios of masses, we elaborate on a form introduced by Allton, which incorporates asymptotic scaling behavior. Ultimately we find that, though still small, our systematic errors are considerably larger than our statistical errors., Comment: 8 pages, 5 figures (lattice 2017 contribution)

Tunable optical devices, in particular, varifocal lenses, have important applications in various fields, including imaging and adaptive vision. Recent advances in metasurfaces, which control the wavefront of light using subwavelength-spaced nanostructures, open up new opportunities to replace bulk optical devices, with thin, flat, lightweight devices. We have demonstrated for the first time an electrically tunable flat lens, based on large area metasurfaces combined with a dielectric elastomer actuator having inline transparent electrodes, that is capable of simultaneously performing focal length tuning (>100%) as well as dynamic corrections, including astigmatism and image shift. This offers control versatility to flat optics hitherto only possible in electron microscopes. The water-based transfer process, which we describe, also enables wide compatibility across materials. The combination of metasurface optics and dielectric elastomer actuators enables a new, versatile platform for creating all kinds of tunable optical devices, through the design of tunable phase, amplitude, and polarization profiles.

We study charge transport through a floating mesoscopic superconductor coupled to counterpropagating fractional quantum Hall edges at filling fraction $\nu=2/3$. We consider a superconducting island with finite charging energy and investigate its effect on transport through the device. We calculate conductance through such a system as a function of temperature and gate voltage applied to the superconducting island. We show that transport is strongly affected by the presence of parafermionic zero modes, leading at zero temperature to a zero-bias conductance quantized in units of $\nu e^2/h$ independent of the applied gate voltage.

Spin-orbit coupled semiconducting nanowires with proximity-induced superconductivity are expected to host Majorana zero modes at their endpoints when a sufficiently strong magnetic field is applied. The resulting phase would be a one-dimensional topological superconductor. However, while a variety of experiments have been performed observing a zero bias conductance peak (suggestive of Majorana zero modes), the topological nature of these physical systems is still a subject of debate. Here we suggest a quantitative test of the degree to which a system displaying a zero bias peak may be considered topological. The experiment is similar to previous measurements of conductance, but is performed with the aid of a quantum dot at the wire's end. We arrive at the surprising result that the non-local nature of the topological system may be identified through a local measurement., Comment: 4+ pages, 3 Figures

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining phase transition, the gradient flow and the cooling flow to set the scale. For the gradient and cooling scales we explore three different energy observables and two distinct reference values for the flow time. When the aim is to follow scaling towards the continuum limit, one gains at least a factor of 100 in computational efficiency by relying on the gradient instead of the deconfinement scale. Using cooling instead of the gradient flow one gains another factor of at least 34 in computational efficiency on the gradient flow part without any significant loss in the accuracy of scale setting. Concerning our observables, the message is to keep it simple. The Wilson action itself performs as well as or even better than the other two observables explored. Two distinct fitting forms for scaling are compared of which one connects to asymptotic scaling. Differences of the obtained estimates show that systematic errors of length ratios, though only about 1%, can be considerably larger than statistical errors of the same observables., Comment: 13 pages, 5 figures

Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an interposed superconductor. Despite substantial experimental progress, we argue that the necessary crossed Andreev reflection in this arrangement is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermionic zero modes from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demonstrated in recent experiments. We show that for a spin-singlet superconductor interacting with loops of spin unpolarized $2/3$ fractional quantum edge, even an array size of order ten should allow one to systematically tune into a parafermionic degeneracy., Comment: 4 pages, 3 figures, 5 pages of supplementary material

Given recent progress in the realization of Majorana zero modes in semiconducting nanowires with proximity-induced superconductivity, a crucial next step is to attempt an experimental demonstration of the predicted braiding statistics associated with the Majorana mode. Such a demonstration should, in principle, confirm that observed zero-bias anomalies are indeed indicative of the presence of anyonic Majorana zero modes. Moreover, such a demonstration would be a breakthrough at the level of fundamental physics: the first clear demonstration of a non-Abelian excitation. It is therefore important to clarify the expected signals of Majorana physics in the braiding context, and to differentiate these signals from those that might also arise in non-topological variants of the same system. A definitive and critical distinction between signals expected in topological (i.e. anyonic) and non-topological (i.e. trivial) situations is therefore essential for future progress in the field. In this manuscript, we carefully examine the expected signals of braiding and fusion experiments in topological and non-topological variants of the experimental nanowire systems in which Majoranas are predicted to occur. We point out situations where `trivial' and `anyonic' signatures may be similar experimentally, necessitating a certain level of caution in the interpretation of various proposed fusion and braiding experiments. We find in particular that braiding experiments consisting of full braids (two Majorana exchanges) are better at distinguishing between topological and non-topological systems than fusion experiments or experiments with an odd number of Majorana exchanges., Comment: 10 pages, 3 figures, Updated to published version