Strongly angle-dependent magnetoresistance in Weyl semimetals with long-range disorder

The chiral anomaly in Weyl semimetals states that the left- and right-handed Weyl fermions, constituting the low energy description, are not individually conserved, resulting, for example, in a negative magnetoresistance in such materials. Recent experiments see strong indications of such an anomalous resistance response; however, with a response that at strong fields is more sharply peaked for parallel magnetic and electric fields than expected from simple theoretical considerations. Here, we uncover a mechanism, arising from the interplay between the angle-dependent Landau level structure and long-range scalar disorder, that has the same phenomenology. In particular, we ana- lytically show, and numerically confirm, that the internode scattering time decreases exponentially with the angle between the magnetic field and the Weyl node separation in the large field limit, while it is insensitive to this angle at weak magnetic fields. Since, in the simplest approximation, the internode scattering time is proportional to the anomaly-related conductivity, this feature may be related to the experimental observations of a sharply peaked magnetoresistance.Comment: 8 pages, 4 figure

Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes k Majorana fermions with random all-to-all four-body interactions. We consider the SYK model in the framework of a many-body Altland-Zirnbauer classification that sees the system as belonging to one of eight (real) symmetry classes depending on the value of k mod 8. We show that, depending on the symmetry class, the system may support exact many-body zero modes with the symmetries also dictating whether these may have a nonzero contribution to Majorana fermions, i.e., single-particle weight. These zero modes appear in all but two of the symmetry classes. When present, they leave clear signatures in physical observables that go beyond the threefold (Wigner-Dyson) possibilities for level spacing statistics studied earlier. Signatures we discover include a zero-energy peak or hole in the single-particle spectral function, depending on whether symmetries allow or forbid zero modes to have single-particle weight. The zero modes are also shown to influence the many-body dynamics, where signatures include a nonzero long-time limit for the out-of-time-order correlation function. Furthermore, we show that the extension of the four-body SYK model by quadratic terms can be interpreted as realizing the remaining two complex symmetry classes; we thus demonstrate how the entire tenfold Altland-Zirnbauer classification may emerge in the SYK model

Transversal magnetotransport in Weyl semimetals: Exact numerical approach

Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work, we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.Comment: 10 pages, 4 figure

Walk the dog, or: products of open balls in the space of continuous functions

Let C[0,1] be the Banach algebra of real valued continuous functions on [0,1], provided with the supremum norm. For f,g\in C[0,1] and balls B_{f}, B_{g} with center f and g, respectively, it is not necessarily true that f\cdot g is in the interior of B_{f}\cdot B_{g}. In the present paper we characterize those pairs f, g where this is the case. The problem is illustrated by using a suitable translation. One studies walks in a landscape with hills and valleys where an accompanying dog can move in a certain prescribed way

A study of the need for curriculum adjustments in Weeping Water high school

The purpose of this thesis is to build a curriculum that will meet the needs of the pupils in this locality. The procedure consists in examining past practices, making a scientific survey of prevailing conditions, helping each pupil select the type of work for which he is best fitted, and permitting the results to emerge as the needs of the school demand. The results will be used not only to build a more suitable offering for the high school pupil, but also to serve the instructor as as introduction to the school philosophy and community conditions