Scattering states of a vortex in the proximity-induced superconducting state at the interface of a topological insulator and an s-wave superconductor

We consider an isolated vortex in the two-dimensional proximity-induced superconducting state formed at the interface of a three-dimensional strong topological insulator (TI) and an s-wave superconductor (sSC). Prior calculations of the bound states of this system famously revealed a zero-energy state that is its own conjugate, a Majorana fermion bound to the vortex core. We calculate, not the bound states, but the scattering states of this system, and ask how the spin-momentum-locked massless Dirac form of the single-particle Hamiltonian, inherited from the TI surface, affects the cross section for scattering Bogoliubov quasiparticles from the vortex. As in the case of an ordinary superconductor, this is a two-channel problem with the vortex mixing particle-like and hole-like excitations. And as in the ordinary case, the same-channel differential cross section diverges in the forward direction due to the Aharonov-Bohm effect, resulting in an infinite total cross section but finite transport and skew cross sections. We calculate the transport and skew cross sections numerically, via a partial wave analysis, as a function of both quasiparticle excitation energy and chemical potential. Novel effects emerge as particle-like or hole-like excitations are tuned through the Dirac point.Comment: 16 pages, 7 figures; modified title, improved figures, as published in PR

Computing rotation and self-linking numbers in contact surgery diagrams

We give an explicit formula to compute the rotation number of a nullhomologous Legendrian knot in contact (1/n)-surgery diagrams along Legendrian links and obtain a corresponding result for the self-linking number of transverse knots. Moreover, we extend the formula by Ding-Geiges-Stipsicz for computing the d3-invariant to (1/n)-surgeries.Comment: 19 pages, 6 figures; V2: Added the section on the d3-invariant and fixed a few misprints; V3: Minor corrections and clarifications; V4: Added a missing "n" in the formula for computing the Euler class of the contact structure in Theorem 5.

Universal Labeling Algebras as Invariants of Layered Graphs

In this work we will study the universal labeling algebra A(Gamma), a related algebra B(Gamma), and their behavior as invariants of layered graphs. We will introduce the notion of an upper vertex-like basis, which allows us to recover structural information about the graph Gamma from the algebra B(Gamma). We will use these bases to show that several classes of layered graphs are uniquely identified by their corresponding algebras B(Gamma)

Whole-Farm Approaches to a Safety Net

In recent farm policy debates, proposals for a whole-farm revenue safety net program have been put forward that could provide a farm-income safety net for a wide variety of farming activities. These proposals include income- stabilization accounts and whole-farm revenue insurance. Risk protection from income-stabilization accounts would depend on the reserves in individual accounts and the structure of program benefits. Experience with farm savings accounts in Canada and Australia suggests that lack of adequate account balances and buildup of balances beyond the level required for risk management can reduce program effectiveness. Whole-farm revenue insurance could overcome these problems since coverage would not depend on the farmer's ability to build an account balance and benefits would only be realized when the farmer suffers a drop in income. However, the complexity of factors affecting income variability raises questions about the feasibility of a whole-farm insurance plan.Agricultural and Food Policy, Risk and Uncertainty,

Quasiparticle scattering from vortices in d-wave superconductors I: Superflow contribution

In the vortex state of a d-wave superconductor, massless Dirac quasiparticles are scattered from magnetic vortices via a combination of two basic mechanisms: effective potential scattering due to the superflow swirling about the vortices and Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex. In this paper, we study the superflow contribution by calculating the differential cross section for a quasiparticle scattering from the effective non-central potential of a single vortex. We solve the massless Dirac equation in polar coordinates and obtain the cross section via a partial wave analysis. We also present a more transparent Born-limit calculation and in this approximation we provide an analytic expression for the differential cross section. The Berry phase contribution to the quasiparticle scattering is considered in a separate paper.Comment: 22 pages, 6 figure