How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions, which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermions is the supression of topological superconductivity by disorder. We show that Majorana fermions protected by a robust topological gap can occur at the ends of a chain of quantum dots connected by s-wave superconductors. In the appropriate parameter regime, we establish that the quantum dot/superconductor system is equivalent to a 1D Kitaev chain, which can be tuned to be in a robust topological phase with Majorana end modes even in the case where the quantum dots and superconductors are both strongly disordered. Such a spin-orbit coupled quantum dot - s-wave superconductor array provides an ideal experimental platform for the observation of non-Abelian Majorana modes.Comment: 8 pages; 3 figures; version 2: Supplementary material updated to include more general proof for localized Majorana fermion

Finding Cuts of Bounded Degree: Complexity, FPT and Exact Algorithms, and Kernelization

A matching cut is a partition of the vertex set of a graph into two sets A and B such that each vertex has at most one neighbor in the other side of the cut. The Matching Cut problem asks whether a graph has a matching cut, and has been intensively studied in the literature. Motivated by a question posed by Komusiewicz et al. [IPEC 2018], we introduce a natural generalization of this problem, which we call d-Cut: for a positive integer d, a d-cut is a bipartition of the vertex set of a graph into two sets A and B such that each vertex has at most d neighbors across the cut. We generalize (and in some cases, improve) a number of results for the Matching Cut problem. Namely, we begin with an NP-hardness reduction for d-Cut on (2d+2)-regular graphs and a polynomial algorithm for graphs of maximum degree at most d+2. The degree bound in the hardness result is unlikely to be improved, as it would disprove a long-standing conjecture in the context of internal partitions. We then give FPT algorithms for several parameters: the maximum number of edges crossing the cut, treewidth, distance to cluster, and distance to co-cluster. In particular, the treewidth algorithm improves upon the running time of the best known algorithm for Matching Cut. Our main technical contribution, building on the techniques of Komusiewicz et al. [IPEC 2018], is a polynomial kernel for d-Cut for every positive integer d, parameterized by the distance to a cluster graph. We also rule out the existence of polynomial kernels when parameterizing simultaneously by the number of edges crossing the cut, the treewidth, and the maximum degree. Finally, we provide an exact exponential algorithm slightly faster than the naive brute force approach running in time O^*(2^n)

Iron oxide waste to clean arsenic-contaminated water.

Serious manifestations of arsenic toxicity in majority of human population consuming contaminated water has led to development of number of remedial methods including adsorption onto iron oxide based natural and synthetic materials. Iron oxide adsorbents generated as waste in industrial processes may be utilised for arsenic remediation. These adsorbents can be considered better in terms of least production cost as well as minimal environmental implications. Here, we studied arsenic removal from contaminated water using iron oxide wastes generated in pickling unit of a steel plant. The iron oxide obtained by steel pickling was subjected to controlled reduction in fluidised bed reactor using gaseous reductant producing magnetic iron oxide. Prior to adsorption studies, physicochemical characterisation of both the iron oxides was undertaken. This was followed by batch equilibrium and kinetics adsorption tests to investigate arsenic (V) removal properties. Several parameters such as time, pH, arsenic concentration, adsorbent dose etc were investigated using synthetic solutions. Arsenic affected ground water samples collected from West Bengal (India) were also tested using both iron oxide adsorbents. Experimental results showed more than 90% arsenic removal within 10 min, not depending on pH of water with appreciable loading (0.12-0.17 mg As/g) on both adsorbents. Presence of anions such as SO42-and PO43- adversely affected arsenic adsorption. While testing real ground water samples, initial arsenic level of 0.010–0.018 mg/L was brought down to 0.002–0.008 mg/L. Our study has established potential use of an industrial waste for the removal of arsenic (V) from water

Phase diagram and excitations of a Shiba molecule

We analyze the phase diagram associated with a pair of magnetic impurities trapped in a superconducting host. The natural interplay between Kondo screening, superconductivity and exchange interactions leads to a rich array of competing phases, whose transitions are characterized by discontinuous changes of the total spin. Our analysis is based on a combination of numerical renormalization group techniques as well as semi-classical analytics. In addition to the expected screened and unscreened phases, we observe a new molecular doublet phase where the impurity spins are only partially screened by a single extended quasiparticle. Direct signatures of the various Shiba molecule states can be observed via RF spectroscopy.Comment: 13 pages, 7 figure