Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

Current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case that the junction length is finite and magnetic impurity exists. The similarity and difference with conventional Josephson junction is discussed. The current is calculated in the semiconductor picture. Both the $2\pi$- and $4\pi$-period current-phase relations ($I_{2\pi}(\phi), I_{4\pi}(\phi)$) are studied. There is a sharp jump at $\phi=\pi$ and $\phi=2\pi$ for $I_{2\pi}$ and $I_{4\pi}$ respectively in the clean junction. For $I_{2\pi}$, the sharp jump is robust against impurity strength and distribution. However for $I_{4\pi}$, the impurity makes the jump at $\phi=2\pi$ smooth. The critical (maximum) current of $I_{2\pi}$ is given and we find it will be increased by asymmetrical distribution of impurity.Comment: 7 pages, 5 figure

Formula for Sediment Transport Subject to Vertical Flows

Sediment transport is a geophysical phenomenon in which sediment particles are driven to move in streamwise and vertical directions by various forces. Almost all existing formulas of sediment transport were derived without considering vertical flows V, resulting in a large discrepancy between measured and predicted transport rates, as has been reported in the literature. This paper investigates the effect of vertical motion on sediment transport. It was found that upward fluid velocity increases particles\u27 mobility, and downward motion increases particles stability. Furthermore, the investigation showed that decelerating flows can promote upward flow and vice versa. New equations were developed to express the influence of vertical motion on sediment transport. A reasonably good agreement between measured and predicted sediment transport rates was achieved

A simple model to extend 1-D hydraulics to 3-D hydraulics

the core of fluid mechanics is the study of friction on a solid/liquid interface, the friction force can be divided into skin friction and form drag. Nikuradse\u27s experiments reveal that the friction factor depends on the Reynolds number (Re) and relative roughness (r), this observation implies the co-existence of skin friction and form drag, but the definitions of Re and r given by Nikuradse cannot be linked with the skin friction and form drag, this leads to the invalidity of existing theory to predict the friction factor in a complex flow, like a channel flow with vegetation. To establish a universal relationship, the hydraulic radius, Reynolds numbers and relative roughness are redefined, and the connection of these parameters with the skin friction and form drag is established. For the flowing fluid, the separation region is generated after passing the fluid, and these eddies form a dead zone , this study reveals that the drag force is proportional to the volume of dead zone. By analyzing the measured data available in the literature, an equation has been established to express the drag force and the volume of dead zone, thus it provides an alternative way to interpret Nikuradse\u27s work and extends the existing outcomes to complex flows. KEY WORDS: Hydrauli

Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices

The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $\pi$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a $\frac{1}{3}$-filling topological phase on a background of trivial charge-density-wave or Mott insulators.Comment: 6 pages, 8 figures. Accelpted for publication in Phys. Rev.

The valley filter efficiency of monolayer graphene and bilayer graphene line defect model

In addition to electron charge and spin, novel materials host another degree of freedom, the valley. For a junction composed of valley filter sandwiched by two normal terminals, we focus on the valley efficiency under disorder with two valley filter models based on monolayer and bilayer graphene. Applying the transfer matrix method, valley resolved transmission coefficients are obtained. We find that: i) under weak disorder, when the line defect length is over about $15\rm nm$, it functions as a perfect channel (quantized conductance) and valley filter (totally polarized); ii) in the diffusive regime, combination effects of backscattering and bulk states assisted intervalley transmission enhance the conductance and suppress the valley polarization; iii) for very long line defect, though the conductance is small, polarization is indifferent to length. Under perpendicular magnetics field, the characters of charge and valley transport are only slightly affected. Finally we discuss the efficiency of transport valley polarized current in a hybrid system.Comment: 6 figure