Majorana Fermion Induced Resonant Andreev Reflection

We describe experimental signatures of Majorana fermion edge states, which form at the interface between a superconductor and the surface of a topological insulator. If a lead couples to the Majorana fermions through electron tunneling, the Majorana fermions induce \textit{resonant} Andreev reflections from the lead to the grounded superconductor. The linear tunneling conductance is $0$ ($2 e^2/h$) if there is an even (odd) number of vortices in the superconductor. Similar resonance occurs for tunneling into the zero mode in the vortex core. We also study the current and noise of a two-lead device.Comment: 4 pages, 3 figures. Discussion on STM tunneling into the Majorana zero mode in the vortex core is adde

Magnetoconductivity in Weyl semimetals: Effect of chemical potential and temperature

We present the detailed analyses of magneto-conductivities in a Weyl semimetal within Born and self-consistent Born approximations. In the presence of the charged impurities, the linear magnetoresistance can happen when the charge carriers are mainly from the zeroth (n=0) Landau level. Interestingly, the linear magnetoresistance is very robust against the change of temperature, as long as the charge carriers mainly come from the zeroth Landau level. We denote this parameter regime as the high-field regime. On the other hand, the linear magnetoresistance disappears once the charge carriers from the higher Landau levels can provide notable contributions. Our analysis indicates that the deviation from the linear magnetoresistance is mainly due to the deviation of the longitudinal conductivity from the $1/B$ behavior. We found two important features of the self-energy approximation: 1. a dramatic jump of $\sigma_{xx}$, when the $n=1$ Landau level begins to contribute charge carriers, which is the beginning point of the middle-field regime, when decreasing the external magnetic field from high field; 2. In the low-field regime $\sigma_{xx}$ shows a $B^{-5/3}$ behavior and results the magnetoresistance $\rho_{xx}$ to show a $B^{1/3}$ behavior. The detailed and careful numerical calculation indicates that the self-energy approximation (including both the Born and the self-consistent Born approximations) does not explain the recent experimental observation of linear magnetoresistance in Weyl semimetals.Comment: The accepted version. Extending the previous version by including the discussions of self-consistent Born approximatio

Selective Equal-Spin Andreev Reflections Induced by Majorana Fermions

In this work, we find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counter propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors.Comment: 5 pages, 3 figures. Comments are welcome. Title changed to match published versio

Sewage Pollution In Kelang River and its Estuary

High faecal coliform counts detected in Kelang River reveal that the River is being heavily polluted by domestic sewage discharge. The average faecal coliform counts in water from Stations I, II, III, IV, V and VI were 113/100 ml, 1 x 106 /100 ml, 1 x 105 /100 ml, 1.6 x 106 /100 ml, 5.8 x 103 /100 ml and 260/100 ml respectively. As compared to the WHO recommended guide limit of100 faecal califorms/100 ml for bathing water, counts in all stations except Station I were much higher than the recommended limit. The average concentration of faecal coliforms in sediment of Stations I, II, III and IV were 17.9/g, 1 x 104 /g, 3.2 x 104 /g and 1.6 x 104 /g respectively. The faecal coliform coun ts at the estuary ofKelang River were much lower than those of the coastal waters of Penang and Johore. The reason is not clear. Most probably the suspended solids play an important role in the disappearance of faecal coliforms in the estuary

Robustness of Majorana Fermion induced Fractional Josephson Effect

It is shown in previous works that the coupling between two Majorana end states in superconducting quantum wires leads to fractional Josephson effect. However, in realistic experimental conditions, multiple bands of the wires are occupied and the Majorana end states are accompanied by other fermionic end states. This raises the question concerning the robustness of fractional Josephson effect in these situations. In this work, we show that the absence of the avoided energy crossing which gives rise to the fractional Josephson effect is robust, even when the Majorana fermions are coupled with arbitrary strengths to other fermions. Moreover, we calculate the temperature dependence of the fractional Josephson current and show that it is suppressed by thermal excitations to the other fermion bound states.Comment: 4+ pages, 3 figure

Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State

The tunneling current and shot noise of the current between two Fractional Quantum Hall (FQH) edges in the $\nu=12/5$ FQH state in electronic Mach-Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of $k=3$ parafermion statistics in the $\nu=12/5$ FQH state. More specifically, the dependence of the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric under the change of the sign of the applied voltage. This property is absent in the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron charges in the $\nu=12/5$ FQH state . This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\nu=5/2$ Moore-Read state which was shown previously to be $e$ and $3.2 e$ respectively.Comment: 10 pages, 6 figure

Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so in the small ensemble size limit. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with resepct to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise

Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states

One of the simplest proposed experimental probes of a Majorana bound-state is a quantized (2e^2/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a non-quantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this paper we analyze the relation of the zero-bias peak to the presence of Majorana end-states, by simulating the tunneling conductance for multi-band wires with realistic amounts of disorder. We show that this system generically exhibits a (non-quantized) zero-bias peak even when the wire is topologically trivial and does not possess Majorana end-states. We make comparisons to recent experiments, and discuss the necessary requirements for confirming the existence of a Majorana state.Comment: 5 pages, 4 Figure

Petroleum Hydrocarbon along the Coastal Areas of Port Dickson

The petroleum hydrocarbon content in water and sand along the coast of Port Dickson was studied between December 1984 and November 1985. The mean and range of petroleum hydrocarbon in water were 32.24 ppb and 2.52-73.34 ppb respectively, while for the sand, the range was between 2.1 and 70.4 mg/kg d1)1 sand. A pronounced fluctuation of hydrocarbon level in water with sampling date was detected at the sampling stations during the sampling period. The results indicated that the coastal area of Port Dickson carried some degree of hydrocarbon pollution

Sewage Pollution in the Coastal Waters off Port Dickson, Straits of Malacca

The distribution of fecal colifonn bacteria in the near-shore waters and coastal waters of Port Dickson was studied between August 1987 and August 1989. Although a significantly high level of fecal coliform bacteria was found in the near- shore waters, very low levels were detected in the sediments and in roastal waters between 0.5 km and 5 kIn away from the roast. The results indirate that the coastal waters of Port Dickson are suitable for recreational and aquaculture uses