We report electron transport studies of a thin InAs-Al hybrid semiconductor-superconductor nanowire device using a four-terminal design. Compared to previous works, thinner InAs nanowire (diameter less than 40 nm) is expected to reach fewer sub-band
regime. The four-terminal device design excludes electrode contact resistance, an unknown value which has inevitably affected previously reported device conductance. Using tunneling spectroscopy, we find large zero-bias peaks (ZBPs) in differential conductance on the order of $2e^2/h$. Investigating the ZBP evolution by sweeping various gate voltages and magnetic field, we find a transition between a zero-bias peak and a zero-bias dip while the zero-bias conductance sticks close to $2e^2/h$. We discuss a topologically trivial interpretation involving disorder, smooth potential variation and quasi-Majorana zero modes.
A dual-gate InSb nanosheet field-effect device is realized and is used to investigate the physical origin and the controllability of the spin-orbit interaction in a narrow bandgap semiconductor InSb nanosheet. We demonstrate that by applying a voltag
e over the dual gate, efficiently tuning of the spin-orbit interaction in the InSb nanosheet can be achieved. We also find the presence of an intrinsic spin-orbit interaction in the InSb nanosheet at zero dual-gate voltage and identify its physical origin as a build-in asymmetry in the device layer structure. Having a strong and controllable spin-orbit interaction in an InSb nanosheet could simplify the design and realization of spintronic deceives, spin-based quantum devices and topological quantum devices.
Hybrid semiconductor-superconductor InAs-Al nanowires with uniform and defect-free crystal interfaces are one of the most promising candidates used in the quest for Majorana zero modes (MZMs). However, InAs nanowires often exhibit a high density of r
andomly distributed twin defects and stacking faults, which result in an uncontrolled and non-uniform InAs-Al interface. Furthermore, this type of disorder can create potential inhomogeneity in the wire, destroy the topological gap, and form trivial sub-gap states mimicking MZM in transport experiments. Further study shows that reducing the InAs nanowire diameter from growth can significantly suppress the formation of these defects and stacking faults. Here, we demonstrate the in situ growth of ultra-thin InAs nanowires with epitaxial Al film by molecular-beam epitaxy. Our InAs diameter (~ 30 nm) is only one-third of the diameters (~ 100 nm) commonly used in literatures. The ultra-thin InAs nanowires are pure phase crystals for various different growth directions, suggesting a low level of disorder. Transmission electron microscopy confirms an atomically sharp and uniform interface between the Al shell and the InAs wire. Quantum transport study on these devices resolves a hard induced superconducting gap and $2e^-$ periodic Coulomb blockade at zero magnetic field, a necessary step for future MZM experiments. A large zero bias conductance peak with a peak height reaching 80% of $2e^2/h$ is observed.
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and non-stationary
noises with a power-law variance function. In this paper we study sample path properties of the generalized fractional Brownian motion, including Holder continuity, path differentiability/non-differentiability, and functional and local Law of the Iterated Logarithms.
We introduce a system-wide safety staffing (SWSS) parameter for multiclass multi-pool networks of any tree topology, Markovian or non-Markovian, in the Halfin-Whitt regime. This parameter can be regarded as the optimal reallocation of the capacity fl
uctuations (positive or negative) of order $sqrt{n}$ when each server pool employs a square-root staffing rule. We provide an explicit form of the SWSS as a function of the system parameters, which is derived using a graph theoretic approach based on Gaussian elimination. For Markovian networks, we give an equivalent characterization of the SWSS parameter via the drift parameters of the limiting diffusion. We show that if the SWSS parameter is negative, the limiting diffusion and the diffusion-scaled queueing processes are transient under any Markov control, and cannot have a stationary distribution when this parameter is zero. If it is positive, we show that the diffusion-scaled queueing processes are uniformly stabilizable, that is, there exists a scheduling policy under which the stationary distributions of the controlled processes are tight over the size of the network. In addition, there exists a control under which the limiting controlled diffusion is exponentially ergodic. Thus we have identified a necessary and sufficient condition for the uniform stabilizability of such networks in the Halfin-Whitt regime. We use a constant control resulting from the leaf elimination algorithm to stabilize the limiting controlled diffusion, while a family of Markov scheduling policies which are easy to compute are used to stabilize the diffusion-scaled processes. Finally, we show that under these controls the processes are exponentially ergodic and the stationary distributions have exponential tails.
We report on a low-temperature transport study of a single-gate, planar field-effect device made from a free-standing, wurtzite-crystalline InAs nanosheet. The nanosheet is grown via molecular beam epitaxy and the field-effect device is characterized
by gate transfer characteristic measurements and by magnetic field orientation dependent transport measurements. The measurements show that the device exhibits excellent electrical properties and the electron transport in the nanosheet is of the two-dimensional nature. Low-field magnetoconductance measurements are performed for the device at different gate voltages and temperatures, and the characteristic transport lengths, such as phase coherent length, spin-orbit length and mean free path, in the nanosheet are extracted. It is found that the spin-orbit length in the nanosheet is short, on the order of 150 nm, demonstrating the presence of strong spin-orbit interaction in the InAs nanosheet. Our results show that epitaxially grown, free-standing, InAs nanosheets can serve as an emerging semiconductor nanostructure platform for applications in spintronics, spin qubits and planar topological quantum devices.
We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection, those function being i.i.d. for the various individ
uals in the population. This approach models infection-age dependent infectivity, and extends the classical SIR and SEIR models. We focus on the infectivity process (total force of infection at each time), and prove a functional law of large number (FLLN). In the deterministic limit of this LLN, the infectivity process and the susceptible process are determined by a two-dimensional deterministic integral equation. From its solutions, we then derive the exposed, infectious and recovered processes, again using integral equations. For the early phase, we study the stochastic model directly by using an approximate (non--Markovian) branching process, and show that the epidemic grows at an exponential rate on the event of non-extinction, which matches the rate of growth derived from the deterministic linearized equations. We also use these equations to derive the basic reproduction number $R_0$ during the early stage of an epidemic, in terms of the average individual infectivity function and the exponential rate of growth of the epidemic.
We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of in
fection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these models. In the FLLN, the limits are a unique solution to a system of deterministic Volterra integral equations, while in the FCLT, the limit processes are multidimensional Gaussian solutions of linear Volterra stochastic integral equations. In the proof of the FCLT, we provide an important Poisson random measures representation of the diffusion-scaled processes converging to Gaussian components driving the limit process.
A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We consider in
detail two types of Markov random environments: a pure jump process and a reflected jump-diffusion. In both cases, the joint dynamics is constructed so that the stationary distribution can be explicitly found in a simple form (weighted geometric). We also derive an explicit estimate for exponential rate of convergence to the stationary distribution via coupling.
Single crystalline InSb nanosheet is an emerging planar semiconductor material with potential applications in electronics, infrared optoelectronics, spintronics and topological quantum computing. Here we report on realization of a quantum dot device
from a single crystalline InSb nanosheet grown by molecular-beam epitaxy. The device is fabricated from the nanosheet on a Si/SiO2 substrate and the quantum dot confinement is achieved by top gate technique. Transport measurements show a series of Coulomb diamonds, demonstrating that the quantum dot is well defined and highly tunable. Tunable, gate-defined, planar InSb quantum dots offer a renewed platform for developing semiconductor-based quantum computation technology.
