Gate-Tunable Critical Current of the Three-Dimensional Niobium Nano-Bridge Josephson Junction

Recent studies have shown that the critical currents of several metallic superconducting nanowires and Dayem bridges can be locally tuned using a gate voltage {V_g}. Here, we report a gate-tunable Josephson junction structure constructed from a three-dimensional (3D) niobium nano-bridge junction (NBJ) with a voltage gate on top. Measurements up to 6 K showed that the critical current of this structure can be tuned to zero by increasing {V_g}. The critical gate voltage Vgc was reduced to 16 V and may possibly be reduced further by reducing the thickness of the insulation layer between the gate and the NBJ. Furthermore, the flux modulation generated by Josephson interference of two parallel 3D NBJs can also be tuned using {V_g} in a similar manner. Therefore, we believe that this gate-tunable Josephson junction structure is promising for superconducting circuit fabrication at high integration levels.Comment: 15 pages, 5 figure

Geometric Scaling of the Current-Phase Relation of Niobium Nano-Bridge Junctions

The nano-bridge junction (NBJ) is a type of Josephson junction that is advantageous for the miniaturization of superconducting circuits. However, the current-phase relation (CPR) of the NBJ usually deviates from a sinusoidal function which has been explained by a simplified model with correlation only to its effective length. Here, we investigated both measured and calculated CPRs of niobium NBJs of a cuboidal shape with a three-dimensional bank structure. From a sine-wave to a saw-tooth-like form, we showed that deviated CPRs of NBJs can be described quantitatively by its skewness {\Delta}{\theta}. Furthermore, the measured dependency of {\Delta}{\theta} on the critical current {I_0} from 108 NBJs turned out to be consistent with the calculated ones derived from the change in geometric dimensions. It suggested that the CPRs of NBJs can be tuned by their geometric dimensions. In addition, the calculated scaling behavior of {\Delta}{\theta} versus {I_0} in three-dimensional space was provided for the future design of superconducting circuits of a high integration level by using niobium NBJs.Comment: 20 pages, 10 figure

The Ninth Visual Object Tracking VOT2021 Challenge Results

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The largest matching roots of unicyclic graphs with a fixed matching number The largest matching roots of unicyclic graphs with a fixed matching number

Abstract: In this note, we study the largest matching roots of unicyclic graphs with a given number of fixed matching number. We also characterize the extremal graph with respect to the largest matching roots. In addition, we also study this problem on the trees with a given number of fixed matching number

Constrained Steiner trees in Halin graphs

In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem

The largest matching roots of unicyclic graphs with a fixed matching number

In this note, we study the largest matching roots of unicyclic graphs with a given number of fixed matching number. We also characterize the extremal graph with respect to the largest matching roots. In addition, we also study this problem on the trees with a given number of fixed matching number

An improved algorithm for a two-stage production scheduling problem with an outsourcing option

We consider a two-stage production scheduling problem where each operation can be outsourced or processed in-house. For each operation in the same machine, the ratio of its outsourcing cost to its processing time is constant. The objective is to minimize the sum of the makespan and the total outsourcing cost. It is known that this problem is either polynomial time solvable or NP-hard according to the conditions of the ratios. Even though approximation algorithms for NP-hard cases had been developed, their tight worst-case performance ratios are still open. In this paper, we carefully analyze the approximation algorithms to identify their tight worst-case performance ratios for cases. In one case, we propose a new approximation algorithm with a better and tight worst-case performance ratio. In the process of analyzing the algorithm, we propose a technique utilizing nonlinear optimization. (C) 2021 Elsevier B.V. All rights reserved.11Nsciescopu