arXiv subjects

Xiaozhou Yang

Publications and source records attributed to Xiaozhou Yang.

14 recordsLinked to original sources

arXiv2026

Gap reopening as a possible signature of coupling between Majorana zero modes in Sn-(Bi,Sb)2(Te,S)3-based Josephson trijunctions

In the past two decades, enormous efforts have been made to search for possible platforms and schemes to implement topological quantum computation (TQC). In exploring the Fu-Kane scheme of TQC based on Josephson trijunctions constructed on topological insulators, the predicted Majorana phase diagram of an individual trijunction has already been verified experimentally. If Majorana zero modes indeed exist in this kind of trijunction, coupling between them in multiple trijunction devices should be further expected. In this study, we fabricated Josephson devices containing two adjacent Josephson trijunctions on the surface of Sn-(Bi, Sb)2(Te, S)3 and observed a possible signature of the coupling effect manifesting as the reopening of a minigap in both trijunctions where a closure would otherwise be expected if the trijunctions existed individually. While alternative interpretations cannot be fully ruled out, our findings provide experimental support for the validity of the Fu-Kane theory and provide further motivation for advancing the TQC scheme proposed by Fu and Kane.

cond-mat.supr-con↗

arXiv2026

Deterministic non-local parity control and supercurrent-based detection in an Andreev molecule

The ability to manipulate and detect the parity of quantum states in superconductor-semiconductor hybrid systems is pivotal to realizing the promise of topological quantum computation. However, as these architectures scale toward artificial Kitaev chains with phase-control loops, local accessibility becomes restricted, constraining conventional local parity control and detection. While Andreev molecules offer a platform for non-local intervention, deterministic protocols for parity manipulation have yet to be experimentally established. Here, we demonstrate deterministic non-local control over the parity configuration of a quantum dot (QD) by electrically modulating the coherent hybridization with a spatially adjacent QD within an Andreev molecule. By systematically investigating three distinct joint parity configuration regimes in the elastic co-tunneling limit, we experimentally uncover the operational conditions for this non-local control. In conjunction with theoretical simulations establishing a global phase diagram, we identify a set of universal selection rules governing parity transitions, dictated by the symmetry-imposed interplay between the joint parity configuration and the dominant inter-dot coupling mechanism (elastic co-tunneling vs. crossed Andreev reflection). Furthermore, we establish the supercurrent, directly signaled by zero-bias conductance peaks, as an intrinsic, sensor-free probe of the parity configuration, obviating the need for auxiliary charge sensors. Our results provide a validated physical framework for parity engineering, offering a key building block for scalable, multi-QD superconducting architectures.

cond-mat.mes-hall↗

arXiv2025

Exchange operation of Majorana zero modes in topological insulator-based Josephson trijunctions

Majorana zero modes are anyons obeying non-Abelian exchange statistics distinct from fermions or bosons. While significant progresses have been achieved in the past two decades in searching for these exotic excitations in solid-state systems, their non-Abelian nature remains unverified, as definitive proof requires braiding operations. Here, we report preliminarily experimental advances in creating, manipulating, and exchanging the presumed Majorana zero modes in an envelope-shaped Josephson device composed of multiple trijunctions on a topological insulator surface. We observed the signatures of in-gap states migration consistent with the expectations of the Fu-Kane model, supporting the realization of an exchange operation. This work would establish a critical pathway toward ultimately braiding Majorana zero modes in the Fu-Kane scheme of topological quantum computation.

cond-mat.mes-hall↗

arXiv2025

Well-Posedness of the Cauchy Problem for First-order Quasilinear Equations with Non-Lipschitz Source Terms and Its Applications

We are concerned with the well-posedness of the Cauchy problem for the first-order quasilinear equations with non-Lipschitz source terms and the global structures of the multi-dimensional Riemann solutions. For such quasilinear equations with initial data in $L^\infty$, when the source term $g(t, x, u)$ is only right-Lipschitz (not necessarily left-Lipschitz) in $u$, we first prove that the Kruzkov entropy condition is sufficient to guarantee the well-posdeness of entropy solutions. Next, we analyze the structures of global multi-dimensional Riemann solutions for scalar conservation laws with non-Lipschitz source terms, where the Riemann-type initial data consist of two different constant states separated by a smooth hypersurface. More precisely, we construct the global multidimensional Riemann solutions with non-selfsimilar structures, including nonselfsimilar shock waves and nonselfsimilar rarefaction waves, and prove that these two kinds of basic waves can be expressed via the implicit functions of functional equation determined by the initial discontinuity, the flux functions, and the non-Lipschitz source term. Moreover, we discover two new phenomena: (i) such kinds of basic waves can disappear in a finite time and (ii) the new-type rarefaction wave can contain some weak discontinuities in its interior. These behaviors are in stark contrast to the case of the Lipschitz source term, where these two kinds of basic waves persist globally and the rarefaction waves remain smooth in the interior. Finally, we provide two examples to respectively demonstrate the uniqueness of Riemann solutions in the case of the source term being non-Lipschitz from left (necessarily right-Lipschitz), and the non-uniqueness of Riemann solutions in the case of the source term being non-Lipschitz from right.

math.AP↗

arXiv2025

Josephson diode effect in nanowire-based Andreev molecules

Superconducting systems exhibit non-reciprocal current transport under certain conditions of symmetry breaking, a phenomenon known as the superconducting diode effect. This effect allows for perfect rectification of supercurrent, and has received considerable research interest. We report the observation of the Josephson diode effect (JDE) in nanowire-based Andreev molecules, where the time-reversal and spatial-inversion symmetries of a Josephson junction (JJ) can be nonlocally broken by coherently coupling to another JJ. The JDE can be controlled using both non-local phase and gate voltages. Notably, the non-local phase can induce a sign reversal of the diode efficiency, a manifestation of regulating the probabilities of double elastic cotunneling and double-crossed Andreev reflection. Additionally, the diode efficiency can be further modulated by local and non-local gate voltages, exhibiting a central-peak feature in the gate-voltage space. Our theoretical calculations of the energy spectrum and the Josephson currents align well with the experimental results. These results demonstrate the non-local regulation of the JDE in Andreev molecules, offering significant implications for the control of multi-JJ devices and the development of advanced superconducting devices.

cond-mat.mes-hall↗

arXiv2025

Procedure of tuning up a three-site artificial Kitaev chain based on transmon measurements

Artificial Kitaev chains (AKCs), formed of quantum dot-superconductor linear arrays, provide a promising platform for hosting Majorana bound states (MBSs) and implementing topological quantum computing. The main challenges along this research direction would include the tuning up of AKCs for hosting MBSs and the readout of the parity of the chains. In this work, we present a step-by-step procedure for tuning up a three-site AKC to its sweet spots based on the spectra of a transmon circuit which is integrated with the chain for the purpose of reading out the parity of the chain. The signatures of the transmon's plasma modes in each step, particular those related to the appearance of MBSs in the chain, will be given. We find that the sweet spots in a three-site AKC can be classified into three types based on the relative strengths of elastic cotunneling (ECT) and crossed Andreev reflection (CAR): ECT-dominated sweet spots, genuine sweet spots and CAR-dominated sweet spots. We show that the ECT-dominated and CAR-dominated sweet spots can be more conveniently accessed and utilized in transmon-based measurements.

cond-mat.mes-hall↗

arXiv2025

Measurement of parity-dependent energy-phase relation of the low-energy states in a potential artificial Kitaev chain utilizing a transmon qubit

Artificial Kitaev chains have emerged as a promising platform for realizing topological quantum computing. Once the chains are formed and the Majorana zero modes are braided/fused, reading out the parity of the chains is essential for further verifying the non-Abelian property of the Majorana zero modes. Here we demonstrate the feasibility of using a superconducting transmon qubit, which incorporates an end of a four-site quantum dot-superconductor chain based on a Ge/Si nanowire, to directly detect the singlet/doublet state, and thus the parity of the entire chain. We also demonstrate that for multiple-dot chains there are two types of 0-π transitions between different charging states: the parity-flip 0-π transition and the parity-preserved 0-π transition. Furthermore, we show that the inter-dot coupling, hence the strengths of cross Andreev reflection and elastic cotunneling of electrons, can be adjusted by local electrostatic gating in chains fabricated on Ge/Si core-shell nanowires. Our exploration would be helpful for the ultimate realization of topological quantum computing based on artificial Kitaev chains.

cond-mat.mes-hall↗

arXiv2025

Controllable creation of topological boundary states in topological-insulator-based Josephson corner junctions

Majorana zero modes (MZMs) in condensed matter systems have attracted great attention in the past two decades, due to their interesting physics and potential application in topological quantum computing (TQC). However, the topologically protected nature of MZMs still need more experimental verifications. In this study, we have realized controllable creation of a topological boundary state at the corner of topological insulator (TI)-based Josephson corner junctions. This state demonstrates protected existence across a broad region in parametric space, and exhibits a non-2π-period but 4π-period-compatible energy-phase relation. Our study suggests that TI-based Josephson junctions, as proposed in the Fu-Kane scheme of TQC, may provide a promising platform for hosting and braiding MZMs.

cond-mat.mes-hall↗

arXiv2025

New Formula for Entropy Solutions for Scalar Hyperbolic Conservation Laws with Flux Functions of Convexity Degeneracy and Global Dynamic Patterns of Solutions

We are concerned with a new solution formula and its applications to the analysis of properties of entropy solutions of the Cauchy problem for one-dimensional scalar hyperbolic conservation laws, wherein the flux functions exhibit convexity degeneracy and the initial data are in $L^\infty$. We first introduce/validate the novel formula for entropy solutions for the Cauchy problem, which generalizes the Lax-Oleinik formula. Then, by employing this formula, we obtain a series of fine properties of entropy solutions and discover several new structures and phenomena, which include: (i) Series of results on the fine structures of entropy solutions, especially including the new criteria for all six types of initial waves for the Cauchy problem, the new structures of entropy solutions inside the backward characteristic triangle, and the new features of the formation and development of shocks such as all five types of continuous shock generation points, along with their criteria and the optimal regularities of the corresponding resulting shocks; (ii) Series of results on the global structures of entropy solutions, including the four new invariants of entropy solutions, the new criteria for the locations and speeds of divides, and the exact determination of the global structures of entropy solutions; (iii) Series of new results on the asymptotic behaviors of entropy solutions, including the asymptotic profiles and decay rates of entropy solutions for initial data in $L^\infty$, respectively in the $L^\infty$--norm and the $L^p_{\rm loc}$--norm. Through these results above, we obtain the global dynamic patterns of entropy solutions for scalar hyperbolic conservation laws with the flux functions satisfying (1.3) and general initial data in $L^\infty$. Moreover, the new solution formula is also extended to more general scalar hyperbolic conservation laws.

math.AP↗

arXiv2024

Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation

We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation $u_t+uu_x+uu_y=Δu$, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, seperated by a curve $y=φ(x)$, and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. Furthermore, we also get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large.

math.AP↗

arXiv2022

LASSO-Based Multiple-Line Outage Identification In Partially Observable Power Systems

Phasor measurement units (PMUs) create ample real-time monitoring opportunities for modern power systems. Among them, line outage detection and identification remains a crucial but challenging task. Current works on outage identification succeed in full PMU deployment and single-line outages. Performance however degrades for multiple-line outage with partial system observability. We propose a novel framework of multiple-line outage identification using partial nodal voltage measurements. Using alternating current (AC) power flow model, phase angle signatures of outages are extracted and used to group lines into minimal diagnosable clusters. Identification is then formulated into an underdetermined sparse regression problem solved by lasso. Tested on IEEE 39-bus system with 25% and 50% PMU coverage, the proposed identification method is 93% and 80% accurate for single- and double-line outages. Our study suggests that the AC power flow is better at capturing outage patterns and sacrificing some precision could yield substantial improvement in identification accuracy. These findings could contribute to the development of future control schemes that help power systems resist and recover from outage disruptions in real time.

eess.SY↗

arXiv2021

Dynamic Power Systems Line Outage Detection Using Particle Filter and Partially Observed States

Real-time transmission line outage detection is difficult because of partial phasor measurement unit (PMU) deployment and varying outage signal strength. Existing detection approaches focus on monitoring PMU-measured nodal algebraic states, i.e., voltage phase angle and magnitude. The success of such approaches, however, is largely predicated on strong outage signals and the presence of PMUs in the outage location's vicinity. To overcome these limitations, a unified framework is proposed in this work by utilizing both nodal voltage information and generator dynamic states, e.g., rotor angular position. The proposed scheme is shown to be faster and more robust to unknown outage locations through the incorporation of generator dynamics. Using the IEEE 39-bus system simulation data, the proposed scheme's properties and performances compared to existing approaches are presented. The new approach could help improve operators' real-time situational awareness by detecting outages faster and providing a breakdown of outage signals for diagnostic purposes, making future power systems more resilient.

eess.SY↗

arXiv2020

A Control Chart Approach to Power System Line Outage Detection Under Transient Dynamics

Online transmission line outage detection over the entire network enables timely corrective action to be taken, which prevents a local event from cascading into a large scale blackout. Line outage detection aims to detect an outage as soon as possible after it happened. Traditional methods either do not consider the transient dynamics following an outage or require a full Phasor Measurement Unit (PMU) deployment. Using voltage phase angle data collected from a limited number of PMUs, we propose a real-time dynamic outage detection scheme based on alternating current (AC) power flow model and statistical change detection theory. The proposed method can capture system dynamics since it retains the time-variant and nonlinear nature of the power system. The method is computationally efficient and scales to large and realistic networks. Extensive simulation studies on IEEE 39-bus and 2383-bus systems demonstrated the effectiveness of the proposed method.

eess.SY↗

arXiv2020

Optimal Placement of Limited PMUs for Transmission Line Outage Detection and Identification

Phasor Measurement Unit (PMU) technology is increasingly used for real-time monitoring applications, especially line outage detection and identification (D&I) in the power system. Current outage D&I schemes either assume a full PMU deployment or a partial deployment with fixed PMU placement. However, the placement of the PMUs has a fundamental impact on the effectiveness of the D&I scheme. Building on a dynamic relationship between the substation voltage phase angle and active power, we formulated the optimal PMU placement problem for outage D&I as an optimization problem readily solvable by any heuristic algorithm. We tested the formulation using a genetic algorithm and simulated outages of IEEE 39 bus system. The optimal placement found produces a better D&I result of single-line outages than a randomly scattered, tree-like, and degree-based placements.

eess.SY↗