arXiv subjects

Jie Shen

Publications and source records attributed to Jie Shen.

At least 73 records · Page 4Linked to original sources

arXiv2025

Phase-Field Modeling and Energy-Stable Schemes for Osmotic Flow through Semi-Permeable

We present a thermodynamically consistent phase-field model for simulating fluid transport across semi-permeable membranes, with a particular focus on osmotic pressure effects. The model extends the classical Navier-Stokes-Cahn-Hilliard (NSCH) system by introducing an Allen-Cahn-type transmembrane flux governed by chemical potential imbalances, resulting in a strongly coupled system involving fluid motion, solute transport, and interface dynamics. To solve this system efficiently and accurately, we develop high-order, energy-stable numerical schemes. The local discontinuous Galerkin (LDG) method is employed for spatial discretization, offering high-order accuracy and geometric flexibility. For temporal integration, we first construct a first-order decoupled scheme with rigorous energy stability, and then improve temporal accuracy via a semi-implicit spectral deferred correction (SDC) method. Numerical experiments confirm the theoretical properties of the proposed scheme and demonstrate the influence of osmotic pressure and membrane permeability on droplet morphology at equilibrium. The framework offers a robust and versatile tool for modeling transmembrane fluid transport in both biological and industrial applications.

physics.flu-dyn↗

arXiv2025

Enhanced and modulable induced superconducting gap and effective Landé g-factor in Pb-InSb hybrid devices

The hybrid system of a conventional superconductor (SC) on a semiconductor (SM) nanowire with strong spin-orbit coupling (SOC) represents a promising platform for achieving topological superconductivity and Majorana zero modes (MZMs) towards topological quantum computation. While aluminum (Al)-based hybrid nanowire devices have been widely utilized, their limited superconducting gap and intrinsic weak SOC as well as small Landé g-factor may hinder future experimental advancements. In contrast, we demonstrate that lead (Pb)-based hybrid quantum devices exhibit a remarkably large and hard proximity-induced superconducting gap, exceeding that of Al by an order of magnitude. By exploiting electrostatic gating to modulate wavefunction distribution and SC-SM interfacial coupling, this gap can be continuously tuned from its maximum value (~1.4 meV, matching the bulk Pb gap) down to nearly zero while maintaining the hardness. Furthermore, magnetic-field-dependent measurements reveal a radial evolution of the gap structure with anti-crossing feature, indicative of strong SOC and huge effective g-factors up to 76. These findings underscore the superior functionality of Pb-based hybrid systems, significantly advancing their potential for realizing and stabilizing MZMs and the further scalable topological quantum architectures.

cond-mat.mes-hall↗

arXiv2025

Circuit-level-configurable Zero-field Superconducting Diodes: A Universal Platform Beyond Intrinsic Symmetry Breaking

Modern industry seeks next-generation microelectronics with ultra-low dissipation and noise beyond semiconducting systems, where the superconducting electronics offer promise. Its physical foundation is the superconducting diode effect (SDE) with nonreciprocal supercurrent. SDE has hitherto mainly relied on material-specific intrinsic symmetry breaking in superconductors, suffering from low yield, controllability, and compatibility with further functional extension - an undesirable aspect for applications. Here, we demonstrated a field-free SDE due to the chemical potential shift from external circuit line resistance, which is generic and challenges the previous interpretations of the intrinsic symmetry breaking in superconductivity for zero-field SDE. Moreover, this SDE is circuit-level configurable since it can be electrically switched on/off with its polarity and efficiency precisely modulated via gate voltage and circuit reconfiguration, facilitating functional extension. Such a generic, controllable and extensible SDE addresses critical challenges in dissipationless circuit towards application, and thus establishes a robust platform for scalable superconducting electronics.

cond-mat.supr-con↗

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

Adaptive time-stepping and maximum-principle preserving Lagrangian schemes for gradient flows

We develop in this paper an adaptive time-stepping approach for gradient flows with distinct treatments for conservative and non-conservative dynamics. For the non-conservative gradient flows in Lagrangian coordinates, we propose a modified formulation augmented by auxiliary terms to guarantee positivity of the determinant, and prove that the corresponding adaptive second-order Backward Difference Formulas (BDF2) scheme preserves energy stability and the maximum principle under the time-step ratio constraint $0<r_n\le r_{\max}\le\frac{3}{2}$. On the other hand, for the conservative Wasserstein gradient flows in Lagrangian coordinates, we propose an adaptive BDF2 scheme which is shown to be energy dissipative, and positivity preserving under the time-step ratio constraint $0<r_n\le r_{\max}\le\frac{3+\sqrt{17}}{2}$ in 1D and $0<r_n\le r_{\max}\le \frac{5}{4}$ in 2D, respectively. We also present ample numerical simulations in 1D and 2D to validate the efficiency and accuracy of the proposed schemes.

math.NA↗

arXiv2025

Deep collocation method: A framework for solving PDEs using neural networks with error control

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and computational efficiency. To address these challenges, we propose an adaptive method that uses single-hidden-layer neural networks to construct basis functions guided by the equation residual. The approximate solution is computed within the space spanned by these basis functions, employing a collocation least squares scheme. As the approximation space gradually expands, the solution is iteratively refined; meanwhile, the progressive improvements serve as reliable {\it a posteriori} error indicators that guide the termination of the sequential updates. Additionally, we introduce adaptive strategies for collocation point selection and parameter initialization to enhance robustness and improve the expressiveness of the neural networks. We also derive the approximation error estimate and validate the proposed method with several numerical experiments on various challenging PDEs, demonstrating both high accuracy and robustness of the proposed method.

math.NA↗

arXiv2025

Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model

We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-parabolic form. We prove that this linear, decoupled, first-order scheme preserves unconditionally the important properties of Keller-Segel equations at the semi-discrete level, including the mass conservation and positivity preserving of the cell density, and the energy dissipation. We also establish optimal error estimates in $L^p$-norm $(1<p<\infty)$.

math.NA↗

arXiv2025

We Need to Effectively Integrate Computing Skills Across Discipline Curricula

Computing is increasingly central to innovation across a wide range of disciplinary and interdisciplinary problem domains. Students across noncomputing disciplines need to apply sophisticated computational skills and methods to fields as diverse as biology, linguistics, and art. Furthermore, computing plays a critical role in "momentous geopolitical events", such as elections in several countries including the US, and is changing how people "work, collaborate, communicate, shop, eat, travel, get news and entertainment, and quite simply live". Traditional computing courses, however, fail to equip non-computing discipline students with the necessary computing skills - if they can even get into classes packed with CS majors. A pressing question facing academics today is: How do we effectively integrate computing skills that are useful for the discipline into discipline curricula? We advocate an approach where courses in discipline X include the computing relevant to the learning outcomes of that course, as used by practitioners in X. We refer to the computing skills relevant to a course in discipline X as an "ounce of computing skills", to highlight our belief regarding the amount of computing to be integrated in that course. In this article, we outline our insights regarding the development of an ounce of computing skills for a discipline course, and the evaluation of the developed ounce. The key takeaways are that the goal has to be to advance students in their disciplines, and only the disciplinary experts can tell us how computing is used in that discipline. Computer scientists know how to teach computing, but the classes can't be about CS values. The disciplinary values are paramount.

cs.CY↗

arXiv2025

Efficient PAC Learning of Halfspaces with Constant Malicious Noise Rate

Understanding noise tolerance of machine learning algorithms is a central quest in learning theory. In this work, we study the problem of computationally efficient PAC learning of halfspaces in the presence of malicious noise, where an adversary can corrupt both instances and labels of training samples. The best-known noise tolerance either depends on a target error rate under distributional assumptions or on a margin parameter under large-margin conditions. In this work, we show that when both types of conditions are satisfied, it is possible to achieve constant noise tolerance by minimizing a reweighted hinge loss. Our key ingredients include: 1) an efficient algorithm that finds weights to control the gradient deterioration from corrupted samples, and 2) a new analysis on the robustness of the hinge loss equipped with such weights.

cs.LG↗

arXiv2025

Evidence of P-wave Pairing in K$_2$Cr$_3$As$_3$ Superconductors from Phase-sensitive Measurement

P-wave superconductors hold immense promise for both fundamental physics and practical applications due to their unusual pairing symmetry and potential topological superconductivity. However, the exploration of the p-wave superconductors has proved to be a complex endeavor. Not only are they rare in nature but also the identification of p-wave superconductors has been an arduous task in history. For example, phase-sensitive measurement, an experimental technique which can provide conclusive evidence for unconventional pairing, has not been implemented successfully to identify p-wave superconductors. Here, we study a recently discovered family of superconductors, A$_2$Cr$_3$As$_3$ (A = K, Rb, Cs), which were proposed theoretically to be a candidate of p-wave superconductors. We fabricate superconducting quantum interference devices (SQUIDs) on exfoliated K$_2$Cr$_3$As$_3$, and perform the phase-sensitive measurement. We observe that such SQUIDs exhibit a pronounced second-order harmonic component sin(2$π$) in the current-phase relation, suggesting the admixture of 0- and $π$-phase. By carefully examining the magnetic field dependence of the oscillation patterns of critical current and Shapiro steps under microwave irradiation, we reveal a crossover from 0- to $π$-dominating phase state and conclude that the existence of the $π$-phase is in favor of the p-wave pairing symmetry in K$_2$Cr$_3$As$_3$.

cond-mat.supr-con↗

arXiv2025

Observation of topological Anderson Chern insulator phase in MnBi$_4$Te$_7$ monolayer

The correlation of topology and disorder has attracted great intention due to appropriate disorder could induce the phase transition between trivial and nontrivial topological states. While it is widely recognized that strong disorder can produce rich phase diagrams in topological nontrivial states, moderate disorder has been proposed to induce transitions into topologically nontrivial phases counter-intuitively, leading to the concept of topological Anderson insulators. This phenomenon has been theoretically explored and simulated in various systems, yet experimental realization in solid state systems has remained elusive due to challenges in controlling disorder. Here, we report the experimental observation of Chern insulator state signed by the coexistence of quantized Hall plateau and zero longitudinal resistance in monolayer MnBi$_4$Te$_7$ Hall bar device, which originally hosts a trivial insulating state with Chern number $C$ = 0 in clean limit. We demonstrate that the observed trivial to nontrivial transition in this monolayer device can be attributed to disorder, evidenced by universal conductance fluctuations. Our findings substantiate the existence of a long-sought topological Anderson Chern insulator in real materials, a unique variant of the topological Anderson insulator characterized by broken time-reversal-symmetry.

cond-mat.mes-hall↗

arXiv2025

Absence of diode effect in chiral type-I superconductor NbGe2

Symmetry elegantly governs the fundamental properties and derived functionalities of condensed matter. For instance, realizing the superconducting diode effect (SDE) demands breaking space-inversion and time-reversal symmetries simultaneously. Although the SDE is widely observed in various platforms, its underlying mechanism remains debated, particularly regarding the role of vortices. Here, we systematically investigate the nonreciprocal transport in the chiral type-I superconductor NbGe2. Moreover, we induce type-II superconductivity with elevated superconducting critical temperature on the artificial surface by focused ion beam irradiation, enabling control over vortex dynamics in NbGe2 devices. Strikingly, we observe negligible diode efficiency (Q < 2%) at low magnetic fields, which rises significantly to Q ~ 50% at high magnetic fields, coinciding with an abrupt increase in vortex creep rate when the superconductivity of NbGe2 bulk is suppressed. These results unambiguously highlight the critical role of vortex dynamics in the SDE, in addition to the established symmetry rules.

cond-mat.supr-con↗

arXiv2025

Strong superconducting pairing strength and pseudogap features in a putative multiphase heavy-fermion superconductor CeRh2As2 by soft point-contact spectroscopy

CeRh2As2 is a newly discovered candidate of multiphase heavy-fermion superconductor (Tc=0.3 K) with intriguing physical properties. Here, we employ soft point-contact spectroscopy to investigate its energy gap behaviors in both the normal and superconducting states. The differential conductance below Tc reveals an estimated superconducting energy gap of 2ΔSC=0.24 meV and thus an extremely strong superconducting pairing strength 2ΔSC/kBTc=8.8, which is comparable to those of cuprates and iron-based high-Tc superconductors as well as infinite-layer nickelates. Above Tc, a well-defined pseudogap feature is manifested as a V-shaped dip in the differential conductance spanning an energy scale of 2Δg=0.95-3.0 meV. The pseudogap feature persists to the highest characteristic temperature of Tg=8-9 K and is gradually suppressed by magnetic field of Bg=9.0T regardless of its direction relative to the crystallographic axes. The observation of pseudogap features prior to the superconducting phase transition enriches the phase diagram of CeRh2As2 and provides a novel platform to study the interplay of unconventional superconductivity and pseudogap phenomena.

cond-mat.supr-con↗

arXiv2024

The ball-covering property of non-commutative spaces of operators on Banach spaces

A Banach space is said to have the ball-covering property (BCP) if its unit sphere can be covered by countably many closed or open balls off the origin. Let $X$ be a Banach space with a shrinking $1$-unconditional basis. In this paper, by constructing an equivalent norm on $B(X)$, we prove that the quotient Banach algebra $B(X)/K(X)$ fails the BCP. In particular, the result implies that the Calkin algebra $B(H)/ K(H)$, $B(\ell^p)/K(\ell^p)$ ($1 \leq p <\infty$) and $B(c_0)/K(c_0)$ all fail the BCP. We also show that $B(L^p[0,1])$ has the uniform ball-covering property (UBCP) for $3/2< p < 3$.

math.FA↗

arXiv2024

Interfering Josephson diode effect in Ta2Pd3Te5 asymmetric edge interferometer

Edge states in topological systems have attracted great interest due to their robustness and linear dispersions. Here a superconducting-proximitized edge interferometer is engineered on a topological insulator Ta2Pd3Te5 with asymmetric edges to realize the interfering Josephson diode effect (JDE), which hosts many advantages, such as the high efficiency as much as 73% at tiny applied magnetic fields with an ultra-low switching power around picowatt. As an important element to induce such JDE, the second-order harmonic in the current-phase relation is also experimentally confirmed by half-integer Shapiro steps. The interfering JDE is also accompanied by the antisymmetric second harmonic transport, which indicates the corresponding asymmetry in the interferometer, as well as the polarity of JDE. This edge interferometer offers an effective method to enhance the performance of JDE, and boosts great potential applications for future superconducting quantum devices.

cond-mat.mes-hall↗

arXiv2024

Unique quantum metallic state in the titanium sesquioxide heterointerface superconductor

The emergence of quantum metallic state marked by a saturating finite electrical resistance in the zero-temperature limit in a variety of two-dimensional superconductors injects an exciting momentum to the realm of heterostructure superconductivity. Despite much research efforts over last few decades, there is not yet a general consensus on the nature of this unexpected quantum metal. Here, we report the observation of a unique quantum metallic state within the hallmark of Bose-metal in the titanium sesquioxide heterointerface superconductor Ti$_2$O$_3$/GaN. Remarkably, the quantum bosonic metallic state continuously tuned by a magnetic field in the vicinity of the two-dimensional superconductivity-metal transition persists in the normal phase, indicating the existence of composite bosons formed by electron Cooper pairs even in the normal phase. Our findings provide a distinct evidence for electron pairing in the normal phase of heterointerface superconductors, and shed fresh light on the pairing nature underlying heterointerface superconductivity.

cond-mat.supr-con↗