arXiv subjects

Zhi-Lei Zhang

Publications and source records attributed to Zhi-Lei Zhang.

8 recordsLinked to original sources

arXiv2026

Landscape geometry of Majorana zero modes in inhomogeneous superconductors

Spatial inhomogeneity breaks translational symmetry and prevents conventional Bloch-band topological invariants from directly answering a practical question: do Majorana zero modes survive in a given inhomogeneous superconducting device? In this Letter, we develop a real-space landscape approach to address this question. Rather than solving the zero-energy equation as a boundary-value problem, we treat the spatial coordinate as an evolution parameter and recast the equation as a first-order dynamical system. A Majorana zero mode is then identified with a stable trajectory that satisfies the physical boundary condition and approaches the origin at large distance. We show that the landscape geometry fixes the dimensions of the stable and unstable subspaces, while the intersection of the stable subspace with the physical boundary subspace determines the number of Majorana zero modes. In the homogeneous limit, the topological phase transition is manifested as a geometric transition of the landscape. Applied to one-dimensional spinless $p$-wave superconductors and nanowire--superconductor systems, the approach yields sufficient bounds on both the amplitude and spatial gradient of the inhomogeneity, providing quantitative criteria for the design of Majorana devices.

cond-mat.mes-hall↗

arXiv2026

Adverse Selection with Quality Variance: A Maximum-Entropy Approach

The adverse-selection mechanism in markets explains how asymmetric information between buyers and sellers can drive high-quality goods out of the market, thereby causing market deterioration. In its simplest formulation, only the mean quality is used to describe the market, and this is insufficient to determine how fast the market deteriorates or how the quality distribution evolves. To resolve the two problems, we describe the adverse selection as a dynamic truncation of the quality distribution: buyers set an upper bound proportional to the mean quality by a rate $ξ$ that is larger than unity, and sellers whose quality exceeds this upper bound reject an offer and exit the market. The retained market is then characterized by the conditional distribution obtained after this truncation, and the corresponding evolution process is iterated until market quality reaches a stable state. This statistical approach gives three results. (i) We identify a mechanism for preventing complete adverse selection, defined as the process where the quality of the market is driven down to the minimum quality floor. (ii) A larger quality variance or a smaller price premium, defined as the amount by which the payment upper bound exceeds the current mean quality, raises the upper bound on the deterioration in mean quality. (iii) A maximum-entropy benchmark shows numerically how quality variance and the payment rate jointly determine market deterioration and the final stable quality platform. This approach also clarifies how market interventions can slow adverse selection: they may raise buyers' payment rate, reduce quality variance, or increase the minimum quality floor.

cond-mat.stat-mech↗

arXiv2026

Sensitive dependence of Poor Man's Majorana modes on the length of the superconductor

In a hybrid system where two quantum dots (QDs) are coupled to a conventional $s$-wave superconductor, Poor Man's Majorana modes (PMMs) have been proposed. Existing theories often idealize the superconductor (SC) as a bulk system or an infinitely long chain, or treat it as another quantum dot with proximity-induced superconductivity, while experiments employ superconducting segments of finite length. Here, we model the SC as a finite-length 1D chain and treat the QDs and SC on equal footing. We obtain the conditions for the existence of PMMs, valid for arbitrary SC length and applicable to arbitrary tunneling strengths and magnetic fields. We find that the number of PMMs is highly sensitive to the SC length: it oscillates between zero and two with a period set by the Fermi wavelength ($\sim1\,\textÅ$), while four PMMs appear in the long-SC limit where the effective coupling between the two QDs becomes negligible. We further demonstrate that the PMMs that are separately localized at the two ends of the hybrid system do not exist in the finite-length case. Consequently, only nearly localized PMMs can be identified when the magnetic field is strong enough. In this way, the generalized `sweet spot' of the practical system can be found.

cond-mat.mes-hall↗

arXiv2025

Size optimization for observeing Majorana fermions

Majorana fermions (zero modes) are predicted to emerge in nanowire-superconductor heterostructures. This theoretical prediction typically relies on an oversimplified model, where both the nanowire and the superconductor are idealized as one-dimensional systems. In reality, heterostructures have finite sizes that deviate from this idealization-and as a result, smoking-gun evidence confirming the existence of these zero modes remains elusive. Here, we investigate the finite-size effects of both the nanowire and the superconductor, and optimize their sizes to ensure that only one Majorana fermion exists at each end of the heterostructure. It is discovered that the optimal transverse sizes of the nanowire are less than 100nm in width and approximately 1nm in thickness. For the superconductor layer, its optimal thickness (a key aspect of its size) must exceed its coherence length. We also present the optimal sizes of the two types of materials used in the experiment in a quantitative manner. Notably, the identified optimal thickness of the superconductor (Al films, $\sim$1000nm)--a critical size parameter--is two orders of magnitude larger than the thickness of Al films currently utilized in experimental devices (e.g., InSb-Al and InAs-Al heterostructures). Our findings could explain why Majorana fermions have not been observed in current experiments, and offer guidance for the size selection of heterostructures to implement Majorana fermions in future studies.

cond-mat.mes-hall↗

arXiv2025

Poor Man's Majoranon in Two Quantum Dots Dressed by Superconducting Quasi-Excitations

In a hybrid system consisting of two quantum dots (QDs) coupled to a superconductor (SC), zero-bias peaks in the differential conductance spectrum have been reported as potential signatures of Majorana fermions (MFs). However, such signatures typically appear only at specific parameter values of the QDs--so-called `sweet spots'--and are referred to as the Poor Man's Majorana (PMM). To investigate whether these signatures can be conclusively attributed to genuine MFs emerging over a continuous parameter range, we present an alternative approach that microscopically incorporates the superconducting effects into the QDs, rather than simply attribute them into two phenomenological parameters of QDs. This forms the dressed Majorana fermions (DMFs), which can be viewed as superpositions of quasi-excitations from both the QDs and the SC. We show that DMFs can localize at one end of a one-dimensional SC and persist across a continuous parameter range, thereby enhancing the feasibility of experimental detection. Our results provide a more accurate description of the PMM in such hybrid systems and offer practical guidance for observing end-localized PMM modes in continuous one-dimensional SC.

cond-mat.mes-hall↗

arXiv2024

Feynman Paradox about the Josephson effect and a sawtooth current in the double junction

We revisit the Feynman approach to the Josephson effect, which employs a pair of linear coupling equations for its modeling. It is found that while the exact solutions can account for the AC Josephson effect when the coupling strength is significantly less than the voltage, they fail to produce the DC Josephson effect in any practical scenario. To address this fundamental discrepancy, we derive the coupled Ginzburg-Landau (GL) equations for two interconnected superconductors based on BCS theory. These equations reveal that the nonlinear coupling, which is overlooked in the Feynman method, is crucial in describing the spontaneous symmetry breaking in superconductors, a critical factor for achieving the DC Josephson effect. When the coupled GL equations are applied to a double junction, a sawtooth current pattern emerges, a result unattainable via the Feynman approach.

cond-mat.supr-con↗

arXiv2023

Limits of single-photon storage in a single $Λ$-type atom

We theoretically investigate the limits of single-photon storage in a single $Λ$-type atom, specifically the trade-off between storage efficiency and storage speed. We show that a control field can accelerate the storage process without degrading efficiency too much. However, the storage speed is ultimately limited by the total decay rate of the involved excited state. For a single-photon pulse propagating in a regular one-dimensional waveguide, the storage efficiency has an upper limit of $50 \%$. Perfect single-photon storage can be achieved by using a chiral waveguide or the Sagnac interferometry. By comparing the storage efficiencies of Fock-state and coherent-state pulses, we reveal the influence of quantum statistics of light on photon storage at the single-photon level.

quant-ph↗

arXiv2023

Controlling superconducting transistor by coherent light

The Josephson junction is typically tuned by a magnetic field or electrostatic gates to realize a superconducting transistor, which manipulates the supercurrent in integrated superconducting circuits. However, this tunable method does not achieve simultaneous control for the supercurrent phase (phase difference between two superconductors) and magnitude. Here, we propose a novel scheme for the light-controlled superconducting transistor, which is composed of two superconductor leads linked by a coherent light-driven quantum dot. We discover a Josephson-like relation for supercurrent $I_{\mathrm{s}}=I_{c}(Φ)\,\sinΦ$, where both supercurrent phase $Φ$ and magnitude $I_{c}$ could be entirely controlled by the phase, intensity, and detuning of the driving light. Additionally, the supercurrent magnitude displays a Fano profile with the increase of the driving light intensity, which is clearly understood by comparing the level splitting of the quantum dot under light driving and the superconducting gap. Moreover, when two such superconducting transistors form a loop, they make up a light-controlled superconducting quantum interference device (SQUID). Such a light-controlled SQUID could demonstrate the Josephson diode effect, and the optimized non-reciprocal efficiency achieves up to $54\%$, surpassing the maximum record reported in recent literature. Thus, our feasible scheme delivers a promising platform to perform diverse and flexible manipulations in superconducting circuits.

cond-mat.mes-hall↗