arXiv subjects

Guo-Jian Qiao

Publications and source records attributed to Guo-Jian Qiao.

13 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

Chirality Breaking of Majorana Edge Modes Induced by Chemical Potential Shifts

Quantum anomalous Hall insulator-superconductor heterostructures are predicted to host chiral Majorana fermions as edge modes, which is essential for topological quantum computing applications. Although the edge states have been extensively studied at zero chemical potential $μ= 0$, the practically relevant regime with a shifted chemical potential ($μ\neq 0$) remains less explored. Here, we present an analytical treatment of the edge states for $μ\neq 0$, deriving an approximate but highly accurate solution applicable to realistic experimental parameters. Surprisingly, we find that the energy dispersion of the edge band exhibits nonlinearity and transforms into a twisted, braid-like structure within specific parameter ranges. This unique braid-like band leads to non-chirality of the edge modes, allowing propagation in both directions.

cond-mat.mes-hall↗

arXiv2026

Third Quantization for Order Parameters (II): Local Field Quantization in Superconducting Quantum Circuits

The quantization of superconducting transmission-line resonators is usually introduced phenomenologically by modeling the resonator as an effective LC circuit and imposing canonical commutation relations on macroscopic variables such as charge and flux. Although this approach is highly successful, it leaves open why these macroscopic variables should obey quantum commutation relations and how this behavior emerges from the superconducting state. In this work, starting from the microscopic pairing Hamiltonian underlying BCS superconductivity, we derive the low-energy effective Hamiltonian of a circuit-QED architecture containing a superconducting transmission line with distributed capacitive and inductive elements. We establish quantitative relations between macroscopic observables, including current and voltage, and the spatially local superconducting phase, as well as the microscopic parameters of the electron-phonon system. We then extend the third quantization of the superconducting order parameter, introduced in Paper (I) for the global phase, to the spatially local case. This gives a macroscopic field quantization of the superconducting phase. We show that, after restriction to the low-energy excitation subspace, the local superconducting phase becomes a genuine quantum dynamical variable. Thus, the quantum behavior of transmission-line resonators need not be postulated at the macroscopic level, but follows from the third quantization of the superconducting order parameter. These results suggest that capacitive and inductive superconducting circuit elements share the same microscopic origin, providing a unified framework for superconducting circuit quantization.

quant-ph↗

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↗

arXiv2026

Third Quantization for Order Parameter (I): BCS-BEC crossover with macroscopically coherent state

We revisit the quantization of the order parameter, which we refer to as third quantization, from the perspective of the commutation relation between the phase operator of the order parameter and the particle-number operator. We show that this macroscopic commutation relation does not constitute an independent fundamental postulate added to quantum mechanics, but instead emerges naturally from second quantization in the thermodynamic limit for both bosonic and fermionic many-body systems. In this sense, both Bose-Einstein condensates (BECs) and Bardeen-Cooper-Schrieffer (BCS) states can be understood as macroscopic quantum states described by bosonic coherent states: in BEC, bosons condense into a single coherent mode with a well-defined phase, while in BCS systems, collective excitations of Cooper pairs can also acquire an effectively bosonic coherent description. On this basis, we propose a new macroscopic interpretation of the BCS-BEC crossover. To characterize this crossover, we model a conventional superconductor as an assembly of macroscopically separated superconducting segments. As the intra-segment coupling increases, the system evolves from a BCS-like regime toward a BEC-like regime, in which the segments collectively behave as macroscopic coherent states. Inter-segment tunneling then locks their phases, establishes global phase coherence, and gives rise to a bulk Bose-Einstein condensate. The phase diagram of the BCS-BEC crossover can thus be understood as a manifestation of a macroscopic quantum process governed by the coherent-state dynamics of the order parameter. Our results provide a unified perspective on BEC, BCS superconductivity, and the BCS-BEC crossover within the framework of third quantization.

quant-ph↗

arXiv2026

Finite Thickness Effects on Metallization Vs. Chiral Majorana Fermions

The search for chiral Majorana fermions in quantum anomalous Hall insulator/\textit{s}-wave superconductor heterostructures has attracted intense interest, yet remains controversial due to the lack of conclusive evidence. A key issue is that the heterostructure's metallization can produce half-integer conductance signatures resembling those of chiral Majorana fermions, thereby complicating their identification. In this Letter, we investigate how the competition between metallization and chiral Majorana fermions depends on superconductor thickness, revealing its critical role through three distinct regimes: (i) For thin superconductors ($\sim$10 nm), metallization shows periodic oscillations with thickness, matching the Fermi wavelength. (ii) Intermediate thicknesses ($\sim$100 nm) exhibit periodic windows for observing chiral Majorana fermions. (iii) Thick superconductors ($\sim$1000 nm) sustain stable chiral Majorana fermions that are insensitive to thickness variations. These results suggest that superconductor thickness is a key control parameter for advancing efforts to conclusively identify chiral Majorana fermions.

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↗

arXiv2024

Dressed Majorana fermion in a hybrid nanowire

The low-energy theory of hybrid nanowire systems fails to define Majorana fermion (MF) in the strong tunneling and magnetic field strength. To address this limitation, we propose a holistic approach to define MF in which the quasi-excitation in nanowire and superconductor constitutes together its own ``antiparticles''. This definition is general, beyond the constraint presented in the low-energy theory. It reveals that the Majorana phase depends not only on the chemical potential and Zeeman energy in nanowire but also on those of superconductor, and that the mismatch of chemical potential leads not to observe MF. Such a broader perspective provides more specific experimental guidance under various conditions

cond-mat.mes-hall↗

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↗

arXiv2023

Refined Majorana phase diagram in topological insulator-superconductor hybrid system

The edge state of the topological insulator coupled to a superconductor system is able to simulate the Majorana fermion in zero energy mode since the Kitaev-type pairing is induced by exchanging quasi-excitations in electron tunneling. However, the present study has revealed that this physical simulation is not valid for a larger surface gap, which is the energy gap of the insulator's surface states. To address this issue, a refined pairing term that depends on the surface gap has been obtained as a second-order effect of the proximity effect, whereas the lowest order produces a constant pairing strength. By carefully considering the dependence of pairing strength on the surface gap, the Majorana phase diagram is re-achieved and a significant difference from previous work is observed, where the pairing strength was assumed to be independent of the surface gap and resulted in a conical phase boundary.

cond-mat.mes-hall↗

arXiv2021

Do Majorana zero modes emerge in the hybrid nanowire under a strong magnetic field?

The hybrid nanowire consisting of semiconductor with proximity to superconductor is expected to serve as an experimental platform to display Majorana zero modes. By rederiving its effective Kitaev model with spins, we discover a novel topological phase diagram, which assigns a more precise constraint on the magnetic field strength for the emergence of Majorana zero modes. It then turns out the effective pairing strength dressed by the proximity effect exhibits a significant dependence on the magnetic field, and thus the topological phase region is refined as a closed triangle in the phase diagram with chemical potential vs. Zeeman energy(which is obviously different from the open hyperbolic region known before). This prediction is confirmed again by an exact calculation of quantum transport, where the zero bias peak of $2e^{2}/h$ in the differential conductance spectrum, as the necessary evidence for the Majorana zero modes, disappears when the magnetic field grows too strong. For illustrations with practical hybrid systems, in the InSb nanowire coupled to NbTiN, the accessible magnetic field range is around 0.1--1.5T; when coupled to aluminum shell, the accessible magnetic field range should be smaller than 0.12T. These predictions obviously clarify the current controversial issues about some experiments of Majorana zero modes with hybrid nonawire.

cond-mat.mes-hall↗