Search Results (15)

We present a comprehensive investigation into the emergence of interface-bound states, particularly Majorana zero modes (MZMs), in a lateral heterostructure composed of two three-dimensional topological insulators (TIs), Bi₂Se₃ and Sb₂Te₃, under the influence of proximity-induced superconductivity from niobium (Nb) contacts. We develop an advanced two-dimensional Dirac model for the topological surface states (TSS), incorporating spatially varying chemical potentials and s-wave superconducting pairing. Using the Bogoliubov–de Gennes (BdG) formalism, we derive analytical solutions for the bound states and compute the local density of states (LDOS) at the interface, revealing zero-energy modes characteristic of MZMs. The topological nature of these states is rigorously analyzed through winding numbers and Pfaffian invariants, and their robustness is explored under various physical perturbations, including gating effects. Our findings highlight the potential of this heterostructure as a platform for topological quantum computing, with detailed predictions for experimental signatures via tunneling spectroscopy. Full article

We present a topologically protected teleportation protocol based on projective parity measurements between spatially separated Majorana zero modes (MZMs), eliminating the need for dynamic braiding. Unlike conventional teleportation schemes, our method preserves logical information through nonlocal encoding and suppresses decoherence exponentially with Majorana separation. We provide a rigorous mathematical framework that includes six theorems and a lemma, proving fidelity bounds, no entropy increase under ideal QND parity measurement under quantum non-demolition (QND) measurements, and compliance with the no-cloning theorem. We demonstrate that all correction operations lie within the Clifford group, enabling efficient, fault-tolerant implementation. Furthermore, we outline a scalable architecture for multi-qubit teleportation and relate our framework to recent experimental advances in quantum-dot-based Kitaev chains and superconducting nanowire platforms. These results position Majorana-based teleportation as a thermodynamically stable and experimentally viable approach to scalable quantum information transfer. All operations discussed are Clifford-only; achieving universality requires non-Clifford resources and lies outside our scope. Full article

In the context of quantum computing, error correction remains a pivotal challenge, primarily due to imperfect gate operations and environmental interactions. This study introduces a machine learning-based method to simulate and analyze these errors. Utilizing a minimal scalable 2-Majorana-zero-mode (2-MZM) island model within a one-dimensional p-wave topological superconductor, this research employs a detailed Hamiltonian approach combined with a bosonic thermal bath interaction. The analysis is conducted using the Pauli master equation and Monte Carlo simulations. This work’s novel contribution lies in applying Boosted Decision Tree with Gradient boosting (BDTG) and Multi-Layer Perceptron (MLP) machine learning techniques. These methods, trained on Monte Carlo simulation data, showed proficiency in predicting the evolution of error probabilities in the quantum system. The results indicate a significant potential for machine learning to offer a more efficient alternative for simulating quantum computing errors, thereby contributing to developing more robust quantum computing systems. Full article

The problems of disorder and insufficient system length are generally regarded as central problems in the realization of Majorana zero modes (MZM), which are a promising platform for realizing fault-tolerant topological quantum computing (TQC). In this work, we analyze eigenenergy spectra and transport properties of finite Kitaev chains using quantum transport simulations in a wide design space of hopping amplitude (t), superconductor pairing (Δ), and electrochemical potential. Our goal is to determine critical or minimum acceptable chain lengths to obtain oscillation-free MZMs with suitable microsecond coherence times, and observable zero-bias conductance peaks (ZBCP) quantized almost at ~2e²/h. Due to qualitative equivalence of the Kitaev and Oreg–Lutchyn models, we approximately determine the foreseeable critical length of topological superconducting nanowires (TS NWs) as well. We find that the ZBCP length requirement is looser in comparison to the limit imposed by the coherence time. For a large t/Δ mismatch of ~40 corresponding to the experimental TS NWs, the first condition sets the minimum length to 344 sites (≈5.5 μm), while the second condition requires 605 sites (≈9.7 μm). The calculated lengths are far from the reported experimental hybrid device dimensions, explaining difficulties in observing MZMs in TS NWs fabricated so far. Nonetheless, a decreasing t/Δ mismatch allows for shorter systems, which argues in favor of the proximitized quantum dot path for MZMs in a solid-state system. Full article

In this paper, a modified Josephson junction model is proposed, which splits the two-dimensional electron gas by inserting a middle superconductor strip into a conventional Josephson junction. This modification enhances the superconducting proximity effect, thus avoiding the appearance of a soft gap and inducing a stable Majorana zero-energy mode. Through numerical simulation, the impact of the middle superconductor strip with different widths on the energy band structure is studied, and a significant increase in the topological energy gap is found. In addition, the modified system maintains a robust topological gap even at a strong in-plane magnetic field. Full article

We present here a theory of Majorana excitons, photo-excited conduction electron-valence band hole pairs, interacting with Majorana Fermions in a Kitaev chain of semiconductor quantum dots embedded in a nanowire. Using analytical tools and exact diagonalization methods, we identify the presence of Majorana zero modes in the nanowire absorption spectra. Full article

A d-dimensional, nth-order topological insulator or superconductor has localized eigenmodes at its $(d-n)$-dimensional boundaries ($n\le d$). In this work, we apply periodic driving fields to two-dimensional superconductors, and obtain a wide variety of Floquet second-order topological superconducting (SOTSC) phases with many Majorana corner modes at both zero and $\pi$ quasienergies. Two distinct Floquet SOTSC phases are found to be separated by three possible kinds of transformations, i.e., a topological phase transition due to the closing/reopening of a bulk spectral gap, a topological phase transition due to the closing/reopening of an edge spectral gap, or an entirely different phase in which the bulk spectrum is gapless. Thanks to the strong interplay between driving and intrinsic energy scales of the system, all the found phases and transitions are highly controllable via tuning a single hopping parameter of the system. Our discovery not only enriches the possible forms of Floquet SOTSC phases, but also offers an efficient scheme to generate many coexisting Majorana zero and $\pi$ corner modes, which may find applications in Floquet quantum computation. Full article

In magneto-photoluminescence (magneto-PL) spectra of quasi two-dimensional islands (quantum dots) having seven electrons and Wigner–Seitz radius r_s~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts, and jumps of the energy of the emission components for filling factors ν > 1 (B < 10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on r_s. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock–Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the r_s-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having an equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ν~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and r_s. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, the Majorana anyon origin of the states having even ν, i.e., composite fermions, which provide new opportunities for topological quantum computing. Full article

A modified real-space-Pfaffian method is applied to characterize the topological superconducting transition of a one-dimensional p-wave superconductor with quasiperiodic potentials. We found that the Majorana zero-energy mode exists in the topological non-trivial phase, and its spatial distribution is localized at ends of the system, whereas in the topological trivial phase, there is no Majorana zero mode. Furthermore, we numerically found that due to the competition between the localized quasi-disorder and the extended p-wave pairing, there are mobility edges in the energy spectra. Our theoretical work enriches the research on the quasiperiodic p-wave superconducting models. Full article

We present a novel controllable platform for engineering Majorana zero modes. The platform consists of a ferromagnetic metallic wire placed among conventional superconductors, which are in proximity to ferromagnetic insulators. We demonstrate that Majorana zero modes emerge localised at the edges of the ferromagnetic wire, due to the interplay of the applied supercurrents and the induced by proximity exchange fields with conventional superconductivity. Our mechanism does not rely on the pairing of helical fermions by combining conventional superconductivity with spin-orbit coupling, but rather exploits the misalignment between the magnetization of the ferromagnetic insulators and that of the ferromagnetic wire. Full article

Magnetic two-dimensional (2D) van der Waals materials have attracted tremendous attention because of their high potential in spintronics. In particular, the quantum anomalous Hall (QAH) effect in magnetic 2D layers shows a very promising prospect for hosting Majorana zero modes at the topologically protected edge states in proximity to superconductors. However, the QAH effect has not yet been experimentally realized in monolayer systems to date. In this work, we study the electronic structures and topological properties of the 2D ferromagnetic transition-metal dichalcogenides (TMD) monolayer $1T-\mathrm{V}{\mathrm{Se}}_2$ by first-principles calculations with the Heyd–Scuseria–Ernzerhof (HSE) functional. We find that the spin-orbit coupling (SOC) opens a continuous band gap at the magnetic Weyl-like crossing point hosting the quantum anomalous Hall effect with Chern number $C=2$. Moreover, we demonstrate the topologically protected edge states and intrinsic (spin) Hall conductivity in this magnetic 2D TMD system. Our results indicate that $1T-\mathrm{V}{\mathrm{Se}}_2$ monolayer serves as a stoichiometric quantum anomalous Hall material. Full article

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe${}_{1-x}$Se${}_x$, intercalated FeSe materials, and monolayer FeSe and FeTe${}_{1-x}$Se${}_x$ on SrTiO${}_3$. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity. Full article

Physics of topological materials has attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological superconductors. A zero-energy mode exists when Dirac fermions couple to objects with soliton-like structure such as kinks, vortices, monopoles, strings, and branes. We discuss a system of Dirac fermions interacting with a vortex and a kink. This kind of systems will be realized on the surface of topological insulators where Dirac fermions exist. The fermion number is fractionalized and this is related to the presence of fermion zero-energy excitation modes. A zero-energy mode can be regarded as a Majorana fermion mode when the chemical potential vanishes. Our discussion includes the case where there is a half-flux quantum vortex associated with a kink in a magnetic field in a bilayer superconductor. A normalizable wave function of fermion zero-energy mode does not exist in the core of the half-flux quantum vortex. The index of Dirac operator and the fermion number have additional contributions when a soliton scalar field has a singularity. Full article

Current computers are made of semiconductors. Semiconductor technology enables realization of microscopic quantum bits based on electron spins of individual electrons localized by gates in field effect transistors. This results in very fragile quantum processors prone to decoherence. Here, we discuss an alternative approach to constructing qubits using macroscopic and topologically protected states realized in semiconductor devices. First, we discuss a synthetic spin-1 chain realized in an array of quantum dots in a semiconductor nanowire or in a field effect transitor. A synthetic spin-1 chain is characterized by two effective edge quasiparticles with spin $1/2$ protected from decoherence by topology and Haldane gap. The spin-$1/2$ quasiparticles of Haldane phase form the basis of a macroscopic singlet-triplet qubit. We compare the spin one chain with a Kitaev chain. Its edge states are Majorana zero modes, possessing non-Abelian fractional statistics. They can be used to encode the quantum information using the braiding processes, i.e., encircling one particle by another, which do not depend on the details of the particle trajectory and thus are protected from decoherence. Full article

In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial. Full article