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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Fusion dynamics of Majorana zero modes

Braiding and fusion of Majorana zero modes are key elements of any future topological Majorana-based quantum computer. In this article, we investigate the fusion dynamics of Majorana zero modes in the spinless Kitaev model, as well as in a spinful model describing magnet-superconductor hybrid structures. We consider various scenarios allowing us to reproduce the fusion rules of the Ising anyon model. Particular emphasis is given to the charge of the fermion obtained after fusing two Majorana zero modes: as long as it remains on the superconductor, charge quantization is absent. When moving the fermion to a nonsuperconducting region, such as a quantum dot, nearly quantized charge can be measured. Our findings confirm for both platforms that fusion dynamics of Majorana zero modes can indeed be used for the readout of Majorana qubits.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Shuttling Majorana zero modes in disordered and noisy topological superconductors

The braiding of Majorana zero modes (MZMs) forms the fundamental building block for topological quantum computation. Braiding protocols which involve the physical exchange of MZMs are typically envisioned on a network of topological superconducting wires. An important component of these protocols is the transport of MZMs, which can be performed by using electric gates to locally tune sections of the wire between topologically trivial and nontrivial phases. In this work, we numerically simulate this transport by tuning a single section of a superconducting wire which contains either disorder (uncorrelated and correlated) or noise. We focus on the impact of these additional effects on the diabatic error, which describes unwanted transitions between the ground state and excited states. We show that the behavior of the average diabatic error is predominantly controlled by the statistics of the minimum bulk energy gap which is suppressed in the presence of disorder. The increase in diabatic error can be several orders of magnitude and is most deleterious when the disorder correlation length is a finite fraction of the transport distance and negligible when these lengths are far apart. In the presence of noise, the diabatic error is significantly enhanced due to optical transitions which depend on the minimum bulk energy gap as well as the frequency modes present in the noise. The results presented here serve to further characterize the diabatic error in disordered and noisy settings, which are important considerations in practical implementations of physical braiding schemes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Nontrivial fusion of Majorana zero modes in interacting quantum-dot arrays

Motivated by recent experimental reports of Majorana zero modes (MZMs) in quantum-dot systems at the “sweet spot,” where the electronic hopping t ℎ is equal to the superconducting coupling Δ, we study the time-dependent spectroscopy corresponding to the nontrivial fusion of MZMs. The term “nontrivial” refers to the fusion of Majoranas from different original pairs of MZMs, each with well-defined parities. We employ an experimentally accessible time-dependent real-space local density-of-states (LDOS) method to investigate the nontrivial MZM fusion outcomes in canonical chains and in a Y-shaped array of interacting electrons. In the case of quantum-dot chains where two pairs of MZMs are initially disconnected, after fusion we find equal-height peaks in the electron and hole components of the LDOS, signaling nontrivial fusion into both the vacuum I and fermion Ψ channels with equal weight. For π-junction quantum-dot chains, where the superconducting phase has opposite signs on the left and right portions of the chain, after the nontrivial fusion we observed the formation of an exotic two-site MZM near the center of the chain, coexisting with another single-site MZM. Furthermore, we also studied the fusion of three MZMs in the Y-shaped geometry. In this case, after the fusion we observed the novel formation of another exotic multisite MZM, with properties depending on the connection and geometry of the central region of the Y-shaped quantum-dot array.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Diabatic error and propagation of Majorana zero modes in interacting quantum dots systems

Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible time-dependent fidelity and local density-of-states using many-body time-dependent numerical methods. Furthermore, our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the timescale required for MZM transfer in a six-quantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.

Density of states↗
DOE OSTI2026

Unveiling in-gap states and Majorana zero modes in superconductor-topological insulator bilayer model

Interfaces between topological insulators and superconductors (SCs) are promising platforms for realizing Majorana zero modes (MZMs) via the superconducting proximity effect. We introduce a bilayer model consisting of the surface states of a three-dimensional topological insulator (3DTI) coupled to an 𝑠-wave superconductor and systematically study the role of interlayer tunneling strength (𝑡⊥) motivated by the recent growth of the Fe⁡(Te,Se)/Bi 2 ⁢Te 3 heterostructure. We find that increasing 𝑡⊥ shifts the proximity-induced (PrI) gap minimum away from the Γ point, giving rise to momentum-selective interference patterns that manifest as spatial oscillations in the in-gap states. We introduce an antidot with a magnetic vortex in the model and investigate the resulting in-gap states, including MZMs and Caroli–de Gennes–Matricon (CdGM) modes. With increasing hybridization strength, the energy separation between MZMs and CdGM states increases, enhancing the isolation of MZMs. Importantly, in the strong hybridization limit, the leading CdGM separation remains large in spite of the decrease in the PrI gap. Spin- and spatially resolved wavefunction analysis reveals angular momentum asymmetries absent in conventional 𝑠-wave systems. A direct comparison with a standalone 𝑠-wave superconductor confirms the emergence of distinct 𝑝-wave-like features in the bilayer geometry. Our results provide experimentally relevant predictions for tuning the stability of MZMs and their differentiation from the CdGM modes in SC-3DTI heterostructures and offer a theoretical framework for probing unconventional superconductivity in engineered topological systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Braiding of Majorana zero modes in vortex cores

Here, we demonstrate the successful simulation of $\sqrt{𝑍-}$, $\sqrt{𝑋-}$, and 𝑋-quantum gates using Majorana zero modes (MZMs) that emerge in magnetic vortices located in topological superconductors. We compute the transition probabilities and geometric phase differences accounting for the full many-body dynamics and show that qubit states can be read out by fusing the vortex core MZMs and measuring the resulting charge density. We visualize the gate processes using the time- and energy-dependent nonequilibrium local density of states. Our results demonstrate the feasibility of employing vortex core MZMs for the realization of fault-tolerant topological quantum computing.

Majorana bound states↗
DOE OSTI2026

STM/S Grid LDOS Data and Analysis Code for Deciphering Majorana Zero Modes in Topological Superconductor

This dataset provides raw millikelvin scanning tunneling microscopy/spectroscopy (STM/S) grid spectroscopy data and Python analysis scripts supporting the manuscript “Deciphering Majorana Zero Modes in Topological Superconductor FeTe0.55Se0.45 with Machine-Learning-Assisted Spectral Deconvolution.” The dataset includes a raw grid spectroscopy file acquired on FeTe0.55Se0.45 at 40 mK under magnetic field, together with Python/Jupytext analysis scripts used for STM/S data processing, visualization, spectral deconvolution, Lorentzian peak fitting, feature extraction, machine-learning-assisted clustering, and figure generation. These files support the analysis of vortex-core local density of states and the identification of zero-bias-peak-related spectral components from complex in-gap states. The dataset is intended to provide a citable archival record of the data and analysis code associated with the published manuscript and to support transparency and reproducibility of the reported STM/S and machine-learning workflow.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Majorana zero modes in a heterogeneous structure of topological and trivial domains in FeSe 1−𝑥 ⁢Te 𝑥

Here, we propose that the existence of vortices in FeSe 1−𝑥 ⁢Te 𝑥 with and without Majorana zero modes (MZMs) can be explained by a heterogeneous mixture of strong topological and trivial superconducting domains, with only vortices in the former exhibiting MZMs. We identify the spectroscopic signatures of topological and trivial vortices and show that they are necessarily separated by a domain wall harboring Majorana edge modes. We demonstrate that when a vortex is moved from a trivial to a topological domain in real time, a domain wall Majorana edge mode is transferred to the vortex as an MZM.

Majorana bound states↗
DOE OSTI2025

Solving the Bernstein-Vazirani problem using Majorana-based topological quantum algorithms

Executing quantum algorithms using Majorana zero modes—a major milestone for the field of topological quantum computing—requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of a Majorana-based, fault-tolerant quantum algorithm to solve the Bernstein-Vazirani problem in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes’ topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Simulating topological quantum gates in two-dimensional magnet-superconductor hybrid structures

The creation of topological quantum gates using Majorana zero modes—an outstanding problem in the field of topological quantum computing—relies on our ability to control the braiding process in time and space. Here, we propose two-dimensional magnet-superconductor hybrid structures as a new platformfor the successful implementation of topologically protected √σ z -, σ z - and σ x -quantum gates using Majorana zero modes. Employing a novel theoretical formalism to compute the full timedependent many-body wave-function and utilizing a braiding protocol motivated by recent advances in electron-spin-resonance techniques we simulate quantum gates in 2D systems up to 600 sites, on timescales from a few femto- to nanoseconds. We demonstrate that the braiding process can be visualized in time and space by computing the non-equilibrium local density of states, which is proportional to the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments, allowing us to directly image Majorana world lines.

Superconducting properties and materials↗
DOE OSTI2026

Majorana Edge Modes in Isolated Wires

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero modes (MZMs), with much of the evidence based on BCS mean-field theory. The direct application of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here, we develop a new correlation-based method for identifying MZMs in interacting, number-conserving systems. Using the density matrix renormalization group, we study fermion number-conserving models with long-range interactions, which under periodic boundary conditions exhibit robust topological and nontopological superconductivity, tuned by the strength of interaction [Ortiz et al., Phys. Rev. Lett. 113, 267002 (2014)]. We find evidence that, on the topological side, Majorana edge modes appear in open chains, manifesting as the vanishing of the energy splitting between odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-point correlation functions show nonlocal, parity-dependent edge effects. These correlations reveal the spatial structure of Majorana modes in the many-body wave function. We show that the correlation diagnostic applies broadly, including to short-range interacting models, where topological superconductivity is more fragile due to the absence of a bulk excitation gap.

Thomas-Markarian, Jaden↗
DOE OSTI2025

First-Principles Assessment of ZnTe and CdSe as Prospective Tunnel Barriers at the InAs/Al Interface

Majorana zero modes are predicted to emerge in semiconductor/ superconductor interfaces, such as InAs/Al. Majorana modes could be utilized for fault tolerant topological qubits. However, their realization is hindered by materials challenges. The coupling between the superconductor and the semiconductor may be too strong for Majorana modes to emerge, due to effective doping of the semiconductor by the metallic contact. This could be mediated by adding a tunnel barrier of controlled thickness. We use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO), to assess ZnTe and CdSe as prospective tunnel barriers for the InAs/Al interface. The results of DFT +U(BO) for ZnTe are validated by comparison to angle resolved photoemission spectroscopy (ARPES). We then study bilayer interfaces of the three semiconductors with each other and with Al, as well as trilayer interfaces with a varying number of ZnTe or CdSe layers inserted between InAs and Al. We find that 16 atomic layers of either material completely insulate the InAs from metal induced gap states (MIGS). However, ZnTe and CdSe differ significantly in their band alignment, such that ZnTe forms an effective barrier for electrons, whereas CdSe forms a barrier for holes. Because of Fermi level pinning in the conduction band at the interface, only electron transport is relevant for InAs-based Majorana devices. Therefore, ZnTe is the better choice. Based on the results of our simulations, we suggest conducting experiments with ZnTe barriers in the thickness range of 6–18 atomic layers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Crystalline-symmetry-protected Majorana modes in coupled quantum dots

We propose a minimalist architecture for achieving various crystalline-symmetry-protected Majorana modes in an array of coupled quantum dots. Our framework is motivated by the recent experimental demonstrations of two-site and three-site artificial Kitaev chains in a similar setup. We find that introducing a π-phase domain wall in the Kitaev chain leads to a pair of mirror-protected Majorana zero modes located at or near the junction. Joining two π junctions into a closed loop, we can simulate two distinct classes of two-dimensional higher-order topological superconducting phases, both carrying symmetry-protected Majorana modes around the sample corners. As an extension of the π junction, we further consider a general vertex structure where n Kitaev chains meet, i.e., a Kitaev n vertex. We prove that such an n vertex, if respecting a dihedral symmetry group D n , necessarily carries n vertex-bound Majorana modes protected by the D n symmetry. Resilience of the junction and vertex Majorana bound states against disorder and correlation effects is also discussed. Our architecture paves the way for designing, constructing, and exploring a wide variety of artificial topological crystalline phases in quantum-dot experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Driven Majorana modes: A route to synthetic $p_x +ip_y$ superconductivity

We propose a protocol to realize synthetic $p_x +ip_y$ superconductors in one-dimensional topological systems that host Majorana fermions. By periodically driving a localized Majorana mode across the system, our protocol realizes a topological pumping of Majorana fermions, analogous to the adiabatic Thouless pumping of electrical charges. Importantly, similar to the realization of a Chern insulator through Thouless pumping, we show that pumping of Majorana zero modes could lead to a $p_x +ip_y$ superconductor in the two dimensions of space and synthetic time. The Floquet theory is employed to map the driven one-dimensional system to a two-dimensional synthetic system by considering frequency as a new dimension. We demonstrate such Floquet $p_x +ip_y$ superconductors using the Kitaev $p$-wave superconductor chain, a prototypical 1D topological system, as well as its more realistic realization in the 1D Kondo lattice model as examples. We further show the appearance of Majorana $π$ mode at the Floquet zone boundary in an intermediate drive frequency region. Our work suggests a driven magnetic spiral coupled to a superconductor as a promising platform for the realization of novel topological superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Observation of Persistent Zero Modes and Superconducting Vortex Doublets in UTe 2

Superconducting vortices can reveal electron pairing details and nucleate topologically protected states. Yet, vortices of bulk spin-triplet superconductors have never been visualized at the atomic scale. Recently, UTe 2 has emerged as a prime spin-triplet superconductor, but its superconducting order parameter is elusive, and whether time-reversal symmetry (TRS) is broken remains unsettled. Here, in this work, we visualize vortices on the (011) surface of ultraclean UTe 2 single crystals (T c = 2.1 K) using scanning tunneling microscopy (STM). We introduce $\frac{d^{2}𝐼}{d𝑉^{2}}$ imaging as an effective technique for vortex visualization in superconductors with substantial residual zero-energy density of states (DOS), as in UTe 2 . Anisotropic single-flux-quantum vortices, with coherence lengths of ∼12 nm (4 nm) parallel (perpendicular) to the a -axis, form a triangular vortex lattice (VL) under a small out-of-plane magnetic field. The invariance of vortex structures and VL under changes of field polarity and cooling history strongly supports time-reversal invariant superconductivity under zero field. At vortex cores (VCs), nonsplit, spectrally sharp zero-bias conductance peaks (ZBPs) persist up 8 T that are consistent with symmetry-protected Majorana zero modes (MZMs) in a topological vortex line. Close examination of vortex structures reveals a mirror-asymmetric doublet─one with ZBPs and another with an enhanced apparent gap, possibly originating from a field-induced multicomponent order parameter.

UTe2↗