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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A topological superconductor tuned by electronic correlations

A topological superconductor, characterized by either a chiral order parameter or a topological surface state in proximity to bulk superconductivity, is foundational to topological quantum computing. A key open challenge is whether electron-electron interactions can tune such topological superconducting phases. Here, we provide experimental signatures of a unique topological superconducting phase in competition with electronic correlations in 10-unit-cell thick FeTe x Se 1-x films grown on SrTiO 3 substrates. When the Te content x exceeds 0.7, we observe a topological transition marked by the emergence of a superconducting surface state. Near the FeTe limit, the system undergoes another transition where the surface state disappears, and superconductivity is suppressed. Theory suggests that electron-electron interactions in the odd-parity xy− band drives this second topological transition. The flattening and eventual decoherence of d xy -derived bands track the superconducting dome, linking correlation effects directly to superconducting coherent transport. Our work establishes many-body electronic correlations as a sensitive knob for tuning topology and superconductivity, offering a pathway to engineer new topological phases in correlated materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Search for 3D topological superconductors using laser-based spectroscopy (Final Technical Report)

The three-dimensional topological superconductor (3D TSC) is a novel quantum phase of matter that is predicted to exhibit exotic thermal and electrical properties, which may serve applications ranging from precision thermal management and sensing technologies to fault-tolerant quantum information processing. Over the past decade, there has been an intensive effort to realize 1D and 2D TSCs by artificially engineering them from combinations of already existing materials. For example, coupling conventional superconductors to spin-orbit coupled 1D nanowires or to 2D topological insulator surfaces by the proximity effect provides a route to realizing 1D and 2D TSCs respectively. However no artificial engineering strategy is available for a 3D TSC. Therefore, current searches are limited to intrinsically superconducting compounds whose topological properties are difficult to predict. The overarching goal of this project was to realize and to identify 3D TSCs in bulk single crystals using novel laser-based spectroscopic techniques. One major thrust was to develop ultralow temperature and ultra-high-resolution angle-resolved photoemission spectroscopy (ARPES) to directly measure the dispersion of Majorana excitations that are predicted to exist on the surfaces of 3D TSCs. Another major thrust was to develop a rational route to realize 3D TSCs by identifying their precursor phases. It is theoretically proposed that the critical fluctuations of certain ordered electronic phases can mediate Cooper pairing in odd-parity channels and lead to topological superconductivity. Therefore, 3D TSCs may potentially emerge upon suppressing these inversion symmetry broken precursor phases to a critical point with external perturbations such as pressure, strain or even light. To test this hypothesis, we studied candidate materials using a suite of symmetry-sensitive optical probes including rotational anisotropy optical second harmonic generation (RA-SHG) and time-resolved coherent phonon spectroscopy, all operable under high-pressure and low temperature environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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

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 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 OSTI2025

Measuring the Debye energy in superconductors via two-electron photoemission spectroscopy

In this work, we demonstrate theoretically that double angle resolved photoemission spectroscopy (2eARPES) can directly probe the existence of Cooper pairs away from the Fermi surface, and can thus provide insight into the characteristic energy scale around the Fermi surface, the Debye energy, in which electrons are bound into Cooper pairs. To this end, we compute the photoelectron counting rate 𝑃 (2) in two different types of unconventional superconductors, a 𝑑 𝑥 2 −𝑦 2 -wave superconductor, and a topological superconductor with a broken time-reversal symmetry. We show that 𝑃 (2) provides insight into the relative strength of intra- and interband pairing in multiband systems, as well as into the spin polarization of the bands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Crossover from Conventional to Unconventional Superconductivity in 2M-WS 2

Leveraging the reciprocal-space proximity effect between superconducting bulk and topological surface states (TSSs) offers a promising way to topological superconductivity. However, elucidating the mutual influence of bulk and TSSs on topological superconductivity remains a challenge. Here, we report pioneering transport evidence of a thickness-dependent transition from conventional to unconventional superconductivity in 2M-phase WS 2 (2M-WS 2 ). As the sample thickness reduces, we see clear changes in key superconducting metrics, including critical temperature, critical current, and carrier density. Notably, while thick 2M-WS 2 samples show conventional superconductivity, with an in-plane (IP) upper critical field constrained by the Pauli limit, samples under 20 nm exhibit a pronounced IP critical field enhancement, inversely correlated with 2D carrier density. This marks a distinct crossover to unconventional superconductivity with strong spin-orbit-parity coupling. Furthermore, our findings underscore the crucial role of sample thickness in accessing topological states in 2D topological superconductors, offering pivotal insights into future studies of topological superconductivity.

2D topological superconductor↗
DOE OSTI2026

Understanding Majorana braiding in superconductors with a fixed total number of particles

Mean-field one-dimensional topological superconductors host edge Majorana zero modes (MZMs) that encode a topologically protected ground-state degeneracy and enable robust braiding operations within this subspace. Mean-field states lack definite particle number and thus cannot represent isolated systems. Nevertheless, projecting them onto fixed particle number can yield good approximations to an isolated superconductor ground state. In earlier work [Sajith et al., Phys. Rev. B 109, 184509 (2024)] we showed that the projected Kitaev wave function of a single wire preserves some important mean-field features, such as the zero-energy spectral peaks near the wire edges. However, uniqueness of the fixed-number ground state does not allow for any nontrivial operations in the ground-state subspace. To overcome this limitation, here we consider the case of multiple wires with a conserved total charge, using the same approach. In the limit of vanishing interwire coupling, this system has a macroscopic ground-state degeneracy. We show how this degeneracy is resolved by coherent single-particle tunneling, and identify special many-body states which play the same role as the MZM parity states in the mean field. In this work, we demonstrate how braiding operations can be implemented and discuss both intrinsic and extrinsic limits on their fidelity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum Anomalies in Condensed Matter

Quantum materials provide a fertile ground in which to test and realize unusual phenomena such as quantum anomalies predicted by quantum field theory. There are three important symmetries that are broken when classical field theory is moved into the quantum regime, the scale anomaly, the axial (chiral) anomaly, and the parity anomaly. Several potential device applications may be realized by the discovery of quantum anomalies in condensed matter, enabled by the new physics they embody, including ultra‐sensitive dark matter detectors, far infrared optical modulators, micro‐bolometric detectors, low‐dissipation ballistic transporters, terahertz‐based qubits, terahertz polarization state controls, passive magnetic field sensors, stable topological superconductors that host Majorana fermions, and qubits topologically protected against decoherence. In this perspective article, the definition of these quantum anomalies is laid out, how little is known in the context of condensed matter, and how quantum anomalies are predicted to manifest as anomalous electronic, thermal, and magnetic behavior in experiments on topological quantum materials, including Weyl and Dirac semimetals. Furthermore, the importance that mechanical strain and defects will play in modifying signatures of quantum anomalies is discussed.

36 MATERIALS SCIENCE↗
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

Chiral superconductivity from a parent Chern band and its non-Abelian generalization

Here, we propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetralayer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose-Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose-Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multilayer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. The chiral superconductor phase of the composite fermion becomes the non-abelian Moore-Read quantum Hall phase. We argue that a chiral (pseudo-)spin liquid phase can emerge in the vicinity of this Moore-Read quantum Hall phase. Our work suggests rhombohedral multilayer graphene as a potential platform for rich correlated topological phases.

Wang, Yan-Qi [University of Maryland, College Park↗
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

High-field superconducting halo in UTe 2

The heavy fermion material UTe 2 is a candidate topological superconductor that exhibits multiple magnetic field–induced superconducting phases. One such phase exists only at fields greater than 40 tesla, a considerable scale given its critical temperature of only 2 K. Here, in this work, we extend measurements of this state with fields outside of the bc crystallographic plane and reveal its core structure: The superconducting phase wraps around the b axis in a halo-like fashion and appears to be stabilized by a field component perpendicular to the magnetic easy axis. This angle dependence points to a multicomponent spin-triplet order parameter with a finite angular momentum of the Cooper pairs. The pairing mechanism remains enigmatic, and UTe 2 ’s specific magnetophilic superconducting tendencies seem incompatible with existing models for field-enhanced superconductivity.

Lewin, Sylvia K. [National Inst. of Standards and ↗
DOE OSTI2025

Magnet-superconductor hybrid quantum systems: a materials platform for topological superconductivity

Magnet–superconductor hybrid (MSH) systems have recently emerged as one of the most significant developments in condensed matter physics. This has generated, in the last decade, a steadily rising interest in the understanding of their unique properties. They have been proposed as one of the most promising platforms for the establishment of topological superconductivity, which holds high potential for application in future quantum information technologies. Their emergent electronic properties stem from the exchange interaction between the magnetic moments and the superconducting condensate. Given the atomic-level origin of such interaction, it is of paramount importance to investigate new magnet–superconductor hybrids at the atomic scale. In this regard, scanning tunneling microscopy (STM) and spectroscopy are playing a crucial role in the race to unveil the fundamental origin of the unique properties of MSH systems, with the aim to discover new hybrid quantum materials capable of hosting topologically non-trivial unconventional superconducting phases. In particular, the combination of STM studies with tight-binding model calculations have represented, so far, the most successful approach to unveil and explain the emergent electronic properties of MSHs. The scope of this review is to offer a broad perspective on the field of MSHs from an atomic-level investigation point-of-view. The focus is on discussing the link between the magnetic ground state hosted by the hybrid system and the corresponding emergent superconducting phase. This is done for MSHs with both one-dimensional (atomic chains) and two-dimensional (atomic lattices and thin films) magnetic systems proximitized to conventional s-wave superconductors. We present a systematic categorization of the experimentally investigated systems with respect to defined experimentally accessible criteria to verify or falsify the presence of topological superconductivity and Majorana edge modes. The discussion will start with an introduction to the physics of Yu–Shiba–Rusinov bound states at magnetic impurities on superconducting surfaces. This will be used as a base for the discussion of magnetic atomic chains on superconductors, distinguishing between ferromagnetic, antiferromagnetic and non-collinear magnetic ground states. A similar approach will be used for the discussion of magnetic thin film islands on superconductors. Given the vast number of publications on the topic, we limit ourselves to discuss works which are most relevant to the search for topological superconductivity.

Majorana states↗
DOE OSTI2025

Supermodulation-driven evolution of the nodal structure of bismuth-based cuprate superconductors

Recent work has shown novel properties of twisted cuprates. In this paper, I point out that related phenomena occur intrinsically in bismuth-based cuprate superconductors due to the presence of the BiO supermodulation. As the ratio of the supermodulation potential to the superconducting energy gap increases, two critical points are found where semi-Dirac nodes form (that is, they have quadratic dispersion in one direction and linear dispersion in the orthogonal direction). The first critical point should be realized in Bi2212, the second in Bi2201. Implications of these findings are discussed.

Cuprates↗
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

Buried Dirac Points in Quantum Spin Hall Insulators: Implications for Majorana Kramers Pair-Based Quantum Computing

Quantum spin Hall insulators (QSHIs) host helical electronic edge states that are protected from backscattering due to time-reversal symmetry (TRS). Despite considerable work investigating QSHI edge states, there is still an open question about their unexpected resilience to large magnetic fields where TRS is undoubtedly broken. In this work, we investigate the transport properties of helical edge states in a QSHI-superconductor (QSHI-SC) junction formed by a In⁢As(15 nm)/Ga⁢Sb(5 nm) double quantum well and a superconducting tantalum (Ta) constriction. We observe a robust conductance plateau up to 2 T, signaling resilient edge-state transport. Using a modified Landauer-Büttiker analysis, we find that the zero-field conductance is consistent with 98% Andreev-reflection probability owing to the high transparency of the (In⁢As/Ga⁢Sb)-Ta interface. Such resilience is consistent with the Dirac point for the edge states being buried in the bulk valence band. We further theoretically show that a buried Dirac point does not affect the robustness of the quasi-one-dimensional topological superconducting phase. We find that a buried Dirac point favors the hybridization of Majorana Kramers pairs (MKPs)—predicted to exist in a QSHI-SC constriction—and fermionic modes in the QSHI vacuum edge resulting in extended MKP states, highlighting the subtle role of buried Dirac points in probing MKPs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Pathways from a chiral superconductor to a composite Fermi liquid

Recent experiments have reported chiral time-reversal broken superconductivity in n-layer rhombohedral graphene for n=4,5,6. Introducing a moiré potential by alignement with a hexagonal boron nitride substrate suppresses the superconductivity but leads instead to various fractional quantum anomalous Hall phenomena. Motivated by these observations, we consider the fate of the phase transition between (a chiral) Landau Fermi liquid (LFL) metal and a Composite Fermi Liquid (CFL) metal in the presence of attractive interactions. These are parent states, respectively, for the superconductor and the fractional quantum Hall states. For weak attractive interactions, the LFL is usually unstable to superconductivity while the CFL is stable. This raises the possibility of a direct continuous phase transition between the chiral superconductor and the CFL. However, we show that generically the LFL close to the transition to the CFL is stable against superconductivity. Furthermore the evolution between the CFL and chiral superconductor goes through an intermediate stable LFL phase for weak attractive interactions. With stronger interactions, the evolution can instead go through a non-Abelian paired quantum Hall state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗