Deciphering Majorana Zero Modes in Topological Superconductor FeTe0.55Se0.45 with Machine-Learning-Assisted Spectral Deconvolution

Unambiguous identification of Majorana zero modes (MZMs) in topological superconductors (TSCs) remains a challenge due to complex in-gap states that can also produce zero-bias conductance peaks (ZBPs). Here we demonstrate a data-driven workflow that integrates pixel-wise spectral deconvolution with machine-learning (ML) to analyze tunneling spectroscopy from FeTe0.55Se0.45, an intrinsic TSC. Based on the local density of states (LDOS) spectra acquired with a millikelvin scanning tunneling microscope under magnetic fields, each spectrum was decomposed into multiple Lorentzian peaks. The extracted peak parameters were assembled into a structured feature set and subsequently embedded and clustered with unsupervised ML algorithms. ML-based clustering identified distinct classes of LDOS spectra, separating superconductor vortices exhibiting ZBPs consistent with established characteristics of MZMs from vortices displaying ZBP-mimicking features of trivial origin. Furthermore, spatially resolved ZBP distributions differentiate isotropic vortex cores with well-defined ZBPs from vortices that exhibit locally distorted ZBPs. By comparing the ZBP distributions to defect locations measured without magnetic field, we found a correlation between local heterogeneity and the ZBP formation, necessitating the systematic, data-driven analysis to disentangle genuine MZM signatures in TSC. This objective and reproducible workflow advances reliable MZM detection in TSCs, providing a foundation for MZM manipulation towards quantum computation.

💡 Research Summary

The authors present a comprehensive, data‑driven workflow for identifying Majorana zero modes (MZMs) in the intrinsic topological superconductor FeTe₀.₅₅Se₀.₄₅ (FTS). Using a dilution‑refrigerator scanning tunneling microscope operating at 40 mK and magnetic fields up to 2 T, they acquire dense grids of dI/dV spectra (≈80 × 80 nm² area with sub‑nanometer spacing), thereby obtaining thousands of local density‑of‑states (LDOS) curves that span both superconducting gaps and vortex cores.

Each spectrum is decomposed into a sum of Lorentzian peaks. Peak positions, amplitudes, and widths are extracted via a two‑step procedure: (i) second‑derivative peak detection provides initial guesses, and (ii) non‑linear least‑squares fitting refines the parameters. Fits are validated by high coefficients of determination (R² > 0.98) and are limited to the sub‑gap window |V| < 0.75 mV, which matches the expected CdGM level spacing.

The resulting peak parameters constitute a high‑dimensional feature tensor (spatial × spatial × peaks × features). To enhance separability, the authors augment this space with physically motivated descriptors such as zero‑bias proximity (ΔE < 0.1 meV) and spectral symmetry. Spatial coordinates are deliberately omitted so that clustering reflects intrinsic spectral characteristics only.

Dimensionality reduction proceeds with principal component analysis (PCA), retaining ~95 % of variance in ~10 components. Outliers are identified and removed using a k‑nearest‑neighbor distance score in PCA space. The cleaned data are then embedded with Uniform Manifold Approximation and Projection (UMAP) and clustered using hierarchical density‑based spatial clustering of applications with noise (HDBSCAN). Three dominant clusters emerge: C₀ (blue), C₁ (orange), and C₂ (green).

Cluster C₀ is sharply concentrated near zero bias and spatially localized at vortex cores, displaying non‑splitting zero‑bias peaks (ZBPs) that are robust against temperature and field variations. Clusters C₁ and C₂ exhibit broader energy distributions and are spread over the sample, correlating with known sources of trivial in‑gap states such as subsurface defects, excess Fe atoms, and domain boundaries. By overlaying the ZBP‑consistent C₀ map with independent defect maps obtained at zero field, the authors find only a weak correlation, supporting the interpretation that C₀ peaks arise from topological origins rather than disorder‑shifted CdGM or YSR states.

The workflow thus provides an objective, reproducible method to separate genuine MZM signatures from a plethora of trivial bound states that can also produce zero‑bias conductance peaks. It moves beyond line‑cut or point spectroscopy by exploiting the full spatial‑spectral dataset, enabling statistical validation of MZM criteria (localization, non‑splitting, symmetry). The authors discuss limitations, including sensitivity of Lorentzian fitting to background conductance and the dependence of clustering outcomes on hyper‑parameters, and suggest extensions such as spin‑polarized STM, non‑local transport, and controlled impurity engineering to further corroborate the Majorana nature of the observed ZBPs. Overall, the study demonstrates that machine‑learning‑assisted spectral deconvolution can become a standard tool for reliable Majorana detection in complex superconducting materials, advancing the path toward topological quantum computation.