Machine learning reveals elusive quantum states in matter

Scientists continue to seek definitive identification of Majorana zero modes (MZMs) in topological superconductors, but their pursuit is complicated by overlapping spectral features that mimic real MZM signals. Jewook Park and Hoyeon Jeon of Oak Ridge National Laboratory’s Nanophase Materials Science Center, along with Dongwon Shin of the institute’s Materials Science and Technology Division, led the study that employed a new machine learning approach to address this challenge. The team collaborated with colleagues including Guannan Zhang from the Computer Science and Mathematics Department and Michael A McGuire and Brian C Sales and An-Ping Li from the Materials Science and Technology Department to develop a data-driven workflow to analyze tunneling spectroscopy data from the intrinsic topological superconductor FeTe0.55Se0.45. This work is important because it introduces an objective and reproducible method to distinguish true MZMs from trivial in-gap states, providing an important step to reliably detect and ultimately manipulate these exotic states in potential quantum computing applications.

Scientists are inching closer to realizing the potential of quantum computing using new techniques to identify elusive quantum particles. The method overcomes a major hurdle in materials science by reliably distinguishing genuine quantum signals from misleading background noise, and is expected to accelerate the development of stable and scalable quantum technologies.

Researchers are developing a new method to reliably identify Majorana zero modes in topological superconductors, a key step toward building more stable quantum computers. Identifying these quasiparticles has proven difficult because their characteristic zero-bias conductance peak can be mimicked by other nontopological phenomena within the material.

The research team demonstrated a data-driven workflow that integrated detailed spectral analysis and machine learning to distinguish genuine Majorana modes from misleading signals in FeTe0.55Se0.45, a promising intrinsic topological superconductor. This study addresses the long-standing challenge of definitively confirming the existence of MZMs, which are predicted to exhibit unique quantum properties.

The approach begins with ultrasensitive scanning tunneling spectroscopy performed at milliKelvin temperatures to map the local density of states across the material surface. Each spectrum is carefully decomposed into its constituent peaks, and the resulting data is fed into an unsupervised machine learning algorithm. These algorithms automatically identify patterns, group spectra with similar properties, and effectively separate vortex cores exhibiting true Majorana features from those exhibiting false peaks.

By analyzing the spatially resolved distribution of these zero-bias peaks, the researchers distinguish between isotropic vortex cores, eddy cores with distinct MZMs, and eddies with distorted peaks indicating trivial origins. Comparing these distributions with defect maps measured without a magnetic field reveals a correlation between local material defects and misleading ZBP formation.

This finding highlights the need for systematic data-driven analysis to accurately identify genuine Majorana modes. An objective and reproducible workflow not only improves MZM detection but also establishes the foundation for future manipulation of these states, bringing the prospects of topological quantum computation closer to reality. FeTe0.55Se0.45 has a relatively large superconducting gap and small Fermi energy, with dense energy levels in nontopological states.

Distinguishing these states from true MZMs requires very high energy resolution in scanning tunneling spectroscopy measurements. This is achieved by operating the STM at 40 mK, allowing accurate separation of subtle spectral features. Analyzing the vast amount of data generated required a new approach that went beyond manual inspection of individual spectra.

The researchers employed pixel-by-pixel analysis to extract key parameters from each spectrum and assemble them into a structured dataset. This dataset was processed using unsupervised machine learning, allowing the algorithm to identify different classes of spectra without prior assumptions about the underlying physics. This process objectively identifies ZBPs, separates potential MZM candidates from other in-gap states, and distinguishes ZBPs arising from Majorana modes from those arising from excess iron atoms, domain boundaries, or shifted Caroli-de-Jenne matricone states.

By reconstructing the gridded LDOS data, the research team highlighted the spatial distribution of ZBP and provided a comprehensive map of potential Majorana modes across the material surface. This objective and scalable framework promises to accelerate the exploration and operation of MZM and pave the way for advances in quantum computing.

Identification of Majorana zero mode in iron selenide telluride by spectral deconvolution

Millikelvin scanning tunneling microscopy supported the study of the intrinsic topological superconductor FeTe0.55Se0.45. Local density of states (LDOS) spectra were acquired with an applied magnetic field and formed the basis of a data-driven workflow designed to identify Majorana zero modes. Each spectrum was subjected to pixel-wise spectral deconvolution to separate the complex signal into its component parts using multiple Lorentzian peak fitting.

This technique assumes that the observed spectrum can be accurately represented as a sum of Lorentzian lines, each corresponding to an electronic state. Initial parameters for these fits were identified using conventional second-order differential methods to ensure a reasonable starting point. Superconducting regions exhibiting featureless subgap conductances were intentionally excluded from the fitting procedure to focus the analysis on informative intragap states.

The energy range of the focus was restricted and following deconvolution, the extracted peak parameters were assembled into a structured feature set with statistical outliers removed. The energy distribution within each cluster showed that C0 had a sharp concentration of energy around zero, whereas C1 and C2 had a more widespread off-center distribution. These clusters showed different energy distributions. Detailed analysis reveals that C0 is sharply concentrated around zero energy, whereas C1 and C2 exhibit a broader off-center distribution. A 0.3D scatter plot of peak centers in (E, rij) space (E represents energy and rij indicates spatial coordinate) further reveals that the peaks within C0 are energetically concentrated around zero bias and spatially localized around the vortex core, unlike C1 and C2, which showed a broader distribution.

This cluster separation confirms the ability of unsupervised clustering to reliably distinguish zero-bias peaks from other subgap states and provides objective classification of spectral features. Each spectrum acquired by millikelvin scanning tunneling microscopy with an applied magnetic field was resolved into multiple Lorentzian peaks and formed the basis of a structured feature set.

An unsupervised machine learning algorithm then embedded and clustered these features, successfully distinguishing eddies exhibiting zero-bias conductance peaks (ZBPs) indicative of Majorana zero modes (MZMs) from eddies exhibiting ZBP-like features with trivial origins. This separation is an important advance in this field. The spatially resolved ZBP distribution clearly distinguished between isotropic vortex cores with well-defined ZBP and eddies exhibiting locally distorted ZBP.

These distortions suggest alternative mechanisms and complicate the identification of genuine MZMs. By directly comparing the ZBP distribution with maps of defect locations measured in the absence of a magnetic field, the researchers found a correlation between local material inhomogeneities and ZBP formation. This highlights the importance of systematic data-driven analysis in disentangling true MZM features within topological superconductors.

Combining the extracted peak parameters into feature sets enabled objective and reproducible classification of LDOS spectra. ML-based clustering can reliably classify eddies, a task that has traditionally relied on subjective interpretation of spectroscopic data. The ability to resolve subtle differences in ZBP shape and distribution is critical, as vortices exhibiting distorted ZBPs tend to cluster around imperfections. This method provides a basis for manipulating MZMs in topological superconductors and opens avenues of exploration in quantum computing.

Disentangling Majorana zero modes from disorder in matter using spectroscopy and machine learning

Scientists pursuing topological quantum computation face the constant hurdle of distinguishing genuine Majorana zero modes from impostors. The detection of these elusive quasiparticles, which hold promise as building blocks for fault-tolerant qubits, has long been plagued by false positives resulting from routine effects within the complex material systems in which they are explored.

The research team presented a workflow that combines detailed spectroscopic analysis and machine learning to provide a more objective approach to identifying these critical conditions. Rather than relying on a single measurement, this method analyzes data and separates meaningful signal from noise with a level of precision never seen before. Achieving a clearer signal is not enough to declare victory.

The problem lies in the inherent disorder within materials like iron-based superconductors, where defects and fluctuations can mimic the characteristics of Majorana modes. Previous attempts often struggled to account for this “background noise”, leading to ambiguous results. This new approach directly addresses this issue by systematically classifying spectral features, correlating spurious signals with material defects and providing a more reliable estimate of true Majorana conditions.

Reliance on spectroscopic data means that this technique is limited by the resolution and sensitivity of the measurement equipment. Although this study did not achieve that, it provides an important step forward by establishing a reproducible method for identifying potential candidates.

Once verified, these candidates can undergo more rigorous testing. Beyond iron-based superconductors, data-driven workflows have the potential to be applied to the analysis of data from other topological materials, accelerating the search for robust Majorana platforms. The broader implications are a move toward more objective, data-centric approaches in the exploration of exotic quantum states, a trend that is likely to define the next stage in this challenging but potentially transformative field.