The work demonstrates that the temperature dependence of magnetic noise near $T_{c}$ deviates from expected behavior based on quasiparticle excitations, a result of enhanced critical superconducting fluctuations caused by even a weak applied magnetic field. By analyzing this magnetic noise, the team was able to distinguish between different vortex phases and extract key physical quantities like vortex oscillation frequencies and diffusivity. This approach complements recent advances in noise magnetometry and reveals a wealth of superconducting dynamical phenomena in an applied field.

Qubit Depolarization Measures Superconducting Dynamics

A single spin qubit’s depolarization rate provides a non-invasive method for characterizing dynamic fluctuations within superconductors, a technique previously challenging to achieve with high spatio-temporal resolution, particularly in two-dimensional materials. This approach uses isolated spin qubits, such as nitrogen vacancy centers in diamond or boron vacancy centers in hexagonal boron nitride, to detect fluctuating magnetic fields generated by these low-dimensional materials with exceptional sensitivity. By optically initializing the qubit in a polarized state near the superconductor, researchers can measure how magnetic field fluctuations, originating from Cooper pair fluctuations or vortex motion, induce qubit depolarization.

The rate of this depolarization, denoted as 1/T_1, is a sensitive indicator of underlying superconducting dynamics when analyzed as a function of temperature, qubit-probe distance and probe frequency. This finding builds on recent advances in noise magnetometry, extending its capabilities to systems under an applied field.

Beyond critical fluctuations, the depolarization rate also provides insight into vortex dynamics, topological defects carrying quantized magnetic flux within the superconductor. The team demonstrated the ability to distinguish between different vortex phases, liquid or a frozen lattice, through noise spectroscopy. This method allows extraction of key physical quantities, including oscillation frequencies of pinned vortices, phonon dispersion within vortex lattices and vortex diffusivity in a vortex liquid.

“Relating depolarization rate to source fluctuations” is a key step in understanding the underlying physics, according to the research. The theoretical framework developed can be extended by incorporating non-linear corrections through self-consistent calculations, offering a more refined understanding of critical noise in an applied field.

Future work could also focus on characterizing noise signatures from thermally assisted flux creep in a vortex-glass phase, potentially revealing further details about the glassy dynamics of these topological defects. The qubit sensor’s heightened sensitivity to fluctuations near the surface, rather than the bulk, is also a notable characteristic of this technique.

Magnetic Fields Induce Superconducting Vortices

The presence of a magnetic field complicates the study of superconductors, introducing challenges for momentum-resolved experiments due to the deflection of probe particles by the field or its gradients. Beyond influencing the superconducting condensate itself, these fields induce topological defects known as vortices, each carrying a quantized unit of magnetic flux. Understanding the dynamics of these vortices is important for designing improved superconducting materials, as flux flow contributes to electrical resistance.

Analysis of magnetic noise allows for the probing of diverse aspects of vortex dynamics in both two- and three-dimensional superconductors, including the oscillatory behavior of isolated vortices and the elastic properties of vortex lattices. Researchers can also determine the diffusivity of vortices within a vortex liquid phase using this method. The theoretical framework extends to describe the behavior of vortices in the presence of disorder, predicting phases ranging from a liquid state to an Abrikosov vortex lattice or a vortex glass phase, each exhibiting unique characteristics.

Temperature Dependence of Noise Near T_c

Magnetic noise measurements reveal a departure from expected behavior in superconductors near their critical temperature, challenging predictions based solely on quasiparticle excitations. The team’s analysis extends beyond zero-field studies of vortex dynamics and Berezinskii-Kosterlitz-Thouless transitions, examining the impact of an external field on superconducting behavior. This saturation effect, observed both at short timescales and close proximity to the sample, is a key finding. The resulting noise scales with the square of the temperature. This work highlights the power of spin-qubit-based spectroscopy as a tool for investigating superconducting dynamics.

By demonstrating how an applied field enhances magnetic noise near the critical temperature due to increased pairing fluctuations, the research opens new avenues for characterizing these complex materials. The ability to non-invasively probe these fluctuations with a single spin qubit represents an advancement in the field, complementing existing noise magnetometry techniques and offering a pathway to unraveling the intricacies of superconductivity in two-dimensional materials. The team’s comprehensive study provides a foundation for future investigations into the interplay between magnetic fields, critical fluctuations, and superconducting dynamics.

Spin Qubit Proximity Detects Magnetic Noise

These discrepancies stem from critical superconducting fluctuations, amplified even by weak applied magnetic fields, suggesting a heightened sensitivity in these materials. The ability to extract these parameters from magnetic noise spectroscopy complements existing methods and provides a powerful tool for investigating the complex interplay between magnetic fields and superconducting dynamics. This work highlights the potential of spin-qubit-based spectroscopy to reveal a wealth of superconducting dynamical phenomena, particularly in two-dimensional materials where traditional characterization methods face limitations.

Vortex Lattice Properties from Noise Spectroscopy

Analysis of magnetic noise reveals detailed properties of vortex lattices, including their phonon dispersion and diffusivity, through a novel application of spin-qubit spectroscopy. The study further demonstrates that the magnetic noise can be used to determine the diffusivity of vortices as a vortex lattice melts into a liquid phase, providing insight into the transition between ordered and disordered superconducting states.

“Further, we showed that magnetic noise spectroscopy is able to detect fluctuations of superconducting vortices, characterize their low-energy dynamics, and diagnose key quantities of physical interest — such as the elastic moduli of vortex lattices and the associated phonon dispersion, as well as the diffusivity of vortices in a liquid phase obtained by melting of the vortex lattice,” the researchers state.

This work complements existing theoretical results on noise spectroscopy of superconductors without an applied magnetic field, and establishes the importance of this technique for interrogating pairing and vortex dynamics in a superconducting sample placed under a field.

Two-Dimensional Superconductor Noise Spectroscopy

This capability expands upon recent advancements in noise magnetometry, previously focused on quasiparticle excitations and Berezinskii-Kosterlitz-Thouless transitions in two-dimensional superconductors lacking an applied field, and demonstrates the potential of noise spectroscopy to uncover a wide range of superconducting dynamical phenomena when a field is present. The study theoretically investigated magnetic noise, initially focusing on thermal metal-insulator transitions within the time-dependent Ginzburg-Landau approach to characterize magnetic noise arising from critical pairing fluctuations in two-dimensional and thin-film superconductors at zero field.

Distinct vortex dynamics characterize different phases, leaving identifiable imprints on the magnetic noise detected by the qubit, and the team directly computed correlations of the magnetic field at the qubit’s location due to these vortices. Calculations began by evaluating the magnetic field generated by a single vortex at the origin in a two-dimensional superconductor, establishing a baseline for more complex analyses. This allowed for the assessment of magnetic noise arising from these collective behaviors, building upon the understanding of single vortex fluctuations.

The researchers summarized the scaling of magnetic noise across various length-scale hierarchies, providing a framework for interpreting experimental results and understanding the interplay between different length scales. The work demonstrated that an applied magnetic field, known to lower the critical temperature for the superconducting transition, also significantly increases magnetic noise near criticality due to enhanced pairing fluctuations. Recent experiments using depolarization and decoherence noise spectroscopy with nitrogen-vacancy centers have observed a peak in magnetic noise in the GHz range in thin-film cuprate superconductors, shifting to lower temperatures relative to the zero-field transition temperature.

The peak noise spectral density increased linearly with the applied field. While previous interpretations attributed this linear increase to a vortex liquid state, the present results suggest an alternative explanation: field-induced enhancement of order-parameter fluctuations can also produce a similar linear increase.

👉 More information
🗞 Qubit noise spectroscopy of superconducting dynamics in a magnetic field
✍️ Jiajie Cheng, Jaewon Kim, Oriana K. Diessel, Chong Zu and Shubhayu Chatterjee
🧠 DOI: http://link.aps.org/doi/10.1103/dyvk-lwc6

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