[Paper Review] Widefield NV Magnetic Field Reconstruction for Probing the Meissner Effect and Critical Current Density under Pressure

Kin On Ho, Cassandra Dailledouze+4 more|arXiv (Cornell University)|Jan 15, 2026

Physics of Superconductivity and Magnetism0 citations

TL;DR

The paper demonstrates a widefield NV-diamond magnetometry method to reconstruct magnetic field vectors around a Hg-1223 superconductor under 4 GPa, enabling quantitative Meissner effect mapping and extraction of the temperature-dependent critical current density via Brandt’s model.

ABSTRACT

The spatial distribution of a magnetic field can be determined with micrometer resolution using widefield nitrogen vacancy (NV) center magnetic imaging. Nevertheless, reconstructing the magnetic field from the raw data can be challenging due to the degeneracy of the four possible NV axes and the tremendous amount of data. While a qualitative approach is sufficient for most analyses, a quantitative analysis offers deeper insight into the physical system. Here, we apply NV widefield magnetic imaging to a HgBa$_{2}$Ca$_{2}$Cu$_{3}$O$_{8+δ}$ (Hg-1223) superconducting microcrystal at a pressure of 4 GPa. We fit the results with solutions from the Hamiltonian describing the NV center ground state and take into account the relative intensities of the resonances to determine the local magnetic field magnitude and angle. Thus, we reconstruct the temperature-dependent expulsion of the magnetic field due to the Meissner effect around the superconductor. By comparing the resulting parameters to Brandt's model, which describes the magnetic behavior of a type-II superconductor, we extract the critical current density $j_c$. Overall, this work showcases the first widefield quantitative reconstruction of the Meissner effect under pressure and an optical method to study critical current density. Thus, it provides new insights into the application of NV magnetometry to superconductivity research at high pressures.

Motivation & Objective

• Quantitatively map the Meissner expulsion around a superconductor under pressure using widefield NV magnetometry.
• Develop a phenomenological Hamiltonian-based model to reconstruct local magnetic field vectors from ODMR spectra.
• Extract temperature-dependent magnetic-field textures and compare with Brandt’s model to determine j_c.
• Assess pressure effects and provide optical methodology for studying superconductivity under high pressure.

Proposed method

• Represent the magnetic field in spherical coordinates with magnitude, polar angle, and azimuthal angle for each NV orientation.
• Fit ODMR spectra using the NV ground-state Hamiltonian with parameters for field, line shape, and stress environment.
• Incorporate eight fitting parameters including B-field magnitude and angles, ODMR Lorentzian parameters, and pressure-related factors.
• Assume alignment between expelled static magnetic field and microwave field for simulation of ODMR.
• Use constrained global fits with continuity across space and temperature to obtain a self-consistent field map.
• Apply Brandt’s model for a semi-infinite slab to the reconstructed B(x) profile to infer the critical current density j_c.

Experimental results

Research questions

• RQ1 How does the Meissner effect manifest in the spatial magnetic-field texture around Hg-1223 under high pressure?
• RQ2 Can widefield NV magnetometry provide a quantitative reconstruction of magnetic-field vectors during the superconducting transition under pressure?
• RQ3 What is the temperature dependence of the local magnetic-field distribution and how does it relate to critical current density j_c via Brandt’s model?
• RQ4 How does pressure influence the local magnetic environment and Meissner screening in the Hg-1223 microcrystal?
• RQ5 Can NV-based imaging determine lower/upper critical parameters under pressure without electrode-based transport measurements?

Key findings

• The Meissner effect induces stronger magnetic-field expulsion around the superconductor and lower field magnitude near the center at T < T_c.
• The reconstructed magnetic-field vectors show bending and angle changes consistent with Meissner screening approaching T_c (~138 K).
• Brandt’s model applied to the reconstructed B(x) profile yields a temperature-dependent j_c of about 1.5×10^4 A·cm^-2 at 120 K under 4 GPa.
• (j_c) increases as temperature decreases below T_c, with beta showing exponential sensitivity at low j_c.
• Measured j_c values align with literature ranges for Hg-1223 near ambient pressures, supporting the method’s validity under pressure.
• Local pressure variations due to sample-diamond contact are observed and should be considered in high-pressure NV measurements.