Superconductivity is destroyed by a magnetic field, and the upper critical field Hc2 is limited by two mechanisms: the orbital effect (vortices) and the spin effect (the Pauli paramagnetic limit). In two-dimensional materials with an in-plane field, the orbital contribution is suppressed, and the Zeeman splitting, governed by the g-factor, takes center stage. The classical expression for the Pauli limit assumes g = 2, but in many systems with strong spin-orbit coupling, the g-factor deviates from this value. This work sits at the intersection of superconductivity physics and thin-film physics: neighboring studies examine superconductivity in various materials, including gold, copper, nickelates, and UTe2, as well as the influence of magnetic fields on qubits and quantum gravity. However, direct observation of the thickness dependence of the Pauli limit through changes in the g-factor remained a gap.
PdTe2 films with thicknesses from 19 to 50 nm were grown by chemical vapor deposition via tellurization of palladium layers. Structure and thickness were characterized by X-ray diffraction and atomic force microscopy. Resistance measurements in magnetic fields up to 8 T were performed on the SCM1 setup at the National High Magnetic Field Laboratory at temperatures down to 20 mK. The in-plane upper critical field Hc2|| was determined at the point where resistance dropped by half. Analysis used the self-consistent linearized gap equation, including Ising, Zeeman, and orbital interaction parameters. Fitting the temperature dependence of Hc2|| allowed extraction of the effective g-factor and other parameters for each thickness.
The in-plane critical field increases from 0.1 T for the 50 nm film to 8 T for the 19 nm film, a 27-fold enhancement. The superconducting transition temperature Tc0 remains nearly constant for thicknesses from 50 to 26 nm (about 1.5 K), but rises to 2.1 K for the thinnest film. Model fitting shows that the effective g-factor and orbital interaction increase with thickness. Quantum confinement enlarges the energy gap between subbands, which reduces the contribution of higher bands to the g-factor, making it smaller in thin films. Perturbative k·p model calculations reproduce this trend. For the three thinnest films, the model fails to describe data below 100 mK, which may indicate the emergence of unconventional pairing.
This work demonstrates for the first time that quantum confinement in superconducting films can control the Pauli limit through changes in the g-factor. Unlike neighboring studies where the g-factor was assumed constant or measured in the normal state, here a direct link between thickness and the upper critical field in the superconducting state is shown. This broadens our understanding of the role of Zeeman interaction in two-dimensional superconductors and provides a new tool for tuning critical fields. The results also point to a possible violation of the Pauli limit in thin films, which could be a signature of nontrivial pairing symmetry.
Further studies could test whether the thickness dependence of the g-factor persists in other layered superconductors with strong spin-orbit coupling. The influence of strain, doping, or heterostructures on the g-factor and Pauli limit could be explored. Theoretically, it is important to clarify the role of impurities and disorder in renormalizing parameters. The nature of the low-temperature discrepancy between model and data for thin films remains an open question; it could be related to triplet or mixed pairing.
The results will impact the physics of superconducting thin films, spintronics, and the search for topological superconductors, where controlling spin properties is critical.
Measure the g-factor directly via tunneling spectroscopy or Shubnikov–de Haas oscillations in thin films. Check reproducibility in other van der Waals superconductors.
Connection to unsolved problems in superconductivity physics: the pairing mechanism in PdTe2 (conventional or unconventional), the role of spin-orbit interaction in two-dimensional systems, and the origin of Pauli limit violation. This work highlights the need to account for quantum confinement when interpreting critical fields in thin films.
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What the work does
This study examines how quantum confinement affects the Pauli limit in thin films of PdTe2. We measured the in-plane upper critical field for thicknesses ranging from 19 to 50 nm at temperatures down to 20 mK. The field was found to increase by more than an order of magnitude as the film thickness decreased, and the effective g-factor was shown to grow with thickness, a result confirmed by modeling.
Where its strength is
Direct experimental evidence that the Pauli limit can be controlled by film thickness through changes in the g-factor. This opens a new route to tuning superconducting properties via the dimensional effect.
Where it could go next
Worth trying
Why this may matter
Controlling the Pauli limit through the dimensional effect could enable superconductors with improved performance in strong magnetic fields, which is important for applications such as magnets and quantum devices.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.54, against a usual 0.64. It looks like few have drilled nearby.
The 8 T field achieved for the 19 nm film is roughly 200 times stronger than Earth's magnetic field. Yet superconductivity persists at just 20 millikelvin, which is 100 times colder than outer space.
The idea of controlling material properties through size echoes the concept of 'smart matter' from science fiction, where nanostructures are programmed to achieve desired characteristics. In Neal Stephenson's novel The Diamond Age, nanotechnology enables materials with tailored properties, which resonates with tuning superconductivity via film thickness.