Despite intense efforts on all known quasi-two-dimensional superconductors, the origin and exact boundary of the electronic orderings, particularly charge density waves and superconductivity, are still attractive problems with several open questions. Here, in order to reveal how the superconducting gap evolves, we report on high quality complementary measurements of magneto-optical imaging, specific heat, magnetic susceptibility, resistivity measurements, Andreev spectroscopy, and London penetration depth ${\lambda }_{ab}\left(T\right)$ measurements supplemented with theoretical calculations for $2\mathrm{H}\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ and $2\mathrm{H}\text{−}\mathrm{Nb}{\mathrm{S}}_2$ single crystals. The temperature dependence of ${\lambda }_{ab}\left(T\right)$ calculated from the lower critical field and Andreev spectroscopy can be well described by using a two-band model with $s$-wave-like gaps. The effect of pressure on the superconducting gap of both systems illustrates that both bands are practically affected. Upon compression, the Fermi surfaces do not change significantly, and the nesting remains almost unaffected compared to that at ambient condition. However, a strong bending in the upper critical fields ($H_{\mathrm{c}2}$) curves is obtained under pressure and support the presence of a strong Pauli paramagnetic effect. In $\mathrm{Nb}{\mathrm{Se}}_2$, using a two-band model with $s$-wave-like gaps, the temperature dependence $H_{\mathrm{c}2}\left(T\right)$ can be properly described. In contrast to that, the behavior of $H_{\mathrm{c}2}$ for $\mathrm{Nb}{\mathrm{S}}_2$ is ruled by the spin paramagnetic effect. The estimated values of the penetration depth at $T=0\mathrm{K}$ confirm that $\mathrm{Nb}{\mathrm{Se}}_2$ and $\mathrm{Nb}{\mathrm{S}}_2$ superconductors depart from a Uemura-style relationship between $T_{\mathrm{c}}$ with ${\mathit{\lambda }}_{ab}^{-2}\left(T\right)$, the in-plane superconducting penetration depth.

We numerically investigate the effect of an edge indentation on the threshold field of thermomagnetic instabilities in superconducting films subjected to a ramping magnetic field, applied perpendicular to the plane of the film. In particular, we are able to address the question on whether edge indentations promote magnetic flux avalanches. For the magnetic field-independent critical current density model, the triggering of the first magnetic flux avalanche systematically occurs at the edge indentation. In contrast to that, for the more realistic field-dependent critical current density model the first flux avalanche can take place either at or away from the indentation. This selective triggering of magnetic flux avalanches is shown to result from two effects. Namely, (i) the variation of the threshold magnetic field for the first flux avalanche triggered at the indentation and (ii) the reduction of the critical current density by large local magnetic fields at the tip of the indentation which translates in a lower power density dissipated near the tip. We demonstrate that this interplay can be tuned by varying the indentation size, ramp rate of applied field ${\dot{H}}_a$, and working temperature $T_0$. We build up a phase diagram in the ${\mu }_0{\dot{H}}_a-T_0$ plane with well-defined boundaries separating three distinct regimes of thermomagnetic instability.

Superconductors are well known for their ability to screen out magnetic fields. In type-II superconductors, as the magnetic field pressure is progressively increased, magnetic flux accumulates at the periphery of the sample, very much like charges accumulate in a capacitor when voltage is increased. As for capacitors, exceeding certain threshold field causes the blocked magnetic flux to abruptly penetrate into the sample. This phenomenon, triggered by a thermomagnetic instability, is somewhat analogous to the dielectric breakdown of the capacitor and leaves behind a similar Lichtenberg imprinting. Even though electrical breakdown threshold has been extensively studied in dielectrics, little information is known about the statistical distribution of the thermomagnetic breakdown in superconductors. In this work, we address this problem by performing magneto-optical imaging experiments on a Nb film where nanometric heating elements are used to rapidly erase the magnetic history of the sample. We demonstrate that the size and shape distributions of avalanches permits to unambiguously identify the transition between two regimes where either thermal diffusivity or magnetic diffusivity dominates. Clear criteria for discriminating athermal dynamic avalanches from thermally driven avalanches are introduced. This allows us to provide the first precise determination of the threshold field of the thermomagnetic breakdown and unveil the details of the transition from finger-like magnetic burst to dendritic branching morphology. These findings open a new avenue in the interdisciplinary exploration of catastrophic avalanches through non destructive repeatable experiments.

In type-II superconductors, the flux-free state (Meissner state) may be invaded by vortices bearing quantized flux once $H$ is above the lower critical field ${H}_{c1}$. However, the actual first flux penetration does not occur at ${H}_{c1}$ due to the presence of a surface barrier and the fact that the Meissner state may also exist as a metastable state up to a larger (superheating) field. In this work we determine the field for the first vortex penetration in superconductors by directly imaging the first vortex threading a superconducting Pb film with antidots. We find that the first vortex penetration occurs when the surface superconducting currents reach the depairing current, locally breaking superconductivity and allowing a vortex to nucleate.

Superconductors play a crucial role in the advancement of high-field electromagnets. Unfortunately, their performance can be compromised by thermomagnetic instabilities, wherein the interplay of rapid magnetic and slow heat diffusion can result in catastrophic flux jumps, eventually leading to irreversible damage. This issue has long plagued high-J_c Nb₃Sn wires at the core of high-field magnets. In this study, we introduce a large-scale GPU-optimized algorithm aimed at tackling the complex intertwined effects of electromagnetism, heating, and strain acting concomitantly during the quenching process of superconducting coils. We validate our model by conducting comparisons with magnetization measurements obtained from short multifilamentary Nb₃Sn wires and further experimental tests conducted on solenoid coils while subject to ramping transport currents. Furthermore, leveraging our developed numerical algorithm, we unveil the dynamic propagation mechanisms underlying thermomagnetic instabilities (including flux jumps and quenches) within the coils. Remarkably, our findings reveal that the velocity field of flux jumps and quenches within the coil is correlated with the cumulated Joule heating over a time interval rather than solely being dependent on instantaneous Joule heating power or maximum temperature. These insights have the potential to optimize the design of next-generation superconducting magnets, thereby directly influencing a wide array of technologically relevant and multidisciplinary applications.