Low-temperature ($\sim 20$ K) electron irradiation with 2.5 MeV relativistic electrons was used to study the effect of controlled nonmagnetic disorder on the normal and superconducting properties of the type-II Dirac semimetal ${\mathrm{PdTe}}_2$. We report measurements of longitudinal and Hall resistivity, thermal conductivity and London penetration depth using the tunnel-diode resonator technique for various irradiation doses. The normal-state electrical resistivity follows the Matthiessen rule with an increase of the residual resistivity at a rate of $\sim 0.77\mu \mathrm{\Omega }\mathrm{cm}/(\mathrm{C}/{\mathrm{cm}}^2)$. London penetration depth and thermal conductivity results show that the superconducting state remains fully gapped. The superconducting transition temperature is suppressed at a nonzero rate that is about 16 times slower than described by the Abrikosov-Gor'kov dependence, applicable to magnetic impurity scattering in isotropic, single-band $s$-wave superconductors. To gain information about the gap structure and symmetry of the pairing state, we perform a detailed analysis of these experimental results based on insight from a generalized Anderson theorem for multiband superconductors. This imposes quantitative constraints on the gap anisotropies for each of the possible pairing candidate states. We conclude that the most likely pairing candidate is an unconventional $A_{1g}^{+-}$ state. While we cannot exclude the conventional $A_{1g}^{++}$ and the triplet $A_{1u}$, we demonstrate that these candidates require additional assumptions about the orbital structure of the disorder potential to be consistent with our experimental results, e.g., a ratio of inter- to intraband scattering for the singlet state significantly larger than 1. Due to the generality of our theoretical framework, we believe that it will also be useful for irradiation studies in other spin-orbit-coupled multiorbital systems.

High-energy electron irradiation at low temperatures is an efficient and controlled way to create vacancy–interstitial Frenkel pairs in a crystal lattice, thereby inducing nonmagnetic point-like scattering centers. In combination with London penetration depth and resistivity measurements, the electron irradiation was used as a phase-sensitive probe to study the superconducting order parameter in iron-based superconductors (FeSCs), lending strong support to sign-changing s _± pairing. Here, we review the key results of the effect of electron irradiation in FeSCs.

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature T _c acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe_1−x Co _x )₂As₂. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe₂(As_1−x P _x )₂ compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic–magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ(x) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

The London penetration depth $\lambda \left(T\right)$ was measured in a single crystal of ${\mathrm{V}}_3\mathrm{Si}$. The superfluid density obtained from this measurement shows a distinct signature of two almost decoupled superconducting gaps. This alone is insufficient to distinguish between $s_{\pm }$ and $s_{++}$ pairing states, but it can be achieved by studying the effect of controlled nonmagnetic disorder on the superconducting transition temperature $T_c$. For this purpose, the same ${\text{V}}_3\text{Si}$ crystal was sequentially irradiated by 2.5-MeV electrons three times, repeating the measurement between the irradiation runs. A total dose of $10\mathrm{C}/{\mathrm{cm}}^2$ ($6.24\times {10}^{19}$ $\text{electrons}/{\text{cm}}^2$) was accumulated, for which $T_c$ changed from 16.4 K in a pristine state to 14.7 K ($9.3\%$). Not only is this substantial suppression impossible for a single isotropic gap, but also it is not large enough for a sign-changing $s_{\pm }$ pairing state. Our electronic band structure calculations show how five bands crossing the Fermi energy can be naturally grouped to support two effective gaps, not dissimilar from the physics of iron pnictides. We analyze the results using two-gap models for both $\lambda \left(T\right)$ and $T_c$ which describe the data very well. Thus the experimental results and theoretical analysis provide strong support for an $s_{++}$ superconductivity with two unequal gaps, ${\mathrm{\Delta }}_1\left(0\right)\approx 2.53\text{meV}$ and ${\mathrm{\Delta }}_2\left(0\right)\approx 1.42\text{meV}$, and a very weak interband coupling in the ${\text{V}}_3\text{Si}$ superconductor.

A self-consistent two-gap $\gamma$ -model is used to quantitatively describe several thermodynamic properties of MgB ${}_2$ superconductor. The superconducting coupling matrix, ${\nu }_{ij}$ , was obtained from the fitting of the superfluid density in the entire superconducting temperature range. Using this input, temperature-dependent superconducting gaps, specific heat, and upper critical fields were calculated with no adjustable parameters and compared with the experimental data as well as with the first-principles calculations. The observed agreement between fit and data shows that $\gamma$ -model provides adequate quantitative description of the two-gap superconductivity in MgB ${}_2$ and may serve as a relatively simple and versatile self-consistent description of the thermodynamic quantities in multi-gap superconductors.