Temperature-dependent London penetration depth, $lambda(T)$, of a high quality optimally-doped $text{YBa}_{2}text{Cu}_{3}text{O}_{7-delta}$ single crystal was measured using tunnel-diode-resonator technique. Controlled artificial disorder was induced
by low-temperature (20~K) irradiation by 2.5 MeV electrons at two large doses of $3.8times10^{19}$and $5.3times10^{19}$ electrons per $textrm{cm}^{2}$. The irradiation caused significant suppression of the superconductors critical temperature, $T_{c}$, from 94.6 K to 90.0 K, and to 78.7 K, respectively. The low-temperature behavior of $lambdaleft(Tright)$ evolves from a $T-$ linear in pristine state to a $T^{2}-$ behavior after irradiation, expected for a line-nodal $d-$wave superconductor. However, the original theory that explained such behavior assumed a unitary limit of the scattering potential, whereas usually in normal metals and semiconductors, Born scattering is sufficient to describe the experiment. To estimate the scattering potential strength, we calculated the superfluid density, $rho_{s}=lambda^{2}left(0right)/lambda^{2}left(Tright)$, varying the amount and strength of non-magnetic scattering using a self-consistent $t-$matrix theory. Comparing experimental and theoretical coefficients $A$ and $B$ of the low-temperature power series, $rho_{s}approx1-At-Bt^{2}$, we determine the amplitude of the scattering phase shift to be around 65$^{o}$. Knowing this value is important for further theoretical analysis of the microscopic mechanisms of superconductivity in $text{YBa}_{2}text{Cu}_{3}text{O}_{7-delta}$ high$-T_{c}$ superconductor.
Radio-frequency (14.6 MHz) AC magnetic susceptibility, $chi^{prime}_{AC}$, of dytio was measured using a self-oscillating tunnel-diode resonator. Measurements were made with the excitation AC field parallel to the superimposed DC magnetic field up 5
T in a wide temperature range from 50 mK to 100 K. At 14.6 MHz a known broad peak of $chi^{prime}_{AC}(T)$ from kHz - range audio-frequency measurements around 15~K for both [111] and [110] directions shifts to 45~K, continuing the Arrhenius activated behavior with the same activation energy barrier of $E_a approx 230$~K. Magnetic field dependence of $chi^{prime}_{AC}$ along [111] reproduces previously reported low-temperature two-in-two-out to three-in-one-out spin configuration transition at about 1~T, and an intermediate phase between 1 and 1.5~T. The boundaries of the intermediate phase show reasonable overlap with the literature data and connect at a critical endpoint of the first-order transition line, suggesting that these low-temperature features are frequency independent. An unusual upturn of magnetic susceptibility at $T to 0$ was observed in magnetic fields between 1.5~T and 2~T for both magnetic field directions, before fully polarized configuration sets in above 2~T.
Low temperature ($sim$ 20~K) electron irradiation with 2.5 MeV relativistic electrons was used to study the effect of controlled non-magnetic disorder on the normal and superconducting properties of the type-II Dirac semimetal PdTe$_2$. We report mea
surements of longitudinal and Hall resistivity, thermal conductivity and London penetration depth using tunnel-diode resonator technique for various irradiation doses. The normal state electrical resistivity follows Matthiessen rule with an increase of the residual resistivity at a rate of $sim$0.77$ mu Omega$cm/$(textrm{C}/textrm{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 non-zero rate that is about sixteen times slower than described by the Abrikosov-Gorkov 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 multi-band 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 states 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 intra-band scattering for the singlet state significantly larger than one. Due to the generality of our theoretical framework, we think that it will also be useful for irradiation studies in other spin-orbit-coupled multi-orbital systems.
Controlled point-like disorder introduced by 2.5 MeV electron irradiation was used to probe the superconducting state of single crystals of CaKx superconductor at $x = 0$ and 0.05 doping levels. Both compositions show an increase of the residual resi
stivity and a decrease of the superconducting transition temperature, $T_c$ at the rate of $dT_c/drho(T_c) approx$ 0.19 K(textmu$Omega$cm)$^{-1}$ for $x=0$ and 0.38 K(textmu$Omega$cm)$^{-1}$ for $x=:$0.05, respectively. In Ni - doped, $x = 0.05$, compound the coexisting spin-vortex crystal (SVC) magnetic phase is suppressed at the rate of $dT_N/drho(T_N)approx$ 0.16 K(textmu$Omega$cm)$^{-1}$. Low - temperature variation of London penetration depth is well approximated by the power law, $Delta lambda (T) = AT^n$ with $napprox,$2.5 for $x=0$ and $napprox,$1.9 for $x=0.05$ in the pristine state. Electron irradiation leads to the exponent $n$ increase above 2 in $x=0.05$ suggesting superconducting gap with significant anisotropy that is smeared by the disorder scattering. Detailed analysis of $lambda (T)$ and (T_{c}) evolution with disorder is consistent with two effective nodeless superconducting energy gaps due to robust s$_{pm}$ pairing. Overall the behavior of CaKx at $x = 0$ is similar to a slightly overdoped BaK at $y approx$ 0.5 and at $x= 0.05$ to an underdoped composition at $y approx$ 0.2.
The interplay between superconductivity and charge density waves (CDW) in $H$-NbSe2 is not fully understood despite decades of study. Artificially introduced disorder can tip the delicate balance between two competing forms of long-range order, and r
eveal the underlying interactions that give rise to them. Here we introduce disorders by electron irradiation and measure in-plane resistivity, Hall resistivity, X-ray scattering, and London penetration depth. With increasing disorder, $T_{textrm{c}}$ varies nonmonotonically, whereas $T_{textrm{CDW}}$ monotonically decreases and becomes unresolvable above a critical irradiation dose where $T_{textrm{c}}$ drops sharply. Our results imply that CDW order initially competes with superconductivity, but eventually assists it. We argue that at the transition where the long-range CDW order disappears, the cooperation with superconductivity is dramatically suppressed. X-ray scattering and Hall resistivity measurements reveal that the short-range CDW survives above the transition. Superconductivity persists to much higher dose levels, consistent with fully gapped superconductivity and moderate interband pairing.
Measurements of the London penetration depth and tunneling conductance in single crystals of the recently discovered stoicheometric, iron - based superconductor, CaKFe$_4$As$_4$ (CaK1144) show nodeless, two effective gap superconductivity with a larg
er gap of about 6-9 meV and a smaller gap of about 1-4 meV. Having a critical temperature, $T_{c,onset}approx$35.8 K, this material behaves similar to slightly overdoped Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (e.g. $x=$0.54, $T_c approx$ 34 K)---a known multigap $s_{pm}$ superconductor. We conclude that the superconducting behavior of stoichiometric CaK1144 demonstrates that two-gap $s_{pm}$ superconductivity is an essential property of high temperature superconductivity in iron - based superconductors, independent of the degree of substitutional disorder.
