Dirty Regime Research Articles

Anomalous temperature dependence of the superfluid density caused by a dirty-to-clean crossover in superconducting FeSe0.4Te0.6single crystals

We report microwave surface impedances of FeSe$_{0.4}$Te$_{0.6}$ single crystals measured at 12, 19, and 44 GHz. The penetration depth exhibits a power law behavior, $\delta \lambda_L=\lambda_L (T)-\lambda_L (0) \propto CT^n$ with an exponent $n\simeq 2$, which is considered to result from impurity scattering. This behavior is consistent with $s\pm$-wave pairing symmetry. The temperature dependence of the superfluid density largely deviates from the behavior expected in the BCS theory. We believe that this deviation is caused by the crossover from the dirty regime near $T_c$ to the clean regime at low temperatures, which is supported by the rapid increase of the quasiparticle scattering time obtained from the microwave conductivity. We also believe that the previously published data of the superfluid density can be interpreted in this scenario.

Transport and superconducting properties of Fe-based superconductors: a comparison betweenSmFeAsO1−xFx andFe1+yTe1−xSex

In this paper we carry out a direct comparison between transport and superconductingproperties—namely resistivity, magnetoresistivity, Hall effect, Seebeck effect,thermal conductivity, upper critical field—of two different families of Fe-basedsuperconductors, which can be viewed in many respects as end members:SmFeAsO1 − xFx with the largestTc and the largestanisotropy and Fe1 + yTe1 − xSex, with the largest Hc2, the lowest Tc and the lowest anisotropy. In the case of theSmFeAsO1 − xFx series, we find that a single-band description allows us to extract an approximate estimation ofband parameters such as carrier density and mobility from experimental data, although thebehaviour of the Seebeck effect as a function of doping demonstrates that a multibanddescription would be more appropriate. On the contrary, experimental data for theFe1 + y(Te1 − x, Sex) series exhibit a strongly compensated behaviour, which can be described only within amultiband model.In the Fe1 + y(Te1 − x, Sex) series, the role of the excess Fe, tuned by Se stoichiometry, is found to be twofold: on one handit dopes electrons in the system and on the other hand it introduces localized magneticmoments, responsible for Kondo like scattering and likely pairbreaking of Cooper pairs. Hence,Fe excess also plays a crucial role in determining superconducting properties such as theTc and the uppercritical field Hc2. The huge Hc2 values of the Fe1 + yTe1 − xSex samples are described by a dirty limit law, opposed to the clean limit behaviour of theSmFeAsO1 − xFx samples. Hence, magnetic scattering by excess Fe seems to drive the system inthe dirty regime, but its detrimental pairbreaking role seems not to be as severeas predicted by theory. This issue has yet to be clarified, addressing the morefundamental issue of the interplay between magnetism and superconductivity.

Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets

In ferromagnets, the spontaneous magnetization bears the Hall effect through the relativistic spin-orbit interaction. Similar effects also occur in thermoelectric and thermal transport phenomena. Their mechanism, if it is of the intrinsic or extrinsic origin, has been controversial for many decades. We present a unified theory of these Hall transport phenomena in ferromagnetic metals with dilute impurities at the zero temperature, in terms of a fully quantum-mechanical transport theory for multiband systems with the self-consistent $T$-matrix approximation. This theory becomes exact with a single impurity and is appropriate for treating the dilute limit of the impurity concentration ${n}_{\mathrm{imp}}$. With the Fermi energy ${E}_{F}$ and the spin-orbit interaction energy ${E}_{\mathrm{SO}}$ being fixed $({E}_{F}g{E}_{\mathrm{SO}})$, three regimes and the associated two crossovers are found in the anomalous Hall conductivity ${\ensuremath{\sigma}}_{xy}$ as a function of ${n}_{\mathrm{imp}}$ that controls the longitudinal conductivity ${\ensuremath{\sigma}}_{xx}$. (i) In the superclean case with the relaxation rate $\ensuremath{\hbar}∕\ensuremath{\tau}\ensuremath{\lesssim}{u}_{\mathrm{imp}}{E}_{\mathrm{SO}}D$, the skew scattering arising from the vertex correction yields a dominant contribution that is inversely proportional to ${n}_{\mathrm{imp}}$, where ${u}_{\mathrm{imp}}$ is the impurity potential strength and $D$ is the density of states. With increasing $\ensuremath{\hbar}∕\ensuremath{\tau}$, this extrinsic skew-scattering contribution rapidly decays. (ii) In the moderately dirty regime ${u}_{\mathrm{imp}}{E}_{\mathrm{SO}}D\ensuremath{\lesssim}\ensuremath{\hbar}∕\ensuremath{\tau}\ensuremath{\lesssim}{E}_{F}$, ${\ensuremath{\sigma}}_{xy}$ becomes insensitive to the scattering strength because of the intrinsic dissipationless topological Berry-phase contribution. It is resonantly enhanced to the order of the quantization unit of conductance when an accidental degeneracy of band dispersions around the Fermi level is lifted by the spin-orbit interaction. Further increasing $\ensuremath{\hbar}∕\ensuremath{\tau}$, another crossover occurs to (iii) the scaling regime of ${\ensuremath{\sigma}}_{xy}\ensuremath{\propto}{\ensuremath{\sigma}}_{xx}^{\ensuremath{\varphi}}$ with $\ensuremath{\varphi}\ensuremath{\sim}1.6$, which has recently been verified by experiments on a wide class of ferromagnets. Similar behaviors also appear in the temperature-linear coefficient of the thermal Hall conductivity ${\ensuremath{\kappa}}_{xy}$. The thermoelectric Hall conductivity ${\ensuremath{\alpha}}_{xy}$ strongly diverges in the clean limit when the Fermi level crosses edges of the avoided crossing, which may be observed by careful experiments. With increasing $\ensuremath{\hbar}∕\ensuremath{\tau}$, there occurs an interference between positive and negative contributions to ${\ensuremath{\alpha}}_{xy}$, which often leads to a sign change and obscures similar crossovers in the anomalous Nernst effect.

Clean and dirty superconductivity in pure, Al-doped, and neutron irradiatedMgB2: A far-infrared study

The effects of Al substitution and neutron irradiation on the conduction regime (clean or dirty) of the $\pi$- and $\sigma$-band of MgB$_{2}$ have been investigated by means of far-infrared spectroscopy. The intensity reflected by well characterized polycrystalline samples was measured up to 100 cm$^{- 1}$ in both normal and superconducting state. The analysis of the superconducting to normal reflectivity ratios shows that only the effect of the opening of the small gap in the dirty $\pi$-band can be clearly observed in pure MgB$_{2}$, consistently with previous results. In Al-doped samples the dirty character of the $\pi$-band is increased, while no definitive conclusion on the conduction regime of the $\sigma $-band can be drawn. On the contrary, results obtained for the irradiated sample show that the irradiation-induced disorder drives the $\sigma$-band in the dirty regime, making the large gap in $\sigma$-band observable for the first time in far-infrared measurements.

Critical field of Al-dopedMgB2samples: Correlation with the suppression of theσ-band gap

In this Letter, the study of the effect of Al substitution on the upper critical field, Bc2, in AlxMg1-xB2 samples is presented. We find a straightforward correlation between Bc2 and the sigma-band gap, Delta_sigma, evaluated by point-contact measurements. Up to x=0.2 Bc2 can be well described within a clean limit model and its decrease with x is directly related to the suppression of Delta_sigma. For larger doping we observed the crossover to the dirty regime driven mostly by the strong decrease of Delta_sigma rather than by the increase of the sigma-band scattering rate