The longitudinal resistivity (rho_{xx}) and transverse resistivity (rho_{xy}) of MgB2 thin films in the mixed state were studied in detail. We found that the temperature dependencies of rho_{xx} and ρ_{xy} at a fixed magnetic field (H) satisfy the scaling law of $ρ_{xy}=Aρ_{xx}^β$, where the exponent beta varies around 2.0 for different fields. In the low field region (below 1T), beta maintains a constant value of 2.0 due to the weak pinning strength of the vortices, mainly from the superfluid of the pi band. When H>1T, beta drops abruptly to its lowest value at about 2T because of the proliferation of quasiparticles from the pi-band and, hence, the motion of the vortices from the superfluid of the sigma-band dominates the dissipation. As the field is increased further, the vortex pinning strength is weakened and beta increases monotonically towards 2.0 at a high field. All the results presented here are in good agreement with the expectation of the vortex physics of a multi-band superconductor.
We report resistivity and the Hall effect measurements in the normal and superconducting states of MgB2 single crystal. The resistivity has been found to be anisotropic with slightly temperature dependent resistivity ratio of about 3.5. The Hall constant, with a magnetic field parallel to the Mg and B sheets is negative in contrast to the hole-like Hall response with a field directed along the c-axis indicating presence of both types of charge carriers and, thus, multi-band electronic structure of MgB2. The Hall effect in the mixed state shows no sign change anomaly reproducing the Hall effect…
The normal state resistivity of high temperature superconductors can be probed in the region below Tc by suppressing the superconducting state in high magnetic fields. Here we present the normal state properties of YBa2Cu3Ox thin films in the underdoped regime and the normal state resistance of La2-xSrxCuO4 thin films under epitaxial strain, measured below Tc by applying pulsed fields up to 60 T. A universal rho(T) behaviour is reported. We interpret these data in terms of the recently proposed 1D quantum transport model with the 1D paths corresponding to the charge stripes.
The mixed-state Hall resistivity and the longitudinal resistivity in superconducting MgB2 thin films have been investigated as a function of the magnetic field over a wide range of current densities from 100 to 10000 A/cm^2. We observe a universal Hall scaling behavior with a constant exponent of 2.0, which is independent of the magnetic field, the temperature, and the current density. This result can be interpreted well within the context of recent theories.
Phase slips creation in the thin film in perpendicular magnetic filed with edge superconductivity is studied. These centers are due to thermal activation of the order parameter below superconducting temperature transition leading to the suppression of the superconductivity. The corresponding resistance is calculated. The Alsamazov- Larkin correction to the conductivity above the critical magnetic field destroying the surface superconductivity is studied. Such structures could be applied as a new system for the study of the phase slip phenomenon in one- dimensional superconducting wires.
NdFeAs(O,F) thin films having different fluorine contents were grown on 5 deg. or 10 deg. vicinal cut MgO and CaF2 single crystalline substrates by molecular beam epitaxy. Structural characterisations by reflection high-energy electron diffraction and x-ray diffraction confirmed the epitaxial growth of NdFeAs(O,F). The resistivities of the ab-plane and along the c-axis were derived from the resistivity measurements in the longitudinal and transversal directions. The c-axis resistivity was always higher than the ab-plane resistivity, resulting from the anisotropic electronic structure. The resi…
An important predicted, but so far uncharacterized, property of the new superconductor MgB2 is electronic anisotropy arising from its layered crystal structure. Here we report on three c-axis oriented thin films, showing that the upper critical field anisotropy ratio Hc2par/Hc2perp is 1.8 to 2.0, the ratio increasing with higher resistivity. Measurements of the magnetic field-temperature phase diagram show that flux pinning disappears at H* ~ 0.8Hc2perp(T) in untextured samples. Hc2par(0) is strongly enhanced by alloying to 39 T for the highest resistivity film, more than twice that seen in bu…
Electrical transport measurements are used to study the Rh-doped NaFeAs superconductor series with a focus on the tetragonal phase. The resistivity curvature has an anomalous temperature dependence evidencing in the phase diagram two crossover regions of changes in the scattering rate, the effective mass as well as of the charge carrier density. The first crossover region is directly connected to the structural transition and resembles the onset of resistivity anisotropy. The second crossover region can as well be deduced from the temperature dependent Hall coefficient. A comparison to literat…
The resistivity tensor correlations $ρ_{xy}$($B$)$\sim$ $[ρ_{xx}(B)]^β$ for the mixed state magnetic field dependencies of the resistivity tensor of electron-doped Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$/SrTiO$_3$ single crystal films near the antiferromagnetic (AF) - superconducting (SC) phase transition and with varying degree of disorder ($δ$) were studied. The decrease of $β$ from 1.2$\pm$0.2 at $x$ = 0.14 to 0.6$\pm$0.1 at $x$ = 0.15 points out on the evidence of the change from the anisotropic $s$ - wave to the $d$ - wave pairing symmetry in the external magnetic field at the transition from underdo…
The temperature dependence of the resistivity of epitaxial Ba(Fe_(1-x)Co_x)2As2 thin films (with nominal doping x = 0.08, 0.10 and 0.15) has been analyzed and compared with analogous measurements on single crystals taken from literature. The rho(T) of thin films looks different from that of single crystals, even when the cobalt content is the same. All rho(T) curves can be fitted by considering an effective two-band model (with holes and electrons bands) in which the electrons are more strongly coupled with the bosons (spin fluctuations) than holes, while the effect of impurities is mainly con…
Upper critical fields of four MgB2 thin films were measured up to 28 Tesla at Grenoble High Magnetic Field Laboratory. The films were grown by Pulsed Laser Deposition and showed critical temperatures ranging between 29.5 and 38.8 K and resistivities at 40 K varying from 5 to 50 mWcm. The critical fields in the perpendicular direction turned out to be in the 13-24 T range while they were estimated to be in 42-57 T the range in ab-planes. In contrast to the prediction of the BCS theory, we did not observe any saturation at low temperatures: a linear temperature dependence is exhibited even at lo…
Investigations of the resistivity and the Hall effect as a function of electric field and temperature in the normal state and upper part of the superconducting transition of an optimally doped, very thin film of YBa$_{2}$Cu$_{3}$O$_{7-δ}$ are reported. Using a fast pulsed-current technique allowed to reduce the self-heating of the sample and to reach electric fields up to 1 kV/cm. An intrinsic non-Ohmic behavior of the Hall conductivity above the critical temperature that appears to originate from two different, partially counteracting effects is revealed. The major contribution stems from the…
We report measurements of the complex resistivity in $YBCO$ and $MgB_2$ thin films over a continuous frequency spectrum in the microwave range, making use of a Corbino disk geometry. The paper mainly focuses on the extraction of the resistivity from raw data, displaying data analisys procedure and its limits of validity. We obtain and show resistivity curves as a function of frequency and temperature denoting a frequency dependent widening of the superconductive transition.
The normal-state Hall coefficient R_H and the in-plane resistivity ρ_{ab} are measured in La-doped Bi_{2}Sr_{2}CuO_{y} (T_c \simeq 13 K) single crystals and La_{2-x}Sr_{x}CuO_{4} thin films by suppressing superconductivity with 61-T pulsed magnetic fields. In contrast to data above T_c, the R_H below \sim 10 K shows little temperature dependence in all the samples measured, irrespective of whether ρ_{ab} exhibits insulating or metallic behavior. Thus, whatever physical mechanism gives rise to insulating behavior in the low-temperature normal state, it leaves the Hall conductivity relatively un…
The mixed-state Hall resistivity and the longitudinal resistivity in HgBa_{2}CaCu_{2}O_{6}, HgBa_{2}Ca_{2}Cu_{3}O_{8}, and Tl_{2}Ba_{2}CaCu_{2}O_{8} thin films have been investigated as functions of the magnetic field up to 18 T. We observe the universal scaling behavior between ρ_{xy} and ρ_{xx} in the regions of the clean and the moderately clean limit. The scaling exponent βis 1.9 in the clean limit at high field and low temperature whereas βis 1.0 in the moderately clean limit at low field and high temperature, consistent with a theory based on the midgap states in the vortex cores. This f…
LiFeAs is unique among the broad family of FeAs-based superconductors, because it is superconducting with a rather large $T_c\simeq 18$ K under ambient conditions although it is a stoichiometric compound. We studied the electrical transport on a high-quality single crystal. The resistivity shows quadratic temperature dependence at low temperature giving evidence for strong electron-electron scattering and a tendency towards saturation around room temperature. The Hall constant is negative and changes with temperature, what most probably arises from a van Hove singularity close to the Fermi ene…
The electrical resistivity (Rxx) and Hall resistivity (Rxy) of LaFeAsO1-xFx have been measured over a wide fluorine doping range 0 =< x =< 0.14 using 60 T pulsed magnets. While the superconducting phase diagram (Tc, x) displays the classic dome-shaped structure, we find that the resistive upper critical field (Hc2) increases monotonically with decreasing fluorine concentration, with the largest Hc2 >= 75 T for x = 0.05. This is reminiscent of the composition dependence in high-Tc cuprates and might correlate with opening of a pseudo-gap in the underdoped region. Further, the temperature depend…
We present measurements of the field induced changes in the 47 GHz complex resistivity, $Δ\tilde ρ(H,T)$, in Tl$_{2}$Ba$_{2}$CaCu$_{2}$O$_{8+x}$ (TBCCO) thin films with $T_{c}\simeq$ 105 K, prepared on CeO$_{2}$ buffered sapphire substrates. At low fields ($μ_{0}H<$10 mT) a very small irreversible feature is present, suggesting a little role of intergranular phenomena. Above that level $Δ\tilde ρ(H,T)$ exhibits a superlinear dependence with the field, as opposed to the expected (at high frequencies) quasilinear behaviour. We observe a crossover between predominantly imaginary to predominantly …
The longitudinal electrical resistivity and the transverse Hall resistivity of CeFeAsO are simultaneously measured up to a magnetic field of 45T using the facilities of pulsed magnetic field at Los Alamos. Distinct behaviour is observed in both the magnetoresistance Rxx(μ0H) and the Hall resistance Rxy(μ0H) while crossing the structural phase transition at Ts \approx 150K. At temperatures above Ts, little magnetoresistance is observed and the Hall resistivity follows linear field dependence. Upon cooling down the system below Ts, large magnetoresistance develops and the Hall resistivity deviat…
Longitudinal and Hall voltages are measured in a clean twinned YBCO single crystal in the liquid and solid vortex phases. For magnetic fields tilted away from the c-axis more than about 2 deg, a scaling law |rho_xy|=A (rho_xx)^beta with beta approx.=1.4 is observed, which is unaffected by the vortex-lattice melting transition. The vortex-solid Hall conductivity is non-linear and diverges to negative values at low temperature. When the magnetic field is aligned to the c-axis, the twin-boundary correlated disorder modifies the scaling law, and beta approx.=2. The scaling law is unaffected by the…
A pronounced step-like (kink) behavior in the temperature dependence of resistivity $ρ(T)$ is observed in the optimally-doped $Sm_{1.85}Ce_{0.15}CuO_4$ thin films around $T_{sf}=87K$ and attributed to manifestation of strong spin fluctuations induced by $Sm^{3+}$ moments with the energy $\hbar ω_{sf}=k_BT_{sf}\simeq 7meV$. In addition to fluctuation induced contribution $ρ_{sf}(T)$ due to thermal broadening effects (of the width $ω_{sf}$), the experimental data are found to be well fitted accounting for residual (zero-temperature) $ρ_{res}$, electron-phonon $ρ_{e-ph}(T)=AT$ and electron-electr…
Critical fields of four MgB2 thin films with a normal state resistivity ranging from 5 to 50 mWcm and Tc from 29.5 to 38.8 K were measured up to 28 T. Hc2(T) curves present a linear behavior towards low temperatures. Very high critical field values have been found, up to 24 T along the c-axis and 57 T in the basal plane not depending on the normal state resistivity values. In this paper, critical fields will be analyzed taking into account the multiband nature of MgB2; we will show that resistivity and upper critical fields can be ascribed to different scattering mechanisms.
We report resistivity and Hall effect measurements in electron-doped Pr$_{2-x}$Ce$_{x}$CuO$_{4-δ}$ films in magnetic field up to 58 T. In contrast to hole-doped cuprates, we find a surprising non-linear magnetic field dependence of Hall resistivity at high field in the optimally doped and overdoped films. We also observe a crossover from quadratic to linear field dependence of the positive magnetoresistance in the overdoped films. A spin density wave induced Fermi surface reconstruction model can be used to qualitatively explain both the Hall effect and magnetoresistance.
The flux flow regime of high-T$_{\rm c}$ samples of different normal state resistivities is studied in the temperature range where the sign of the Hall effect is reversed. The scaling of the vortex viscosity with normal state resistivity is consistent with the Bardeen-Stephen theory. Estimates of the influence of possible mechanisms suggested for the sign reversal of the Hall effect are also given.
Transport measurements along the node and anti-node directions in the a-b plane of optimally doped and epitaxial thin films of YBCO are reported. Low bias magnetoresistance measurements near and below T_c show that the flux flow resistivity along the node and anti-node directions versus magnetic field are indistinguishable. This result suggests that within the experimental error of our measurements, no correspondence is found between the flux pinning properties in YBCO and the d-wave nature of the order parameter.
The effect of electron doping by trivalent charge state rare-earth ion (RE = La, Ce, Pr, and Nd) substitutions on the superconductivity in BaFe2As2 was examined using epitaxial films. Each of the RE substitutions suppressed the resistivity anomaly associated with the magnetic/structural phase transitions, leading to the resistivity drops and superconductivity transitions. Bulk superconductivity was observed at the maximum onset critical temperature (Tconset) of 22.4 K for La-doping and 13.4 K for Ce-doping, while only broad resistivity drops were observed at 6.2 K for Pr-doping and 5.8 K for N…
In this paper, we analyze the upper critical field of four MgB2 thin films, with different resistivity (between 5 to 50 mWcm) and critical temperature (between 29.5 to 38.8 K), measured up to 28 Tesla. In the perpendicular direction the critical fields vary from 13 to 24 T and we can estimate 42-57 T range in other direction. We observe linear temperature dependence even at low temperatures without saturation, in contrast to BCS theory. Considering the multiband nature of the superconductivity in MgB2, we conclude that two different scattering mechanisms influence separately resistivity and cr…
The effect of damage induced by 2-MeV alpha particles, followed by annealing, on the critical temperature (Tc), resistivity, and upper critical field (Hc2), of three MgB2 films made by different deposition processes has been studied. Damage creates a linear decrease in Tc with residual resistivity, and produces maxima in both Hc2(0)-perpendicular and Hc2(0)-parallel. Below Tcs of about 25 K, Hc2(0) depends roughly linearly on Tc, while the anisotropy of Hc2(0) decreases as Tc decreases. Annealing the films reproduces the Tc vs. residual resistivity dependence but not the Hc2(0) values induced …
We make comments on the paper presented by Kim \textit{et al.} [Phys. Rev. B \textbf{61}, 11317 (2000)]. The authors analyzed activation energies of HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ thin films with a scaling relation, and defined four vortex regions for thin films. We find that the definitions of four vortex regions and the scaling relation are questionable when studying their definition of the resistivity range for thermally activated flux flow. Using the empirical activation energy form suggested by Zhang \textit{et al.} [Phys. Rev. B \textbf{71}, 052502 (2005)] for lower resistivity data, we f…
Resistivity anomalies and intrinsic spin-orbit coupling in superconducting thin film solid solutions of Nb$_{1-x}$U$_x$ for $0.15 < x < 0.40$
School of Physics, University of Bristol（布里斯托大学物理学院）；School of Physics and Astronomy, Queen’s Buildings, 5 The Parade, Newport Road, Cardiff（卡迪夫大学物理与天文学院）
We report resistivity, Hall coefficient, current-voltage characteristics, and magneto-optical imaging measurements of epitaxial Co-doped BaFe_{2}As_{2} thin films deposited on MgO(001) substrate. The Hall resistivity of the films has a substantial contribution arising from anomalous Hall effect of ferromagnetic components. The critical current density (J_{c}) of the films is ~2 MA/cm^{2} at low temperatures. Differential magneto-optical images of the remanent state give similar J_{c} values and also exhibit presence of extended defects in the film.
We report the crystal structure, superconductivity and normal state properties of two iron-based materials, Li0.15(C3H10N2)0.32FeSe(P-4) and Lix(C3H10N2)0.32FeSe(P4/nmm, 0.25<x<0.4) with superconducting transition temperature from 40~46K. The determined crystal structures revealed a coupling between Li concentration and the oritation of 1,2-Diaminopropane molecules within the hyper expanded FeSe layers. Further fitting on resistivity in terms of the Lawence-Doniach model suggests the two superconductors belong to the quasi-two dimonsional system. With increasing temperature, a differences in c…
We have investigated a series of superconducting bridges based on homogeneous amorphous WSi and MoSi films, with bridge widths w ranging from 2 um to 1000 um and film thicknesses d ~ 4-6 nm and 100 nm. Upon decreasing the bridge widths below the respective Pearl lengths, we observe in all cases distinct changes in the characteristics of the resistive transitions to superconductivity. For each of the films, the resistivity curves R(B,T) separate at a well-defined and field-dependent temperature T*(B) with decreasing the temperature, resulting in a dramatic suppression of the resistivity and a s…
The doping and temperature dependence of the Hall coefficient, RH, and ab-plane resistivity in the normal state down to 350mK is reported for oriented films of the electron-doped high-Tc superconductor Pr2-xCexCuO4+d. The doping dependence of b (r=r0+AT^b) and R_sub_H (at 350 mK) suggest a quantum phase transition at a critical doping near x=0.165.
Near the superconducting phase transition, fluctuations significantly modify the electronic transport properties. Here we study the fluctuation corrections to the Hall conductivity in disordered films, extending previous derivations to a broader range of temperatures and magnetic fields, including the vicinity of the magnetic field induced quantum critical point. In the process, we found a new contribution to the Hall conductivity that was not considered before. Recently, our theory has been used to fit measurements of the Hall resistance in amorphous TaN films.
The high resistivity of many bulk and film samples of MgB2 is most readily explained by the suggestion that only a fraction of the cross-sectional area of the samples is effectively carrying current. Hence the supercurrent (Jc) in such samples will be limited by the same area factor, arising for example from porosity or from insulating oxides present at the grain boundaries. We suggest that a correlation should exist, Jc ~ 1/{Rho(300K) - Rho(50K)}, where Rho(300K) - Rho(50K) is the change in the apparent resistivity from 300 K to 50 K. We report measurements of Rho(T) and Jc for a number of fi…
The behaviour of the Hall ratio $R_{H}(T)$ as a function of temperature is one of the most intriguing normal state properties of cuprate superconductors. One feature of all the data is a maximum of $R_{H}(T)$ in the normal state that broadens and shifts to temperatures well above $T_c$ with decreasing doping. We show that a model of preformed pairs-bipolarons provides a selfconsistent quantitative description of $R_{H}(T)$ together with in-plane resistivity and uniform magnetic susceptibility for a wide range of doping.
We report measurements of the microwave complex resistivity at 48 GHz in SmBaCuO thin films. Measurements are performed with a moderate magnetic field, $μ_{0}H<$ 0.8T, applied along the c-axis. We find that the complex resistivity presents clear sublinear field dependences, and that the imaginary part is remarkably sensitive to the moderate magnetic field. Interpretation considering an unusually strong pinning leads to very anomalous field dependences of the single-vortex viscosity and of the pinning constant. By contrast, allowing for a significant effect of the magnetic field on the depletio…
The resistivity and the Hall effect in the copper-oxide high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) are remarkably anisotropic. Using a thin film of YBCO grown on an off-axis cut SrTiO$_3$ substrate allows one to investigate these anisotropic transport properties in a planar and well-defined sample geometry employing a homogeneous current density. In the normal state, the Hall voltage probed parallel to the copper-oxide layers is positive and strongly temperature dependent, whereas the out-of-plane Hall voltage is negative and almost temperature independent. The results c…
Measurements of the nonlinear flux-flow resistivity $ρ$ and the critical vortex velocity $\rm v^*_ϕ$ at high voltage bias close to the instability regime predicted by Larkin and Ovchinnikov \cite{LO} are reported along the node and antinode directions of the d-wave order parameter in the \textit{a-b} plane of epitaxial $YBa_2Cu_3O_{7-δ}$ films. In this pinning-free regime, $ρ$ and $\rm v^*_ϕ$ are found to be anisotropic with values in the node direction larger on average by 10% than in the antinode direction. The anisotropy of $ρ$ is almost independent of temperature and field. We attribute th…
We followed the evolution of the normal and superconducting properties of Al thin films after each session of various successive oxygen irradiations at ambient temperature. Such irradiated films, similar to the granular ones, exhibit enhanced superconductivity, Kondo behavior and negative-curvature resistivity. Two distinct roles of oxygen are identified: as a damage-causing projectile and as an implanted oxidizing agent. The former gives rise to the processes involved in the conventional recovery stages. The latter, considered within the context of the Cabrera-Mott model, gives rise to a mult…
We present the results of a systematic study of thin-films of amorphous indium-oxide near the superconductor-insulator transition. We show that the film's resistivity follows a simple, well-defined, power-law dependence on the perpendicular magnetic field. This dependence holds well into the insulating state. Our results indicate that vortices play a central role in the transport of our films in the superconducting as well as insulating phases.
Superconducting thin films of magnesium diboride (MgB$_2$) were prepared on MgO (001) substrate by a molecular beam epitaxy (MBE) method with the co-evaporation conditions of low deposition rate in ultra-high vacuum. The structural and physical properties of the films were studied by RHEED, XRD, XPS, resistivity and magnetization measurements.All films demonstrated superconductivity without use of any post-annealing process.The highest {\it T}$_{c,onset}$ determined by resistivity measurement was about 33K in the present samples.Anisotropic superconducting properties were evaluated by the resi…
Thin films of the high-temperature superconductor HgBa$_2$CaCu$_2$O$_{6+δ}$ have been prepared on SrTiO$_3$ substrates by pulsed-laser deposition of precursor films and subsequent annealing in mercury-vapor atmosphere. The microstructural properties of such films can vary considerably and have been analyzed by x-ray diffraction and atomic force microscopy. Whereas the resistivity is significantly enhanced in samples with coarse-grained structure, the Hall effect shows little variation. This disparity is discussed based on models for transport properties in granular materials. We find that, des…
We report the temperature dependence of resistivity (rho) and Hall coefficient (R_H) in the normal state of homogeneously disordered epitaxial NbN thin films with kFl~3.27-10.12. The superconducting transition temperature (Tc) of these films varies from 8.13K to 16.8K. While our least disordered film displays usual metallic behavior, for all the films with kFl<8.13, both and are negative up to 300K. We observe that R_H(T) varies linearly with rho(T) for all the films. Measurements performed on a 2nm thick Be film shows similar behavior >. This behavior is inconsistent with existing theories of…
We study the superconductor-insulator transition in nanohole ultrathin films in a transverse magnetic field by numerical simulation of a Josephson-junction array model. Geometrical disorder due to the random location of nanoholes in the film corresponds to random flux in the array model. Monte Carlo simulation in the path-integral representation is used to determine the critical behavior and the universal resistivity at the transition as a function of disorder and average number of flux quanta per cell, $f_o$. The resistivity increases with disorder for noninteger $ f_o$ while it decreases for…
The negative Hall constant R_H measured all over the phase diagram of Ba(Fe(1-x)Cox)2As2 allows us to show that electron carriers always dominate the transport properties. The evolution of R_H with x at low doping (x<2%) indicates that important band structure changes happen for x<2% prior to the emergence of superconductivity. For higher x, an change of the electron concentration with T is required to explain the low T variations of R_H, while the electron scattering rate displays the T^2 law expected for a Fermi liquid. The T=0 residual scattering is affected by Co disorder in the magnetic p…
In the organic superconducting κ-(BEDT-TTF) compounds, various transport phenomena exhibit striking non-Fermi liquid behaviors, which should be the important clues to understanding the electronic state of this system. Especially, the Hall coefficient ($R_H$) shows Curie-Weiss type temperature dependence, which is similar to that of high-Tc cuprates. In this paper, we study a Hubbard model on an anisotropic triangular lattice at half filling, which is an effective model of κ-(BEDT-TTF) compounds. Based on the fluctuation-exchange (FLEX) approximation, we calculate the resistivity ($ρ$) and $R_H…
Nb-doped SrTiO$_{3}$ epitaxial thin films have been prepared on (001) SrTiO$_{3}$ substrates using pulsed laser deposition. A high substrate temperature ($>1000^{\circ}{C}$) was found to be necessary to achieve 2-dimensional growth. Atomic force microscopy reveals atomically flat surfaces with 3.9 Å$ $ steps. The films show a metallic behavior, residual resistivity ratios between 10 and 100, and low residual resistivity of the order of 10$^{-4}$$Ω$cm. At 0.3 K, a sharp superconducting transition, reaching zero resistance, is observed.
