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Transport and Point Contact Measurements on Pr_{1−x}Ce_{x}Pt_{4}Ge_{12} Superconducting Polycrystals

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## Abstract

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_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}pellets. We report the effect of Ce substitution, for x = 0.07, on magnetic field phase diagram H-T. We demonstrate that the upper critical field is well described by the Ginzburg–Landau model and that the irreversibility field line has a scaling behaviour similar to cuprates. We also show that for magnetic fields lower than 0.4 T, the activation energy follows a power law of the type 𝐻

^{−1/2}, suggesting a collective pinning regime with a quasi-2D character for the Ce-doped compound with x = 0.07. Furthermore, by means of a point contact Andreev reflection spectroscopy setup, we formed metal/superconductor nano-junctions as small as tens of nanometers on the PrPt

_{4}Ge

_{12}parent compound (x = 0). Experimental results showed a wide variety of conductance features appearing in the dI/dV vs. V spectra, all explained in terms of a modified Blonder–Tinkham–Klapwijk model considering a superconducting order parameter with nodal directions as well as sign change in the momentum space for the sample with x = 0. The numerical simulations of the conductance spectra also demonstrate that s-wave pairing and anisotropic s-waves are unsuitable for reproducing experimental data obtained at low temperature on the un-doped compound. Interestingly, we show that the polycrystalline nature of the superconducting PrPt

_{4}Ge

_{12}sample can favour the formation of an inter-grain Josephson junction in series with the point contact junction in this kind of experiments.

## 1. Introduction

_{4}X

_{12}, where M is an electropositive metal (Sr, Ba, La, Pr, Th), T is a transition metal (Fe, Os, or Ru), and X usually represents a pnictogen (Sb, As, or P). The first Pr-based superconductor to be discovered was the heavy-fermion PrOs

_{4}Sb

_{12}, with a critical temperature T

_{c}= 1.85 K, showing intriguing properties such as a giant electronic specific heat coefficient [1]. Moreover, experiments of thermal transport [9] on single crystals evidenced the possible existence of a superconducting phase at high magnetic fields in which the energy gap has at least four point nodes, and a second phase at low magnetic fields in which the energy gap is characterized by only two point nodes. Recently, a new Pt-based family of skutterudite, with chemical formula MPt

_{4}Ge

_{12}, was synthetized, showing superconducting properties at relatively high temperatures. In particular, the compound with praseodymium (Pr) as metal shows a transition temperature T

_{c}= 7.9K, while for the compound with Lanthanum (M = La), T

_{c}= 8.3 K has been reported [10], as confirmed by electrical resistivity, magnetic susceptibility and specific heat measurements. Nuclear magnetic resonance experiments have given indications for conventional superconductivity in LaPt

_{4}Ge

_{12}[11].

_{4}Ge

_{12}compounds such as SrPt

_{4}Ge

_{12}(T

_{c}= 5.10 K) and BaPt

_{4}Ge

_{12}(T

_{c}= 5.35 K) [12]. The higher critical temperatures for Pr and La compounds with respect to Sr and Ba compounds have been explained as the existence of a larger density of states at the Fermi level, as resulting from

^{73}Ge nuclear quadrupole resonance experiments at zero field [13]. It has also been suggested that PrPt

_{4}Ge

_{12}and LaPt

_{4}Ge

_{12}can be characterized by two superconducting gaps. Indeed, according to heat capacity measurements as a function of temperature and magnetic field, the superconducting state cannot be explained by considering a single isotropic or anisotropic energy gap [14]. The presence of two distinct linear regions in the magnetic field dependence of the Sommerfeld coefficient of electronic heat capacity was interpreted as a possible indication for two-gap superconductivity in these compounds. The critical current density and pinning force of superconducting PrPt

_{4}Ge

_{12}was measured in magnetization experiments [15], revealing that dependence of both quantities with respect magnetic field can be explained using a double exponential model already developed to explain the properties of the two-band superconductor MgB

_{2}[16,17,18,19].

_{4}Ge

_{12}showed a time-reversal symmetry breaking below T

_{c}[20,21,22,23], in contrast to the results on LaPt

_{4}Ge

_{12}, for which the time-reversal symmetry breaking is absent and a conventional superconductivity with a fully gapped density of states is supposed [21]. The superconducting order parameter of LaPt

_{4}Ge

_{12}has also been studied using specific heat and thermal conductivity measurements [24], showing that the sharp transition in the specific heat and its zero-field temperature dependence are well described in a conventional BCS (Bardeen–Cooper–Schrieffer) scenario characterized by a single energy gap and s-wave symmetry [25]. On the other hand, de Haas–van Alphen measurements have been reported with state-of-the-art band-structure calculations showing that LaPt

_{4}Ge

_{12}and PrPt

_{4}Ge

_{12}have almost identical electronic structures, Fermi surfaces and effective masses [26]. So far, few investigations have been reported that probe the superconducting energy gap in the PrPt

_{4}Ge

_{12}compound, with results supporting both nodal and nodeless energy gaps. Recently, electrical resistivity, magnetic susceptibility, specific heat, and thermoelectric power experiments were performed on Pr

_{(1-x)}Ce

_{x}Pt

_{4}Ge

_{12}to investigate the influence of the magnetic state of the Ce ions on the superconducting properties of the compound [27]. Interestingly, the results indicate a crossover from a nodal to a nodeless superconducting energy gap and that PrPt

_{4}Ge

_{12}could be a two-band superconductor in which the electron scattering due to Ce substitution can suppress the superconductivity within one of the bands.

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}compound for x = 0.07. We measured the resistive transitions for the sample with x = 0.07 in external applied magnetic fields. We deduced the H-T phase diagram of the Ce-doped sample Pr

_{0.93}Ce

_{0.07}Pt

_{4}Ge

_{12}, that is the upper critical field H

_{c2}, as well as the irreversibility line. We also analysed the resistive transition data in the framework of the thermally assisted motion of vortices. We also performed direct measurements of the superconducting energy gap in the parent compound PrPt

_{4}Ge

_{12}(x = 0) by means of point contact spectroscopy experiments, which made it possible to realize metal/superconductor nano-junctions with dimensions of few nanometres. We measured the conductance spectra of the point contact junction at low temperature (4.2 K) and we demonstrated that the conductance feature can be reproduced in a theoretical model that takes into account the symmetry of the superconducting order parameter with nodal directions and change of sign in the momentum space. We also estimated the superconducting energy gap for the sample PrPt

_{4}Ge

_{12}in the range 0.55–0.95 meV.

## 2. Materials and Methods

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}pellets (with x = 0, 0.07, 0.1) were synthesized in argon atmosphere by arc melting, using Pr ingots, Ce rods, Pt sponge, and Ge pieces as preparation materials, weighed in stochiometric ratios. Arc melting and turning over were repeated five times to obtain high chemical homogeneity. The samples were then annealed in a sealed quartz tube in 200 Torr argon atmosphere at 800 °C for 14 days. X-Ray diffractometry (reported elsewhere [27]) confirmed the sample quality evidencing the expected cubic skutterudite crystal structure.

## 3. Results and Discussion

#### 3.1. Transport Properties

_{0.93}Ce

_{0.07}Pt

_{4}Ge

_{12}, the upper critical field H

_{c2}, and the irreversibility line, above which the critical current density becomes zero. Then, the resistive transitions in external applied magnetic fields are analysed in the framework of the thermally assisted motion of vortices.

#### 3.1.1. Magnetic Field Temperature Phase Diagram

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}samples having x = 0, 0.07 and 0.10. The data were normalized to the normal state resistance, R

_{N}, evaluated just before the onset of the superconducting transition. We measured R

_{N}= 4.3 mΩ for the undoped sample, R

_{N}= 34 mΩ for sample with x = 0.07 and R

_{N}= 63 mΩ for sample with x = 0.10. The superconducting critical temperature T

_{c}was estimated at 50% of the onset transition resistance, obtaining T

_{c}= 7.9 K for the undoped sample, T

_{c}= 4.7 K for samples with x = 0.07, and T

_{c}= 3.6 K for samples with x = 0.1. The evolution of the critical temperature T

_{c}as a function of the Ce doping x is summarized in Figure 1b. The effect on T

_{c}of the partial substitution of Pr by Nd has been also reported in samples with Nd content x

_{Nd}up to 0.1 [29]. The critical temperature is weakly dependent by Nd content, being reduced by only 10% at x

_{Nd}= 0.1. On the other hand, the effect of the Ce substitution is much more important; the T

_{c}is reduced by 59% at x = 0.07 and by 45% at x = 0.1. The effect of externally applied magnetic field up to 1 T on the R(T) curve for sample with x = 0.07 is shown in Figure 1c.

_{c2}(T), which separates the normal and the superconducting state, and the irreversibility line ${H}_{irr}\left(T\right)$. In the H-T phase diagram, the ${H}_{irr}\left(T\right)$ line separates the Abrikosov vortex pinned regime and the vortex liquid regime, which is at a given temperature; the critical current density goes to zero at the irreversibility field. To evaluate the upper critical field, μ

_{0}H

_{c2}, we employed to the 90% of normal state resistance R

_{N}criterion, while the irreversibility line, μ

_{0}H

_{irr}, was obtained using the 10% of R

_{N}criterion. To analyse the temperature dependence of the upper critical field, the μ

_{0}H

_{c2}(T) data extracted by the H-T phase diagram are shown in Figure 2b.

_{c2}(0) is the upper critical field at zero temperature and $t=T/{T}_{C}$ is the reduced temperature. The data are very well described by the G-L Equation with μ

_{0}H

_{c2}(0) = 1.23 T, as already reported for (Pr,La)Pt

_{4}Ge

_{12}and Pr

_{1−x}Nd

_{x}Pt

_{4}Ge

_{12}compounds [14,24,29,31,32,33,34]. For comparison, in Figure 2b, we also show the temperature dependence of the upper critical field derived within the Werthamer–Helfand–Hohenberg (WHH) model (blue dashed line), which includes orbital and Zeeman pair breaking [35,36]. In particular, for a single band superconductor in a dirty limit, the model yields:

_{0}H

_{c2}(T) experimental data near ${T}_{c}$, given by $D=4{k}_{B}/\pi e{\mu}_{0}\left|d{H}_{c2}\left(T\right)/dT\right|$. For our sample, ${\mu}_{0}d{H}_{c2}\left(T\right)/dT=-0.23\mathrm{T}{\mathrm{K}}^{-1}$. Within this model, the zero-temperature upper critical field H

_{c2}(0) can be obtained by the well-known WHH formula:

_{0}H

_{c2}(0) = 0.99 T, corresponding to the value experimentally measured at T = 2.1 K (${\mu}_{0}{H}_{c2}=1\mathrm{T}$).

_{4}Ge

_{12}does not seem to modify the behaviour of the temperature dependence of the upper critical field, showing a characteristic positive curvature near ${T}_{c}$, as for the parent compounds (Pr,La)Pt

_{4}Ge

_{12}and the doped Pr

_{1−x}Nd

_{x}Pt

_{4}Ge

_{12}material. To analyse the effects on the upper critical field H

_{c2}(T) curve of the partial substitution of Pr in PrPtGe in Figure 2c, we compare our findings for the sample with Ce doping x = 0.07 with the results reported in the literature for the un-doped parent compound PrPt

_{4}Ge

_{12}[14,29,30] and for Nd-doped samples Pr

_{1−x}Nd

_{x}Pt

_{4}Ge

_{12}[29]. A scaling behaviour described by the G-L formula, Equation (1), is obtained when the normalized upper critical field H

_{c2}(T)/H

_{c2}(0) is plotted as a function of the reduced temperature t = T/Tc. We also point out that the figure includes H

_{c2}(T) curves obtained by resistivity, specific heat, and magnetization measurements. Furthermore, the scaling behaviour is the same for the two different doping, Ce and Nd, despite the different strength of critical temperature lowering induced by the two type of doping.

_{2}Cu

_{3}O

_{7}high-temperature superconductor and interpreted within the thermally activated flux-creep theory [41]. The exponent $n$ = 1.5 is also consistent with the values found for the iron-based 122 and 1111-families and the TlSr

_{2}Ca

_{2}Cu

_{3}O

_{y}compound [42,43,44].

_{2}and up to 85% in (Y

_{0.77},Gd

_{0.23})Ba

_{2}Cu

_{3}O

_{y}films [45,46]. In our sample, the irreversibility field was 70% of the upper critical field at low temperatures, and dropped to less than 20% of ${H}_{c2}$ close to the critical temperature ${T}_{C0}$.

#### 3.1.2. Temperature Dependence of the Vortex Activation Energy

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}, we analysed the field dependence of the pinning activation energy U. This physical parameter was evaluated by a linear fit of the transition region in the R(T) curves represented in an Arrhenius plot, which are shown in Figure 3a. Indeed, the Arrhenius plots show that the resistivity is thermally activated over about two orders of magnitude at low fields; in this regime, the resistance’s dependence on temperature and field can be written in the form: $R\left(T,H\right)={R}_{0}{e}^{-U\left(T,H\right)/{k}_{B}T}$ [47].

_{0}H < 0.4 T and $\alpha $ ≈ 5 for μ

_{0}H > 0.4 T. Both values can be associated with a collective pinning regime, with an exponent value between 0.5 and 1, which is usually found in cuprate superconductors and could be related to the quasi-2D character of these materials [41,49,50]. The existence of a crossover suggests the presence of two different pinning centres with different dimensions within a collective pinning regime, as was observed, for example, in undoped and Nd-doped PrPt

_{4}Ge

_{12}samples [29], as well as YBa

_{2}Cu

_{3}O

_{7}compounds [50] and in Nd

_{2−x}Ce

_{x}CuO

_{4−δ}thin films [51].

#### 3.2. Point Contact Spectroscopy

#### PCAR Experiment

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}sample having x = 0 (T

_{c}= 7.9 K). We used a gold tip as a normal metal electrode, which was gently pushed onto the sample surface to realize the N/S nanoconstriction. The setup was then immersed in a helium liquid bath for low-temperature (T = 4.2 K) characterization. We measured the current–voltage characteristics I–V using a standard four-probe configuration, using a dc current supply to bias the junction and measuring the voltage by a nano-voltmeter. The conductance curves, dI/dV–V, were obtained by numerical derivation of the I–V curves. The PCAR setup also makes it possible to vary the tip pressure on the sample, obtaining a tuning of the barrier transparency and, consequently, different junction resistances. In our experiment, we obtained junction resistances R

_{N}in the range 0.1 Ω−50 Ω. We noticed here that we did not have a direct control of the geometrical dimensions of the N/S junction formed in the PCAR experiment. However, we estimated the junction size through the Sharvin formula ${R}_{N}=4\rho \ell /\left(3\pi {d}^{2}\right)$, in which the normal resistance of the junction is related to the resistivity $\rho $ = 3.5 μΩcm [87] and the mean free path $\ell $ = 103 nm [87] in the superconducting material, as well as to contact dimension $d$.

_{N}of 20 Ω and 0.2 Ω, respectively. Based on the Sharvin formula, we found the junction size to be $d$ = 7 nm and $d$ = 65 nm, respectively. In both cases, this confirms that the point contact is in the ballistic regime [52], in which the size of the junction is smaller than the mean free path in the superconductor ($d<<\ell $). This corresponds to the physical conditions for which an electron can accelerate freely through the point contact, with no heat generated in the contact region, allowing energy-resolved spectroscopy.

_{2}[61], MgCNi

_{3}[89], and Pr

_{1−x}LaCe

_{x}CuO

_{4-y}[57]. In this extended model, we need to take into account that the metallic tip (N electrode) forms a point contact junction on a superconducting grain, and this in turn forms a Josephson junction with another superconducting grain. Consequently, the total voltage drop V (experimentally measured) is given by the sum of the point contact V

_{PC}and the Josephson junction V

_{JJ}contributions $V={V}_{PC}+{V}_{JJ}$. If the flowing current $I$ is lower than ${I}_{JJ}$ there is no voltage drop at the inter-grain junction (${V}_{JJ}=0$). Otherwise, V

_{JJ}can be calculated according to Lee formula [90] as ${V}_{JJ}={R}_{JJ}{I}_{JJ}\sqrt{{\left(I/{I}_{JJ}\right)}^{2}-1}$, where ${R}_{JJ}$ and ${I}_{JJ}$ are the resistance and the critical current of the Josephson junction, respectively. If the flowing current $I$ is lower than ${I}_{JJ}$ there is no voltage drop at the inter-grain junction (${V}_{JJ}=0$). Then, the total conductance $G$ can be calculated from the condition $1/G=\left[\frac{d{V}_{PC}}{dI}+\frac{d{V}_{JJ}}{dI}\right]$. We succeeded in simulating the conductance spectrum reported in Figure 4d assuming Δ = 0.55 meV, Z = 0.54 and α = 0.20. The fitting parameters related to the Josephson junctions were ${R}_{JJ}=$ 0.1 Ω and ${I}_{JJ}=$ 3.2 mA. We notice that these parameters are not completely free, being necessarily ${R}_{N}={R}_{PC}+{R}_{JJ}$ and ${R}_{JJ}{I}_{JJ}<\Delta $. We remark here that neglecting the existence of a Josephson junction in series with the point contact would result in an over-estimation of the superconducting energy gap, because the measured voltage at which the conductance features are observed is larger than the real voltage ${V}_{PC}$ applied to the point contact junction ($V={V}_{PC}+{V}_{JJ}$). We observe that the superconducting energy gap values obtained from the numerical fittings of most of the experimental spectra are in the range 0.85–0.95 meV that correspond to a ratio 2Δ/k

_{B}T

_{C}in the range 2.5–2.8, smaller than the BCS value (3.52). In the case of the conductance curve of Figure 4d, we estimate a superconducting energy even smaller (Δ = 0.55 meV, i.e., 2Δ/k

_{B}T

_{C}= 1.6). This may be an indication of suppressed superconductivity on the probed surface, with the point contact experiments being sensitive to a thin surface layer of tens of nanometres. Consequently, the correct procedure for estimating the ratio 2Δ/k

_{B}T

_{C}would be to use the local critical temperature, which should be estimated based on the temperature evolution of the conductance spectra (not available in this experiment); this local Tc could be lower than the bulk sample Tc, giving an increased 2Δ/k

_{B}T

_{C}ratio. We note that in the case of d-wave symmetry, electrons injected along different directions may experience different pairing amplitudes. Consequently, the shape of the conductance curves does not depend only on the height Z of the potential barrier at the interface, but also on the direction of the current injection. In Figure 5a, we show conductance measurements performed in a different location of the sample. The two spectra are the result of two successive measurements, in which the second spectrum was measured after increasing the tip pressure on the surface to increase the barrier transparency. The lower spectrum shows a ZBCP with limited amplitude (about 1.2) and is reproduced by the extended BTK model by assuming Δ = 0.55 meV, Z = 0.71 and α = 0.46. However, the second spectrum (shifted for clarity) has a much higher and more narrow ZBCP with two relative maxima appearing at the side of the peak. To understand the evolution of the second conductance curve, we show in Figure 5b the expected behaviour of the spectra obtained by keeping fixed the parameters Δ = 0.55 meV and α = 0.46, varying the barrier strength Z in the range 0 < Z < 1. We notice that in this scenario the main effect of the Z parameter is on the ZBCP height. The appearance of further conductance features is explained considering that the increased pressure of the tip on the surface has a double effect: it helps to obtain a more transparent barrier (lower Z), while it favours the formation of an inter-grain junction. Indeed, the numerical simulation of the experimental spectrum is obtained with good agreement by assuming Δ = 0.55 meV, Z = 0.39, α = 0.29 and ${R}_{JJ}=$ 0.22 Ω, ${I}_{JJ}=$ 0.24 mA. In Figure 5c, we show the evolution of conductance spectra numerically calculated by fixing the parameters Δ = 0.55 meV, Z = 0.39, α = 0.29 and varying only ${R}_{JJ}$ in the range 0–0.42 Ω.

## 4. Conclusions

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}pellets, reporting the magnetic field phase diagram H-T for the Ce-doped compound with x = 0.07, as well as the point contact spectroscopy characterization of the parent compound PrPt

_{4}Ge

_{12}(x = 0).

_{0.93}Ce

_{0.07}Pt

_{4}Ge

_{12}, shows a scaling behaviour similar to high-temperature superconducting cuprates. The vortex activation energy was also evaluated at different applied magnetic fields. At magnetic fields lower than 0.4 T, the activation energy follows a power law of the type 𝐻

^{−α}, with the exponents α ≈ 0.5, which could indicate a collective pinning regime with a quasi-2D character.

_{4}Ge

_{12}), we realized normal metal/superconductor nano-junctions, with lateral dimensions of few nanometres, by pushing a gold tip onto the surface of polycrystalline sample. Several conductance spectra were measured at low temperatures, showing zero bias conductance peak with variable amplitude, height and width. All experimental data for the PrPt

_{4}Ge

_{12}sample were consistently interpreted in the framework of extended BTK theory. A small energy gap was observed in the range 0.55 meV–0.95 meV, indicating the possible formation of inter-grain Josephson junctions in series with the point contact.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) The resistance as a function of the temperature normalized to the normal state resistance value for the three different Ce doping. (

**b**) Evaluated critical temperature values as a function of the doping. The inset shows a schematic diagram of the Pr

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}crystal structure, showing the Pr,Ce atoms residing in icosahedral cages formed by tilted PtGe

_{6}octahedral. (

**c**) Magnetic field dependence of the resistance versus temperature curve measured for the sample with x = 0.07 doping.

**Figure 2.**(

**a**). The H-T phase diagram as obtained by R(T) measurements at different applied magnetic fields for the sample with the doping x = 0.07. The irreversibility line (0.1 R

_{N}curve) and the upper critical field behaviour (0.9 R

_{N}curve) are indicated. (

**b**) The upper critical field ${H}_{c2}\left(T\right)$ data are shown as black spheres. The red solid line is a fit of the data by the Ginzburg–Landau Equation (Equation (1) in the text). The blue dashed line is obtained by the single band WHH model (Equation (2) in the text). (

**c**) Scaling plots of the normalized upper critical field H

_{c2}(T)/H

_{c2}(0) plotted as function of the reduced temperature T/T

_{c}for the parent compound PrPt

_{4}Ge

_{12}[14,29,30], Nd-doped samples Pr

_{1−x}Nd

_{x}Pt

_{4}Ge

_{12}[29] and for our Pr

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}sample with x = 0.07. H

_{c2}(T) curves are obtained by resistivity, R, specific heat, C, and magnetization measurements, M. The inset shows the H

_{c2}data as a function of the temperature for the same samples in the main panel. (

**d**) The irreversibility field ${H}_{irr}\left(T\right)$ data are shown as open circles. The red solid line is a fit of the data by Equation (5) in the test.

**Figure 3.**(

**a**) The Arrhenius plot of the R(T) curves for the sample with the doping x = 0.07. (

**b**) The pinning activation energy as a function of the applied magnetic field for the same sample. The dotted lines are obtained by a linear fit on the data in the log–log plot.

**Figure 4.**Normalized conductance spectra, dI/dV–V, measured at low temperature (T = 4.2 K) in different sample locations on the Pr

_{1−x}Ce

_{x}Pt

_{4}Ge

_{12}(with x = 0) sample. Experimental data (empty symbols) in (

**a**,

**b**) are compared to numerically calculated curves for the three different symmetries. The I–V curve is shown in the inset. Experimental data (empty symbols) in (

**c**,

**d**) are compared to numerically calculated curves for d-wave symmetry only. Inset in (

**d**) represent the schematic of model in which an inter-grain Josephson junction is formed in series with the point contact junction.

**Figure 5.**(

**a**) Conductance spectra measured in a different location on the same superconducting sample: the lower (green) spectrum was measured soon after the tip approach on the surface. The upper spectrum was measured after increasing the tip pressure on the surface. The upper (black) spectrum was vertically shifted (+0.2) for clarity. Solid lines represent the numerical fits. (

**b**) Evolution of conductance spectra (solid lines) calculated numerically for Δ = 0.55 meV and α = 0.46, and for 0 < Z < 1. The scattered (green) points refer to experimental data of Figure 5a. (

**c**) Evolution of conductance spectra (solid lines) calculated numerically for Δ = 0.55 meV, Z = 0.39, α = 0.29, and 0 < ${R}_{JJ}$ < 0.42 Ω. The scattered (black) points refer to experimental data of Figure 5a.

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**MDPI and ACS Style**

Romano, P.; Avitabile, F.; Nigro, A.; Grimaldi, G.; Leo, A.; Shu, L.; Zhang, J.; Di Bartolomeo, A.; Giubileo, F.
Transport and Point Contact Measurements on Pr_{1−x}Ce_{x}Pt_{4}Ge_{12} Superconducting Polycrystals. *Nanomaterials* **2020**, *10*, 1810.
https://doi.org/10.3390/nano10091810

**AMA Style**

Romano P, Avitabile F, Nigro A, Grimaldi G, Leo A, Shu L, Zhang J, Di Bartolomeo A, Giubileo F.
Transport and Point Contact Measurements on Pr_{1−x}Ce_{x}Pt_{4}Ge_{12} Superconducting Polycrystals. *Nanomaterials*. 2020; 10(9):1810.
https://doi.org/10.3390/nano10091810

**Chicago/Turabian Style**

Romano, Paola, Francesco Avitabile, Angela Nigro, Gaia Grimaldi, Antonio Leo, Lei Shu, Jian Zhang, Antonio Di Bartolomeo, and Filippo Giubileo.
2020. "Transport and Point Contact Measurements on Pr_{1−x}Ce_{x}Pt_{4}Ge_{12} Superconducting Polycrystals" *Nanomaterials* 10, no. 9: 1810.
https://doi.org/10.3390/nano10091810