Subharmonic gap structures and Josephson effect in $\mathrm{Mg}{\mathrm{B}}_2∕\mathrm{Nb}$ microconstrictions

Superconducting microconstrictions between Nb tips and high-quality $\mathrm{Mg}{\mathrm{B}}_2$ pellets have been realized by means of a point-contact inset, driven by a micrometric screw. Measurements of the current-voltage characteristics and of the dynamical conductance versus bias have been performed in the temperature range between $4.2\mathrm{K}$ and $500\mathrm{K}$. Above the Nb critical temperature $T_C^{\mathit{Nb}}$, the conductance of the $\mathrm{Mg}{\mathrm{B}}_2$/normal-metal constrictions behaves as predicted by the Blonder-Tinkham-Klapwijk model for low-resistance contacts while high-resistance junctions show quasiparticle tunneling characteristics. Consistently, from the whole set of data we infer the value ${\Delta }_{\pi }=2.5\pm 0.2\mathrm{meV}$ for the three-dimensional (3D) gap of $\mathrm{Mg}{\mathrm{B}}_2$. Below $T_C^{\mathit{Nb}}$, low-resistance contacts show Josephson current and subharmonic gap structures, due to multiple Andreev reflections. Simultaneous observations of both features unambiguously indicate a coupling of the 3D band of $\mathrm{Mg}{\mathrm{B}}_2$ with the Nb superconducting order parameter. We found that the temperature dependence of the Josephson critical current follows the classical Ambegaokar-Baratoff behavior with a value $I_C{R}_N=(2.1\pm 0.1)\mathrm{meV}$ at low temperatures.

Figure 1

(a) An electron coming from the normal electrode with energy smaller than the energy gap cannot enter the superconductor. It is reflected as a hole, leaving an extra charge $2e$ in the superconducting condensate (Andreev reflection). At low temperatures, the conductance spectra depend on the barrier strength $Z$, as shown in (b). The scale refers to the curve for $Z=0$; the other curves are shifted for clarity. In the case of superconducting electrodes (c), an electron is reflected back or transmitted. For voltages $\mathit{eV}⩽\Delta$ the Andreev-reflected hole cannot find an empty state in the left electrode but is Andreev reflected in turn as an electron. For energies $2\Delta ∕3⩽\mathit{eV}<\Delta ∕2$ the electron finds an empty state in the right electrode; three charges are transferred in this process [multiple Andreev reflections (MAR’s)]. For smaller voltages, MAR processes that transfer four or more electron charges carry the current. (d) In asymmetric tunnel junctions the conductance enhancements appear at energies $({\Delta }_S+{\Delta }_{S^{\prime }})∕m$, with $m=1,3,5,\dots$, and ${\Delta }_S∕n$ and ${\Delta }_{S^{\prime }}∕n$, with $n=1,2,3,\dots$.

Figure 2

(a) A small $\mathrm{Mg}{\mathrm{B}}_2$ grain remains on the Nb tip realizing two junctions in series: the point contact between the Nb tip and the small grain with resistance $R_{\mathit{PC}}$ and the Josephson junction between the two $\mathrm{Mg}{\mathrm{B}}_2$ grains with resistance $R_J$. The measured voltage $V_{\mathit{meas}}$ is the sum of the voltage drops at both junctions. (b) Tunneling conductance for a high-resistance contact measured at $T=12\mathrm{K}$. Experimental data (scattered graph) are compared to the theoretical simulation (solid line) for a S-I-S tunnel junction between two $\mathrm{Mg}{\mathrm{B}}_2$ with ${\Delta }_{\pi }=2.7\mathrm{meV}$ and $\Gamma =0.7\mathrm{meV}$. (c) Conductance spectrum at $T=12\mathrm{K}$ for a low-resistance contact. The theoretical simulation (solid line) has been obtained with ${\Delta }_{\pi }=2.4\mathrm{meV}$, $Z=0.66$, and $\Gamma =0$ considering the formation of an intergrain $\mathrm{Mg}{\mathrm{B}}_2∕\mathrm{Mg}{\mathrm{B}}_2$ junction in series with $R_J=1.5\Omega$ and $I_J=1.2\mathrm{mA}$.

Figure 3

Conductance spectra for two different contacts measured at $T=7\mathrm{K}$ (scattered graphs). The conductance measured at $T=12\mathrm{K}$—i.e., above $T_C^{\mathit{Nb}}$—is also reported (solid lines). The arrows indicate the energies of the SGS’s. Insets: current-voltage characteristics of the same junctions.

Figure 4

(a) Temperature dependence of the conductance spectra of the junction in Fig. 3a in the range between $4.2\mathrm{K}$ and $12\mathrm{K}$. All the spectra have been shifted, and the scale is valid only for the highest-temperature data. The arrows indicate the energy positions of the $E_3$ feature. (b) Temperature dependence of $E_1$, $E_2$, and $E_3$. Dotted and solid lines are guidelines for the eye. Open symbols correspond to sample in Fig. 3b. (c) Temperature dependence of ${\Delta }^{\mathit{Nb}}\left(T\right)=E_3\left(T\right)-E_2\left(T\right)$ (symbols) and theoretical curve (solid line).

Figure 5

Temperature dependence of the $I_C{R}_N$ product. The experimental data (scattered graph) are compared to the Ambegaokar-Baratoff behavior (solid line).