Local Tunneling Study of Three-Dimensional Order Parameter in the $\pi$-band of Al-doped MgB$_2$ Single Crystals

Abstract

We have performed local tunneling spectroscopy on high quality Mg$_{1-x}$Al$_x$B$_2$ single crystals by means of Variable Temperature Scanning Tunneling Spectroscopy (STS) in magnetic field up to 3 Tesla. Single gap conductance spectra due to c-axis tunneling were extensively measured, probing different amplitudes of the three-dimensional $\Delta_\pi$ as a function of Al content. Temperature and magnetic field dependences of the conductance spectra were studied in S-I-N configuration: the effect of the doping resulted in a monotonous reduction of the locally measured $T_C$ down to 24K for x=0.2. On the other hand, we have found that the gap amplitude shows a maximum value $\Delta_\pi= 2.3$ meV for x=0.1, while the $\Delta_\pi / T_C$ ratio increases monotonously with doping. The locally measured upper critical field was found to be strongly related to the gap amplitude, showing the maximum value $H_{c2}\simeq3T$ for x=0.1 substituted samples. For this Al concentration the data revealed some spatial inhomogeneity in the distribution of $\Delta_\pi$ on nanometer scale.