Effect of disorder in ${\mathrm{MgB}}_2$ thin films

We report on scanning tunneling spectroscopy studies of magnesium diboride $\left({\mathrm{MgB}}_2\right)$ thin films grown by different techniques. The films have critical temperatures ranging between 28 and 41 K with very different upper critical fields. We find that the superconducting gap associated with the $\sigma$ band decreases almost linearly with decreasing critical temperature while the gap associated with the $\pi$ band is only very weakly affected in the range of critical temperatures above 30 K. In the sample with the lowest critical temperature (28 K) we observe a small increase of the $\pi$ gap that can only be explained in terms of an increase in the interband scattering. The tunneling data was analyzed in the framework of the two-band model. The magnetic-field-dependent tunneling spectra and the upper critical field measurements of these disordered samples can be consistently explained in terms of an increase of disorder that mostly affects the $\pi$ band in samples with reduced critical temperatures.

Figure 1

SEM micrograph of (a) film A and (b) film C2.

Figure 2

STM topography of (a) film A, scanning area $200\mathrm{nm}\times 200\mathrm{nm}$, (b) film B1, scanning area $300\mathrm{nm}\times 300\mathrm{nm}$, (c) film B2, scanning area $300\mathrm{nm}\times 300\mathrm{nm}$, (d) film C2, scanning area $1\mu \mathrm{m}\times 1\mu \mathrm{m}$.

Figure 3

Tunneling conductance spectra recorded on films with different $T_c$, at $T=4.2\mathrm{K}$. The tunneling resistance is $0.2\mathrm{G}\Omega$. The spectra have been normalized to the conductance value at high voltage. For each film the spectrum showing two gap features has been acquired close to a step on the film surface and the one showing one gap far away from steps. (a) Film A, (b) film B2, (c) film C1, (d) film C2.

Figure 4

Tunneling conductance spectra recorded on films with different $T_c$, at $T=4.2\mathrm{K}$. (a) $c$-axis spectra on films with $T_c=28\mathrm{K}$ (film C2), 33.5 K (film C1), and 35 K (film B2). (b) Spectra with $a\text{−}b$ component of the tunneling current, recorded on films with $T_c=35\mathrm{K}$ (film B2) and 39 K (film B1). The spectra have been normalized to the conductance value at high voltage. The tunneling resistance is $R_T=0.2\mathrm{G}\Omega (I=100\mathrm{pA},V=20\mathrm{mV})$.

Figure 5

(a) Gap values for films with different $T_c$ compared with values reported in literature. (b) BCS ratios obtained from the gap values in (a) and compared with other data reported in literature.

Figure 6

(a) Zero bias conductance as a function of the applied magnetic field normalized to the upper critical field at zero temperature. (b) Comparison between experimental data and theoretical curves.

Figure 7

Upper critical field for $H$ applied parallel and perpendicular to the film surface for (a) a sample with $T_c=40\mathrm{K}$ (film A), (b) a sample with $T_c=33.5\mathrm{K}$ (film C1).