Anomalous Coherence Peak in the Microwave Conductivity of $c$-Axis Oriented ${\mathrm{M}\mathrm{g}\mathrm{B}}_2$ Thin Films

The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHz obtained from surface impedance measurements of two $c$-axis oriented $\mathrm{M}\mathrm{g}{\mathrm{B}}_{\mathrm{2}}$ thin films reveals a pronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in the frame of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that this maximum corresponds to an anomalous coherence peak resembling the two-gap nature of $\mathrm{M}\mathrm{g}{\mathrm{B}}_{\mathrm{2}}$. Our model assumes there is no interband impurity scattering and a weak interband pairing interaction, as suggested by band structure calculations. In addition, the observation of a coherence peak indicates that the $\pi$ band is in the dirty limit and dominates the total conductivity of our films.

Figure 1

$\log \delta {\lambda }^{\mathrm{e}\mathrm{f}\mathrm{f}}$ vs $T_c/T$ representation of the penetration depth data for two $\mathrm{M}\mathrm{g}{\mathrm{B}}_{\mathrm{2}}$ samples. The solid lines are calculated within the two-gap model in the dirty limit with parameters as described in the text. Note the different scale ranges for the two samples.

Figure 2

Temperature dependence of ${\sigma }_1$ at 17.9 GHz for $\mathrm{M}\mathrm{g}{\mathrm{B}}_{\mathrm{2}}$ samples $S1210$ (squares), $S1211$ (circles), and a Nb thin film (triangles). The lines show the calculations described in the text. The data for $S1210$ and $S1211$ are shifted by 1 and 0.5 units for clarity.

Figure 3

Calculated temperature dependence of the two energy gaps within the two band model and parameters as described in the text. The dashed line represents $\Delta (T)=kT$. The arrow points to the intersection of the dashed line and ${\Delta }_{\pi }(T)$, at which the coherence peak appears.