Effects of the Two- Gap Nature on the Microwave Conductivity of 39 K Polycrystalline MgB2 Films

The surface resistance (Rs) and the real part (sigma_1) of the microwave complex conductivity of a ~380 nm-thick polycrystalline MgB2 film with the critical temperature (Tc) of 39.3 K were investigated at ~8.5 GHz as a function of temperature. Two coherence peaks were observed in the sigma_1 versus temperature curve at temperatures of ~0.5 Tc and ~0.9 Tc, respectively, providing a direct evidence for the two-gap nature of MgB2. The film appeared to have a pi-band gap energy of 1.8 meV. For the MgB2 film ion-milled down to the thickness of ~320 nm, two coherence peaks were still observed with the first conductivity peak at ~0.6 Tc. Reduction of Tc by 3 K and reduced normal-state conductivity at Tc were observed along with an enhanced pi-band gap energy of 2.1 meV and a reduced Rs at temperatures below 15 K for the ion-milled film. Calculations based on the gap energies from the weak coupling Bardeen-Cooper-Schrieffer theory and the strong coupling theory suggest that both the sigma-band and the pi-band contribute to sigma_1 of the polycrystalline MgB2 films significantly. Our results are in contrast with the observation of single coherence peak at ~0.6 Tc and dominant role of the pi-band in the microwave conductivity of c-axis oriented MgB2 films as reported by Jin et al. [Phys. Rev. Lett. 91, 127006 (2003)]. Variations in the inter-band coupling constants with the level of disorder can account for the different Tc and sigma_1 behavior for the as-grown and ion-milled films. Our results suggest that enhanced inter-band scattering can improve microwave properties of MgB2 filims at low temperatures due to the larger pi-band gap despite the reduction of Tc.