Infrared vortex-state electrodynamics in type-II superconducting thin films

The vortex-state electrodynamics of s-wave superconductors has been studied by infrared spectroscopy. Far-infrared transmission and reflection spectra of superc onducting Nb0.5Ti0.5N and NbN thin films were measured in a magnetic field perpendicular to the film surface , and the optical conductivity was extracted. The data show clear reduction of superconducting signature. We consider the vortex state as a twocomponent effective medium of normal cores embedded in a BCS superconductor. The spectral features are well explained by the Maxwell-Garnett theory. Our analysis supports the presence of magnetic-fieldinduced pair-breaking effects in the superconducting component outside of the vortex cores. The vortex or Abrikosov state exists in type-II superconductors subjected to magnetic fields between Bc1 and Bc2. In this state the field penetrates the superconductor in the form of quantized tubes of flux, or vortices. The superconducting gap is zero inside the vortex cores and finite outside so that each vortex may be considered to have a core of normal metal, surrounded by superconductor [1, 2]. Because vortex quantization renders the material an inhomogeneous system, it necessarily affects the electrodynamics of the s uperconductor. The microwave response of the vortex state has been extensively studied theoretically [3‐5] and experimentally [6‐11]. However the picture is still incomplete in the infrared region spanning the superconducting gap [12, 13]. In this Letter we address the infrared electrodynamics of the vortex state. We obtain the complex optical conductivity of type-II superconductors and compare our results to calculations of a superconductor-normal metal mixture using the two key models for the effective conductivity of an inhomogeneous system: that of Garnett [14] (the so-called “Maxwell-Garnett theory” or MGT) and that of Bruggeman [15] (sometimes called the “effective-medium approximation” or EMA). We also compare our results to a theory of viscous motion of vortices driven by currents in the superconductor [3]. We find that only the MGT gives a good description of experiment, and then only when pairbreaking by the magnetic field [16‐18] is considered. That it does so is reasonable considering the topology of the vortex state: normal regions surrounded entirely by a connected superfluid. As pointed out some years ago [19], this is the topology of the MGT: the inclusions are embedded in a host medium and are correlated to stay apart. In contrast, the EMA allows percolation of the minority constituent at some critical concentration, something that does not happen in the vortex state until the upper critical field, when the entire material is in the normal state. We studied type-II superconducting thin films of BCS superconductors Nb0.5Ti0.5N and NbN, which are widely used in superconducting magnets [20], RF cavities [21], and photodetectors [22]. The 10 nm Nb0.5Ti0.5N film was grown on a quartz substrate in Ar and N2 gas with a NbTi target, and the 70 nm NbN film grown on a MgO substrate in N2 atmosphere using Nb, both by reactive magnetron sputtering [23, 24]. The substrates have negligible absorption in the spectral range of interest (10‐ 100 cm −1 ) for T < 20 K. We performed the experiment at Beamline U4IR of the National Synchrotron Light Source, Brookhaven National Laboratory. The beamline is equipped with a Bruker IFS 66v FT-IR spectrometer, modified to use synchrotron radiation and a superconducting magnet for low-temperature magneto-spectroscopy. A composite silicon bolometer operating at T ∼1.5 K detects far-infrared radiation with high sensitivity. Both sample s were cooled to 2 K (≪ Tc) in zero field, and their transmission and reflection measured in magnetic fields from 0‐10 T, with the field direction normal to the sample sur