Experimental evidence for a surface distribution of two-level systems in superconducting lithographed microwave resonators

Abstract

We present measurements of the temperature-dependent frequency shift of five niobium superconducting coplanar waveguide microresonators with center strip widths ranging from 3to50μm, taken at temperatures in the range of 100–800mK, far below the 9.2K transition temperature of niobium. These data agree well with the two-level system (TLS) theory. Fits to this theory provide information on the number of TLSs that interact with each resonator geometry. The geometrical scaling indicates a surface distribution of TLSs and the data are consistent with a TLS surface layer thickness of the order of a few nanometers, as might be expected for a native oxide layer.