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

We present measurements of the temperature-dependent frequency shift of five niobium superconducting coplanar waveguide microresonators with center strip widths ranging from 3 to 50 μ m , taken at temperatures in the range of 100 - 800 mK , far below the 9.2 K 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.