Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.