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=υ _F/ω(υ_f is the Fermi velocity) being smaller or of the order of the penetration depth λ and mean free pathl. For materials withυ _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 λ_L, andR≈μ ₀λ_l/2τ as surface resistance allowing a measure of λ_L and relaxation time τ(T, ω). In the superconducting state the photon interaction scales withξ _F/λ_L=l/γ (ξ _f is the dimension of Cooper pairs for l→∞) and causes at low frequencies an absorption rate growing withγ, which is decreasing withξ _F/l. The rate increase proportional toγ turns to a decrease above 0.1 THz, being accompanied by a decrease ofγ with frequency which is stronger for largeγ and smallξ _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.