Anomalous microwave conductivity due to collective transport in the pseudogap state of cuprate superconductors The microwave surface impedance Z

O 6.5 is found to be anomalous in that R s (TϾT c ) X s (TϾT c ) in the pseudogap state. This implies plasmonlike response and negative permittivities Ј()Ͻ0 at microwave frequencies indicating non-Fermi-liquid transport in the ab plane. The anomalous microwave response is shown to arise from a collective mode characterized by a plasma frequency pCM ϳ0.1 eV and extremely low damping ⌫ CM ϳ10 Ϫ5 -10 Ϫ4 eV, distinctly different from those observed at optical frequencies. The ''normal'' state above T c of the high-temperature cuprate superconductors is well known to be extremely abnormal. A wide variety of experimental techniques ͑photoemis-sion, optical conductivity, NMR, tunneling, neutron scattering, infrared, Raman, etc.͒ ͑Ref. 1͒ have been applied to its study and suggest that there is a common phenomenology for all high-temperature superconductors: the existence of a partial gap or a pseudogap meaning the suppression of the low-energy density of states. An important issue is the nature of the pseudogap, several alternative theoretical models of this having been proposed, such as superconducting fluctuations 2 or islands, 3 competing order parameter, 4 and stripes. Single crystals of Hg:1201 (T c ϭ94.4 K), Hg:1223 (T c ϭ122 K), Tl:2201 (T c ϭ91K), and underdoped YBa 2 Cu 3 O 6.5 (T c ϭ60 K) were prepared by appropriate methods for each material. The high quality of the crystals discussed here has been confirmed by a variety of other techniques. 8 Since Z s ϭR s ϩiX s ϭ ͱ i 0 / , from R s and X s it is possible to obtain 1 and 2 , the real and imaginary parts of the conductivity, using ϭ 1 Ϫi 2 ϭi 0 /(R s ϩiX s ) 2 . In all microwave measurements, R s (T) can be measured absolutely, while relative changes ⌬X s (T)ϵX s (T)ϪX s (0) are typically measured. We obtain X s (0)ϭ 0 ab (0) from estimates of the low-T penetration depth ab (0):130 nm (Hg:1223), 117 nm (Hg:1201), and 260 nm (YBCO6.5). It should be emphasized that because X s (Ṫ ϾT c )ӷX s (0), the results discussed in this paper are not sensitive to X s (0) or (0). The temperature dependences of X s and R s for Hg:1223 when the microwave magnetic field H ʈc axis and of ⌬X s and R s when H Ќc are shown i