Anomalous microwave conductivity due to collective transport in the pseudogap state of cuprate superconductors

Abstract

The microwave surface impedance ${Z}_{s}{=R}_{s}{+iX}_{s}$ of ${\mathrm{HgBa}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{8+\ensuremath{\delta}},$ ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}},$ ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}},$ and underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}$ is found to be anomalous in that ${R}_{s}(T>{T}_{c})\ensuremath{\ne}{X}_{s}(T>{T}_{c})$ in the pseudogap state. This implies plasmonlike response and negative permittivities ${\ensuremath{\varepsilon}}^{\ensuremath{'}}(\ensuremath{\omega})<0$ at microwave frequencies indicating non-Fermi-liquid transport in the $\mathrm{ab}$ plane. The anomalous microwave response is shown to arise from a collective mode characterized by a plasma frequency ${\ensuremath{\omega}}_{\mathrm{pCM}}\ensuremath{\sim}0.1 \mathrm{eV}$ and extremely low damping ${\ensuremath{\Gamma}}_{\mathrm{CM}}\ensuremath{\sim}{10}^{\ensuremath{-}5}--{10}^{\ensuremath{-}4} \mathrm{eV},$ distinctly different from those observed at optical frequencies.