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

The microwave surface impedance $Z_s{=R}_s{+iX}_s$ of ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta },$ ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta },$ ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CuO}}_{6+\delta },$ and underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ is found to be anomalous in that $R_s(T>\mathrm{}{T}_c)\ne X_s(T>\mathrm{}{T}_c)$ in the pseudogap state. This implies plasmonlike response and negative permittivities ${\varepsilon }^{\prime }\left(\omega \right)<\mathrm{}0\mathrm{}$ 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 ${\omega }_{\mathrm{pCM}}\sim 0.1\hspace{0.5em}\mathrm{eV}$ and extremely low damping ${\Gamma }_{\mathrm{CM}}\sim {10}^{-5}–{10}^{-4}\hspace{0.5em}\mathrm{eV},$ distinctly different from those observed at optical frequencies.