In-plane microwave conductivity of the single-layer cuprate<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Tl</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="normal">δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

We have measured the in-plane microwave conductivity of nearly optimally doped single crystals ${(T}_{\mathrm{c}}$=78 K) of ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6+\mathrm{\ensuremath{\delta}}}$ (Tl-2201) at 14.4, 24.8, and 35.9 GHz using cavity perturbation methods. At low temperatures, the in-plane penetration depth has a strong, linear temperature dependence, indicative of an unconventional pairing state with line nodes. The real part of the conductivity shows a broad, frequency-dependent peak near 30 K, similar to that seen in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ crystals. With tetragonal crystal symmetry and a single ${\mathrm{CuO}}_{2}$ plane per unit cell, Tl-2201 is the simplest structure so far to display these features.

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