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Universal phonon softening in the pseudogap state of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Tl</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Ba</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Ca</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>Cu</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</…
Exploring the origin of the pseudogap is important for the understanding of superconductivity in cuprates. Here we report a systematical experimental study on the phonon vibrational properties of ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{Ca}}_{n\ensuremath{-}1}{\mathrm{Cu}}_{n}{\mathrm{O}}_{2n+4+\ensuremath{\delta}}$ ($n=1,2,3$) single crystals based on the Raman scattering measurements over the temperature range from 10--300 K. The temperature evolution of the …