Thermal conductivity of insulating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">YCu</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and superconducting<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CaCu</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>: Failure of the phonon-gas picture
Abstract
The ab-plane thermal conductivity \ensuremath{\kappa}(T) of insulating ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{YCu}}_{2}$${\mathrm{O}}_{8}$ and superconducting ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ is measured from T=10 to 300 K on single-crystal samples. Metallic ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ has a significantly higher \ensuremath{\kappa} than ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{YCu}}_{2}$${\mathrm{O}}_{8}$; the difference \ensuremath{\Delta}\ensuremath{\kappa} agrees well in magnitude with a Wiedemann-Franz estimate of the electronic contribution to \ensuremath{\kappa} in ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$. The shape of \ensuremath{\kappa}(T) in insulating ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{YCu}}_{2}$${\mathrm{O}}_{8}$ differs from normal insulators described by the Peierls-Boltzmann theory. Assuming that atomic vibrations are the main heat carrier, and noting that \ensuremath{\kappa} is more similar to that of silica glass than to a normal insulating crystal like CuO, we suggest that the ``phonon'' mean free path is sufficiently short that the Peierls-Boltzmann theory is not applicable. This is consistent with evidence from neutron scattering that phonons are poorly defined. Our data support the idea that the peak in \ensuremath{\kappa}(T) observed below ${\mathit{T}}_{\mathit{c}}$ in superconducting samples originates from electronic rather than vibrational heat currents.
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