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Large anisotropic thermal conductivity of intrinsically two-dimensional metallic oxide PdCoO$_2$

The highly conductive layered metallic oxide \pdcoo{} is a near-perfect analogue to an alkali metal in two dimensions. It is distinguished from other two-dimensional electron systems where the Fermi surface does not reach the Brillouin zone boundary by a high planar electron density exceeding $10^{15}$ cm$^{-2}$. The simple single-band quasi-2D electronic structure results in strongly anisotropic transport properties and limits the effectiveness of electron-phonon scattering. Measurements on single crystals in the temperature range from 10-300K show that the thermal conductivity is much more weakly anisotropic than the electrical resistivity, as a result of significant phonon heat transport. The in-plane thermoelectric power is linear in temperature at 300\,K and displays a purity-dependent peak around 50K. Given the extreme simplicity of the band-structure, it is possible to identify this peak with phonon drag driven by normal electron-phonon scattering processes.