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UBC Theses and Dissertations

Non-local electrical conductivity in PdCoO₂ Baker, Graham


Electrical conduction becomes non-local when an inhomogeneous electronic distribution is induced with a spatial variation shorter than the mean free path (MFP) between momentum-relaxing scattering processes. Two important methods of inducing such a distribution are via the size and skin effects. In the size effect, one or more dimensions of a medium are reduced below the MFP. The scattering of electrons from the medium's boundaries then induces an inhomogeneous electronic distribution under an applied direct current. In the skin effect, the exponential decay of alternating electromagnetic fields as they propagate into the medium gives rise to a so-called skin layer. The electronic distribution within the skin layer becomes inhomogeneous as the skin depth falls below the MFP. Here we study the size and skin effects in PdCoO₂, both experimentally and theoretically. While previous theoretical treatments of non-local electrical conductivity have assumed a free-electron dispersion, we observe that the anisotropic Fermi surface (FS) in PdCoO₂ results in behaviour that is incompatible with this assumption. Measurements of the size effect in PdCoO₂ revealed two novel phenomena, both of which are symmetry-forbidden for local conduction: anisotropy in the in-plane longitudinal resistivity, and a non-zero transverse resistivity at zero magnetic field. We developed a theory of the size effect for arbitrary FS geometry and used it to reproduce the key features of these measurements. Motivated by recent interest in the possibility that electrons in solids may behave viscously as a result of frequent internal momentum-conserving scattering, we developed a generalized theory of the skin effect, taking into account separate rates of momentum-conserving and momentum-relaxing scattering for arbitrary FS geometry. For an isotropic FS, our theory encompasses several known limiting behaviours. For anisotropic FSs, we explored geometries which lead to changes in the scaling of the surface impedance. By applying bolometric broadband microwave spectroscopy, we studied the skin effect in PdCoO₂ for three different directions of electromagnetic propagation. Using symmetry-based arguments, we determined that our measurements were neither in the local nor purely viscous regime. We argued instead that the data demonstrate a novel, predominantly ballistic effect as a result of the faceted FS.

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