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We employ realistic DFT+DMFT calculations to investigate the charge and heat transport properties of RuO$_2$, a multi-orbital Fermi liquid. The calculations achieve semi-quantitative agreement with experimental optical conductivity, electrical resistivity, and thermopower, establishing a precision many-body description. However, a significant discrepancy in electronic thermal resistivity suggests a puzzle regarding the relative relaxation of charge and heat currents in this material.
RuO$_2$'s thermal conductivity is mysteriously lower than predicted by state-of-the-art DFT+DMFT, hinting at a fundamental breakdown in our understanding of Fermi liquid heat transport.
RuO$_2$ is a multi-orbital Fermi liquid for which an array of complementary experimental measurements has recently become available, making it a stringent testbed for quantitative many-body electronic structure theory. Using realistic dynamical mean-field calculations, we compute the spectroscopic and transport properties of RuO$_2$ in the paramagnetic state. We identify RuO$_2$ as a moderately correlated Fermi liquid and obtain (semi-)quantitative agreement with experiment for its optical conductivity, electrical resistivity, and thermopower. This broad agreement across complementary observables establishes a ``precision''many-body description of RuO$_2$ and allows remaining discrepancies to be identified as meaningful tests of the theory. In particular, the calculated electronic thermal resistivity significantly undershoots the experimentally inferred low-temperature thermal resistivity, raising an important puzzle concerning the relative relaxation of charge and heat currents in the Fermi liquid regime. We explore low-temperature electron-phonon scattering as a possible mechanism for resolving this discrepancy, while a fully quantitative description remains an open problem. More broadly, our results demonstrate the power of combining precision DFT+DMFT calculations with complementary experimental probes to build and critically test quantitative descriptions of correlated quantum materials.