Does DFT+DMFT explain charge and heat transport in RuO2?

A precision test of many-body theory in RuO2

RuO2 has become a stringent testbed for quantitative many-body electronic structure theory because optics and transport measurements now provide clear evidence of Fermi liquid behavior with coherent quasiparticles. The paper asks whether a realistic combination of density-functional theory (DFT) and dynamical mean-field theory (DMFT) can reproduce that behavior in the paramagnetic state, rather than only describing the general electronic and magnetic properties.

The authors build a six-orbital Wannier Hamiltonian for the Ru t2g states, solve a three-orbital quantum impurity model with single-site DMFT, and then compute spectroscopic and transport properties. The goal is a precision description: agreement across complementary observables is what allows any remaining disagreement to be read as a meaningful test of the theory rather than as an obvious failure of the electronic structure calculation.

Moderate correlation with a high coherence scale

The calculations identify RuO2 as a moderately correlated, multi-orbital Fermi liquid with a high coherence scale. That matters because the DMFT self-energy shows Fermi liquid behavior at temperatures well above the experimentally accessible low-temperature regime below about 20 K, which is why the authors can extract low-temperature Fermi liquid coefficients from calculations run between 58 and 290 K.

The paper compares two values of Hund's coupling, J = 0.2 eV and J = 0.4 eV, while fixing the intraorbital Coulomb interaction U to the constrained random phase approximation value of 2.44 eV. The cRPA Hund's coupling is 0.14 eV, but the authors note that for Ru-based oxides this value is often too small to capture experimental phenomenology, so they also test the larger 0.4 eV used in earlier ruthenate studies.

Optical conductivity needs dynamical correlations

At the bare DFT level, the interband transitions appear at roughly the right energies but the calculation dramatically overestimates their intensity and energy position. Including orbital-dependent local self-energies from DMFT renormalizes the interband peaks toward the experimental reflectivity data, especially the intra-t2g transition from occupied x2-y2 states to unoccupied xz/yz states.

The comparison does not uniquely discriminate between different Hund's coupling values, but it does show that dynamical correlations are essential for a quantitative description. The authors therefore describe RuO2 as a moderately correlated multi-orbital metal, and they use this validated electronic structure as the input for the dc transport calculations.

Charge transport agrees with experiment

In a Fermi liquid the electrical resistivity follows ρ = A T², where A is an intrinsic, material-specific coefficient. The DMFT calculations produce an A coefficient of the correct order of magnitude, and for larger Hund's coupling they reproduce the experimental value quantitatively. Experimentally, the quadratic coefficient along the crystallographic c direction is 6.6 to 7.1 × 10⁻⁵ µΩ cm/K², within the 5 to 10 × 10⁻⁵ µΩ cm/K² range established in earlier literature.

The paper also checks the Kadowaki-Woods ratio A/γ², which relates quasiparticle scattering to the density of states through the specific-heat coefficient γ. The calculated ratio remains smaller than the experimentally reported value and is relatively insensitive to variations in the interaction parameters, so this comparison does not resolve the interaction-parameter ambiguity either.

Thermal resistivity falls short of experiment

The electronic contribution to the thermal resistivity is the clearest discrepancy. The experimentally determined B coefficient, the quadratic coefficient of the thermal resistivity, is larger than the DMFT value by a factor of 2 to 7 depending on the interaction parameters. The experimental B/A ratio is about 3 to 4, almost a factor of two larger than both the DMFT calculation and the analytical value of about 1.5442 for a single-band Fermi liquid with a local self-energy.

This is the paper's central puzzle: charge and heat currents appear to relax differently in the Fermi liquid regime of RuO2. The authors note that the discrepancy may reflect limitations of single-site DMFT for heat transport, but before invoking effects beyond single-site DMFT such as vertex corrections or non-local self-energies, they examine a physical contribution absent from their calculation.

Electron-phonon scattering as a candidate explanation

At low temperatures, electron-phonon scattering contributes to the electronic thermal resistivity with a T³ scaling, which is difficult to disentangle from the T² electron-electron contribution. This contrasts with electrical resistivity, where the low-temperature electron-electron and electron-phonon contributions scale as T² and T⁵ respectively, making them easier to separate.

Using a Bloch model with a Debye phonon and a spherical Fermi surface, the authors fit the experimental thermal resistivity with the DMFT B coefficient fixed at 12.25 × 10⁻⁵ µΩ cm/K² for J = 0.4 eV, leaving only the dimensionless Fermi surface radius as an adjustable parameter. The model fits the experimental data well, which suggests that the calculated B coefficient may not be inconsistent with experiment and underscores how hard it is to separate electron-electron and electron-phonon contributions to electronic heat transport.

What remains open in the description

A definitive characterization of the screened Coulomb interaction proved difficult despite the array of high-quality experimental datasets. No single choice of Hund's coupling simultaneously reproduced the optical spectroscopy, the low-temperature transport, and the Sommerfeld coefficient, although several experiments point to a value of order 0.4 eV similar to other ruthenates. The authors flag this tension as a key challenge for DFT+ methods and point to self-consistent GW+EDMFT as a possible route to an ab-initio estimate of J beyond cRPA.

The paper also reports that removing the zero-frequency real part of the DMFT self-energy increases both electrical and thermal resistivity, with a larger increase for larger Hund's coupling, but does not noticeably improve agreement with the available experimental data. A fully quantitative resolution of the transport puzzle requires improvement on both sides of the comparison: a more complete treatment of electron-electron transport and a microscopic understanding of electron-phonon contributions to the electronic heat current.

Where the description holds and where it stops

The quantitative agreement covers the paramagnetic state, the optical conductivity, the electrical resistivity, and the thermopower, with the electrical resistivity treated as approximately isotropic despite the tetragonal crystal structure. The thermal transport discrepancy is specific to the electronic thermal resistivity in the Fermi liquid regime, and the electron-phonon explanation is presented as a possible mechanism rather than a demonstrated resolution.

For readers weighing this paper, the decisive comparison is not whether DFT+DMFT gets RuO2 broadly right, but which observable it fails on and by how much. The charge transport coefficients agree semi-quantitatively, while the thermal resistivity coefficient is off by a factor of 2 to 7 and the Kadowaki-Woods ratio stays below the experimental value regardless of interaction parameters. That split, rather than the overall agreement, is what makes RuO2 a useful platform for testing many-body electronic structure theory.

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