Hugh's knowledge graph identified a gap asking: if T-linear strange-metal behavior in La3Ni2O7 arises from quantum critical fluctuations rather than Planckian dissipation, would that force a revision of universal scaling laws for unconventional superconductors? This framing assumes quantum criticality and Planckian dissipation are competing explanations. They are not.
Gleis, Lee, Kotliar, and von Delft demonstrated via two-site cellular dynamical mean-field theory (2CDMFT) that at a Kondo-breakdown quantum critical point (KB QCP) of the periodic Anderson model, the dynamical staggered-spin susceptibility exhibits omega/T scaling. The current susceptibility follows the same scaling, producing T-linear resistivity. The longest-lived coherent excitations at the QCP have exactly Planckian lifetimes. Crucially, this behavior is driven by strong short-ranged vertex contributions to the current-current correlator, not by single-particle decay rates.
This result dissolves the binary. Quantum critical fluctuations at the KB QCP produce Planckian dissipation as a consequence, not as an alternative. The question is no longer which mechanism causes T-linear resistivity. The question is whether the specific mechanism identified in heavy-fermion systems generalizes beyond f-electron compounds to d-electron systems with flat bands. La3Ni2O7 under pressure is the test case.
In heavy-fermion systems, the periodic Anderson model describes localized f-electrons hybridizing with a dispersive conduction band. At the KB QCP, the hybridization collapses: the Fermi surface volume jumps as f-electrons decouple from the conduction sea. The non-Fermi liquid regime near this QCP exhibits omega/T scaling in the spin susceptibility. Results match experimental observations on YbRh2Si2 and CeCoIn5.
For La3Ni2O7, the mapping requires the following correspondences:
Localized electrons: In heavy fermions, these are 4f or 5f electrons. In La3Ni2O7, the system features strong electronic correlations which significantly reduce the electron's kinetic energy, placing it in proximity to the Mott phase. The correlated electrons occupy Ni-3d orbitals. Below T* ~ 115K, the transition removes the Drude component exhibiting non-Fermi liquid behavior. This loss of coherence in one orbital channel is structurally analogous to the Kondo breakdown where f-electrons decouple from conduction electrons.
Conduction band: In heavy fermions, this is a dispersive sp-band. In La3Ni2O7, the bilayer structure produces bonding and antibonding combinations of the d-z2 orbitals across the two NiO2 layers. The resulting band structure includes flat bands near the Fermi level, which fundamentally changes the density of states compared to heavy-fermion systems.
Quantum critical point: In heavy fermions, this is the Kondo-breakdown QCP where hybridization vanishes. In La3Ni2O7, the pressure-induced transition from density-wave order to superconductivity passes through a strange-metal regime with T-linear resistivity persisting to 300K. The normal state at high pressure shows behavior consistent with proximity to a QCP adjacent to the superconducting phase.
T-linear resistivity: Zhang et al. confirmed zero-resistance superconductivity near 80K in single crystals under pressure, with the normal state exhibiting T-linear resistance. The association between strange-metal behavior and high-temperature superconductivity is consistent with cuprates and Fe-based superconductors.
Flat bands vs. dispersive bands. The bonding/antibonding d-z2 bands in the bilayer produce a flat-band-dominated low-energy landscape. In heavy-fermion 2CDMFT, the conduction band provides a featureless density of states. A flat band concentrates spectral weight at a single energy, which changes how the vertex function enters the current susceptibility. The bubble diagram is suppressed for flat bands because the group velocity vanishes. Transport then depends entirely on vertex corrections, but the structure of those corrections in a flat-band system has not been computed.
Orbital selectivity. The Mott-proximate state involves orbital-selective correlations: the d-z2 orbital loses coherence at T* while the d-x2-y2 orbital remains itinerant. In the periodic Anderson model, there is one localized orbital and one conduction band. The two-orbital structure means the Kondo-breakdown transition, if it occurs, happens in one orbital channel while the other remains coherent. Whether the vertex-dominated scaling survives when only one of two orbital channels breaks down is an open question requiring a multi-orbital extension.
Interlayer coupling. The bilayer structure introduces a new energy scale: the interlayer hopping between NiO2 planes. This has no analogue in the single-site periodic Anderson model. The interlayer coupling generates the bonding/antibonding splitting that creates the flat band. The phase diagram topology may differ qualitatively, producing a first-order transition rather than a continuous QCP, which would destroy the omega/T scaling.
The decisive measurement is optical conductivity on pressurized La3Ni2O7 in the strange-metal regime (T > Tc ~ 80K, P > 14 GPa).
If the Kondo-breakdown vertex mechanism generalizes: the real part of the optical conductivity should exhibit omega/T scaling with the same functional form as observed in YbRh2Si2 and CeCoIn5. The optical scattering rate should be linear in both omega and T with the same slope (Planckian rate). The optical mass should show logarithmic enhancement at low frequencies.
If the flat-band structure introduces new physics: the scaling function will deviate from the heavy-fermion form. Two specific signatures: (a) the low-frequency plateau may be replaced by a power-law onset with exponent alpha != 0; (b) the crossover frequency may scale as T^beta with beta != 1, indicating a different dynamical critical exponent. Additionally, the universal correlation between H-linear magnetoresistance and T-linear resistivity provides a second test.
If the mechanism generalizes: Planckian dissipation at quantum critical points is universal across f-electron and d-electron systems. The KB QCP is a genuine fixed point of the renormalization group for interacting electron systems regardless of orbital character. Strange metallicity is a phase, not a materials property. Engineering a quantum critical point with the right symmetry becomes a design criterion for high-Tc materials.
If it does not generalize: Flat-band physics introduces a distinct universality class for strange metals. Nickelate superconductivity requires its own theoretical framework that accounts for orbital-selective Mott breakdown in a bilayer geometry. The room-temperature superconductor search bifurcates into heavy-fermion-like and flat-band-like routes with different design rules.
What this analysis establishes regardless: Hugh's original gap question was framed as quantum criticality versus Planckian dissipation. The 2025 PRL collapses that binary for heavy fermions. The remaining question is whether the collapse extends to d-electron flat-band systems. This is a sharper question with a specific experimental test and two falsifiable predictions.
Output type: Bridge construction. Outcome: PARTIAL. The mapping from heavy-fermion Kondo-breakdown to nickelate orbital-selective Mott breakdown is structurally motivated and consistent with existing data, but three formal steps remain uncomputed: (1) the two-particle vertex in a flat-band 2CDMFT, (2) the multi-orbital extension of the KB QCP with selective breakdown, and (3) the effect of interlayer coupling on the QCP topology. The experimental prediction is concrete and testable.
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