A new numerical study published in Nature Physics by Simone Fratini, Ivan Duchemin, Arnaud Ralko and Sergio Ciuchi now offers a strikingly simple answer. Working within the two-dimensional t–J model, the canonical minimal model of doped Mott insulators used to describe cuprate superconductors, the team shows that strange metallicity is not an exotic phase requiring special ingredients. Instead, it emerges pervasively across the temperature-doping phase diagram whenever antiferromagnetic order is suppressed. The strange metal, in their results, is the natural descendant of the bad metal that underlies it, and its hallmark properties follow from the quantum statistics of the charge carriers rather than from any special temperature dependence of the processes that scatter them.

The bad metal concept, introduced in the early 2000s, describes a regime in which the electrical resistivity exceeds the Mott–Ioffe–Regel limit, the value at which an electron’s mean free path becomes comparable to its own wavelength. In such a regime, the very notion of a well-defined quasiparticle travelling between collisions breaks down, and transport must be understood through more general principles of quantum diffusion. Bad metallicity had been observed in numerical studies of doped Mott insulators for years, but its relationship to the strange metal phenomenology of the cuprates, with its linear resistivity and Planckian dissipation, remained ambiguous. The new work argues that the two are, in a precise sense, the same phenomenon viewed at different levels of description.

The technical achievement that makes this conclusion possible lies in recent improvements to the finite-temperature Lanczos method, a numerically exact technique for computing the thermodynamic properties of strongly correlated lattice models at finite temperature. The Lanczos approach works by iteratively building a small set of basis vectors that span the low-energy part of the Hilbert space, allowing accurate evaluation of correlation functions without ever handling the exponentially large full space. Recent methodological advances, building on decades of development since the original finite-temperature Lanczos work of the 1990s, now enable exact calculations at low temperatures and with high spectral resolution, precisely the regime where strange metal behaviour lives and where earlier approximations faltered.

Using this machinery, the researchers computed both the direct-current and the frequency-dependent conductivity of the two-dimensional t–J model across a broad range of temperatures and dopings. The t–J model describes holes moving through an antiferromagnetic background of spin-one-half particles, with a superexchange coupling J between neighbouring spins and a hopping amplitude t that is strongly constrained by the no-double-occupancy condition. This constraint, a remnant of the large on-site repulsion of the underlying Hubbard model, is what makes the model so difficult and so rich. It is also, according to the new results, what makes it strange: the interplay of quantum statistics and the constrained motion of carriers produces transport that looks Planckian without requiring any exotic scattering mechanism.

A central question in the strange metal literature concerns the origin of Planckian relaxation, the observation that the scattering time in these materials is of order ħ divided by the Boltzmann constant times temperature, the fastest timescale that quantum mechanics permits for a thermal system. Some theorists have proposed that Planckian behaviour signals proximity to a quantum critical point, where fluctuations occur at all scales and times. Others have pointed to spatially random interactions, to spin fluctuations, or to specific scattering channels as the culprit. The new study addresses this question directly by extending the analysis into the frequency and time domains, where the dynamics of the charge response can be watched as it unfolds rather than merely inferred from the final resistivity.

What emerges from this time-resolved picture is that Planckian behaviour is rooted in the quantum statistical nature of the charge response itself. The carriers in the doped antiferromagnet are incoherent from the outset, and their transport is governed by the statistical mechanics of a dense quantum fluid rather than by the collision history of individual particles. The temperature dependence of the scattering processes, which in conventional thinking would determine the resistivity, turns out to play a secondary role. In effect, the strange metal does not become strange because something unusual starts scattering its electrons at high temperatures; it is strange because the carriers were never the well-behaved quasiparticles of Fermi liquid theory in the first place.

This reframing has significant implications for how physicists interpret experiments on the cuprates and related materials. The linear-in-temperature resistivity observed over wide doping ranges in compounds such as La2−xSrxCuO4 and Bi-based cuprates has often been treated as a fingerprint of a specific mechanism, to be isolated and identified. If the new numerical results are a faithful guide, the linear resistivity instead reflects a generic property of doped Mott insulators once long-range magnetic order gives way to a quantum paramagnet. The experimental phase diagrams of the cuprates, in which the strange metal region tracks the suppression of antiferromagnetism and the pseudogap boundary, are consistent with this picture, and recent measurements of spin-charge correlations at the onset of the pseudogap add further context for testing it.

The study also connects to a broader theoretical programme aimed at understanding transport in systems where quasiparticles fail. Previous work on the Hubbard model, on extremely correlated Fermi liquid theory, and on random-interaction models of strange metals has each highlighted different aspects of non-quasiparticle transport. By demonstrating that a single, well-defined minimal model reproduces the full phenomenology, from bad metallicity at high temperatures to Planckian strange metal behaviour at lower temperatures, the new results provide a unifying numerical benchmark against which analytical theories can be tested. The authors have made both their data and their code publicly available on GitHub, lowering the barrier for other groups to verify and extend the calculations.

For the field of quantum materials, the message is both humbling and clarifying. The strange metal, the state that parents high-temperature superconductivity and has resisted explanation since the discovery of the cuprates in 1986, may not require new particles, hidden criticality, or exotic interactions. It may simply be what a strongly correlated quantum fluid looks like when the usual quasiparticle picture is abandoned and the quantum statistics of the carriers are taken seriously. If further work confirms that the t–J model captures the essential physics, the path toward a complete theory of the cuprates becomes clearer: understand the constrained quantum statistics of doped antiferromagnets, and the strange metal, along with perhaps the superconductivity that emerges from it, will follow. The puzzle is far from solved, but the new results suggest that the answer may have been hiding in one of the oldest and simplest models in the theorist’s toolkit.

Subject of Research: The microscopic origin of strange metal behaviour and Planckian transport in doped Mott insulators

Article Title: Strange metal behaviour from underlying bad metallicity

Article References: Fratini, S., Duchemin, I., Ralko, A., & Ciuchi, S. (2026). Strange metal behaviour from underlying bad metallicity. Nature Physics. https://doi.org/10.1038/s41567-026-03441-x

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03441-x

Keywords: strange metal, bad metal, Planckian dissipation, t–J model, cuprates, high-temperature superconductivity, Mott insulator, finite-temperature Lanczos method, quantum statistics, antiferromagnetism, electrical resistivity, strongly correlated electrons

The material at the heart of the study is a bilayer nickelate, a compound in which pairs of nickel-oxide planes are stacked with a spacing of just a few angstroms. In these structures, each nickel atom sits at the center of an oxygen octahedron, and the electronic states near the Fermi level are dominated by nickel 3d orbitals. Two of these orbitals matter most. The dx2-y2 orbital extends within each plane and governs the in-plane conduction, much as it does in cuprate superconductors. The dz2 orbital, by contrast, points along the crystallographic c axis, out of the plane, and can overlap with the pz orbitals of apical oxygen atoms sitting above and below the nickel. This overlap creates a potential pathway for electrons to hop coherently from one layer to its partner in the bilayer.

Theoretical work had long suggested that this interlayer channel could be crucial. Calculations published since 2023 proposed that pressure-driven changes in the bilayer structure enhance dz2 orbital character at the Fermi level, enabling interlayer pairing mechanisms that range from s-wave states with sign changes between sheets of the Fermi surface to interlayer valence bond scenarios. But theory alone could not settle the matter, because the experiments needed to test these ideas, soft X-ray absorption spectroscopy and resonant inelastic X-ray scattering, are notoriously difficult to perform on superconducting nickelate samples. The materials are chemically sensitive, their surfaces degrade in air, and the superconducting fraction within bulk crystals is often inhomogeneous, making it hard to attribute spectroscopic signatures unambiguously to the superconducting phase.

The Chinese-led collaboration overcame this obstacle with a clever materials engineering strategy. They grew thin films of the bilayer nickelate (La,Pr)3Ni2O7 by pulsed laser deposition and protected them with a capping layer that preserves the delicate oxygen stoichiometry of the buried superconducting layers. Crucially, the team prepared a series of films spanning three distinct electronic ground states: insulating, metallic and superconducting. This controlled family of samples gave the researchers something no single superconducting crystal could provide, namely the ability to track how the electronic structure evolves as the material crosses from one quantum state to another, isolating the features that appear only when superconductivity does.

With the capped films in hand, the researchers deployed the full arsenal of modern synchrotron spectroscopy. X-ray absorption spectroscopy at the oxygen K edge and the nickel L3 edge probed the unoccupied electronic states, revealing the orbital character of the charge carriers. Resonant inelastic X-ray scattering, or RIXS, at the nickel L3 edge then measured the energy and momentum resolved spectrum of orbital excitations and spin excitations, the collective magnetic fluctuations that many theorists believe mediate pairing in unconventional superconductors. Resonant elastic X-ray scattering complemented these measurements by detecting static magnetic order, specifically the spin-density-wave order that competes with superconductivity in these compounds.

The results paint a coherent and strikingly clear multiorbital picture. Across all samples, the in-plane electronic structure is built from itinerant dx2-y2 states, which form the conductive backbone of the material regardless of whether the sample insulates, conducts or superconducts. What separates the superconductors from the rest is the out-of-plane channel. Only in the superconducting films did the spectra show evidence of coherent dz2-pz-dz2 hybridization, meaning that the dz2 orbitals on nickel atoms in adjacent layers, linked through the apical oxygen pz orbitals, merge into well-defined bonding and antibonding bands that straddle the bilayer. In the insulating and metallic samples, this interlayer coherence is absent or incoherent, and the two layers effectively fail to form a unified electronic entity.

The magnetic data reinforce the same conclusion. In the non-superconducting samples, static spin-density-wave order is prominent, indicating that electrons are locked into a periodic magnetic texture that gaps out parts of the Fermi surface and suppresses coherent metallic behavior. As the samples move into the superconducting regime, this static spin order is suppressed, and the spin excitations measured by RIXS become strongly damped, their spectral weight broadening and softening in a manner reminiscent of the paramagnons observed in cuprate superconductors. The coexistence of coherent interlayer hybridization, suppressed static magnetism and heavily damped but persistent spin fluctuations defines the narrow window in which superconductivity emerges, suggesting that magnetic fluctuations surviving the collapse of long-range order may still contribute to the pairing interaction.

Perhaps the most practically important finding concerns the tuning knobs that control the interlayer channel. The researchers found that both oxygen stoichiometry and epitaxial strain, the mechanical distortion imposed on the film by the underlying substrate, directly modulate the strength of the dz2-pz-dz2 hybridization. Oxygen vacancies disrupt the apical oxygen network that mediates the interlayer hopping, while strain alters the geometry of the octahedra and the spacing between layers. Because both parameters tune the same orbital channel, superconductivity in bilayer nickelates occupies only a narrow regime of interlayer coherence, explaining why samples grown or treated slightly differently can show wildly different transport behavior. This insight offers a concrete design rule for future experiments: optimize the apical oxygen environment and the interlayer spacing, and the superconducting fraction and transition temperature should follow.

The broader significance of this work lies in how it positions the nickelates relative to the cuprates. In cuprate superconductors, superconductivity is widely understood through a single-band picture in which doped holes in the dx2-y2 orbital pair through antiferromagnetic fluctuations, with the famous Zhang-Rice singlet capturing the essential physics. The bilayer nickelates refuse to fit into that framework. Their superconductivity requires simultaneous coherence in two orbital channels, an in-plane itinerant channel and an out-of-plane hybridized channel, making them genuinely multiorbital superconductors. This complexity is not a nuisance but an opportunity, because it adds new adjustable degrees of freedom, orbital occupancy, interlayer hopping and Hund’s rule coupling, that have no direct analogue in the cuprates and could in principle be exploited to push transition temperatures higher.

The path forward is now well marked. Thin film growth, already proven capable of ambient-pressure superconductivity in these materials, provides the platform for systematic strain engineering, while oxygen recycling protocols allow fine control of the apical oxygen network. Spectroscopists can now interrogate genuine superconducting samples rather than inferring properties from non-superconducting relatives, and the identification of coherent interlayer hybridization as the superconducting enabler gives theorists a sharp target for microscopic models of the pairing mechanism. If the nickelates continue to follow the trajectory that this study illuminates, the dream of a new family of high-temperature superconductors, one built not on a single orbital but on the quantum coupling of paired atomic planes, looks increasingly within reach.

Subject of Research: The role of interlayer orbital hybridization in superconductivity of bilayer nickelate thin films

Article Title: Interlayer hybridization promotes superconductivity in bilayer nickelates

Article References: Zhang, S., Zhang, M., Luo, Q., Tao, Z., Huang, H.-Y., Weschke, E., Li, K., Channagowdra, G., Li, J., Fu, J., Huang, D.-J., Xie, Y., Lu, Y., & Peng, Y. (2026). Interlayer hybridization promotes superconductivity in bilayer nickelates. Nature Materials. https://doi.org/10.1038/s41563-026-02750-z

Image Credits: AI Generated

DOI: 10.1038/s41563-026-02750-z

Keywords: bilayer nickelates, superconductivity, interlayer hybridization, dz2 orbital, resonant inelastic X-ray scattering, X-ray absorption spectroscopy, spin-density wave, thin films, oxygen stoichiometry, epitaxial strain, multiorbital physics, cuprates