Superconductors’ Unusual Electrical Behaviour Linked to Fundamental Quantum State

Scientists are investigating the microscopic origins of the quantum critical Planckian strange metal phase observed in strongly correlated materials, a phase from which unconventional superconductivity emerges at lower temperatures. K. Remund, K. V. Nguyen, and P. -H. Chou, working at the Physics Division, National Center for Theoretical Sciences in Taipei, alongside P. Giraldo-Gallo, J. A. Galvis, G. S. Boebinger, and C. -H. Chung, who has affiliations with both the National Center for Theoretical Sciences and National Yang Ming Chiao Tung University in Hsinchu, demonstrate the universality of linear-in-temperature and linear-in-field Planckian scattering rates in underdoped cuprate superconductors. This research is significant because it establishes a coherent understanding of these coexisting linear behaviours, linking them to quantum criticality through a spin-based mechanism and offering a unified explanation for Planckian transport in these materials over a broad doping range.

Scientists have uncovered a universal connection between two puzzling behaviours in high-temperature cuprate superconductors, materials with the potential to revolutionize energy transmission; these materials exhibit both electrical resistivity that increases linearly with temperature and resistivity that increases linearly with magnetic field, a phenomenon known as magnetoresistivity. This simultaneous occurrence, and its scaling with both temperature and magnetic field, has long lacked a unifying explanation. This work establishes that these linear behaviours are fundamentally linked, suggesting a common origin rooted in quantum criticality. Experimentally, researchers meticulously examined underdoped lanthanum strontium copper oxide (LSCO), a model cuprate, and confirmed the existence of a linear-in-field Planckian scattering rate, a measure of how electrons lose energy, and its direct relationship to the already-known linear-in-temperature scattering rate. This model suggests that the magnetic field introduces an energy scale similar to that observed near quantum critical points, leading to the observed scaling of resistivity with both temperature and field. Across the doping range of 0.16 to 0.19, the research demonstrates a linear relationship between magnetic field and Planckian scattering rate, quantified by a scaling function with ζ ≈ 3.06. This function accurately describes both the field-dependent scattering and the temperature-dependent scattering observed in previous studies, establishing universality in these Planckian behaviours. Experimentally determined values for the temperature-linear Planckian coefficient, αT, consistently fall around 2.6, while the field-linear coefficient, αB, is approximately 1.4. These values align closely with theoretical predictions of 8/π (approximately 2.54) for αT and 4/π (approximately 1.27) for αB, with the theoretical framework agreeing within approximately 25% of the experimental αT measurements. The ratio of αT to αB remains consistently near 2 across the studied doping range. Analysis of low-temperature magneto-resistivity reveals a doping-insensitive Planckian coefficient, αB, calculated as ħ(ω²p/4π)A₁B/μB, where ω²p represents the plasma frequency and μB is the Bohr magneton. The research establishes a correlation between the slopes of temperature-linear and field-linear resistivities, with A₁T approximately equaling 2A₁B, a relationship also observed in other cuprate compounds exhibiting strange metal behaviour. Estimates of carrier density, n, and effective mass, m*, derived from optical conductivity measurements, provide a reliable basis for calculating these Planckian coefficients. A heavy-fermion formulated slave-boson t-J model serves as the foundation for this work, initially defined on a two-dimensional lattice. This Hamiltonian incorporates hopping strength (t), chemical potential (μ), and Heisenberg coupling (JH) to describe electron interactions. The methodology begins by mapping the hopping term using a Hubbard-Stratonovich transformation, effectively creating a Kondo-like coupling between disordered slave bosons and a fermionic spinon band. This transformation generates an effective conduction electron band comprised of spinon-holon bound fermions, residing on the bonds connecting nearest-neighbour sites. Subsequently, the anti-ferromagnetic Heisenberg exchange coupling is decomposed into Resonating-Valence-Bond (RVB) spin liquid singlets, encompassing both particle-hole and particle-particle d-wave Cooper pairing channels. This decomposition allows for the exploration of four distinct mean-field phases, determined by the condensation of slave bosons and d-wave pairing fields. The Planckian metal phase emerges within the U FL⋆ phase, arising from critical local charge Kondo fluctuations where disordered local bosons couple to a fermionic spinon band and a heavy-electron band near a localized-delocalized quantum critical point. To investigate the phase diagram beyond the mean-field level, fluctuations of both the t- and J-terms are included in the effective action. The research deliberately omits U gauge fluctuations, reasoning that the spinons remain deconfined and stable due to the presence of a spinon Fermi surface. A perturbative expansion in bare couplings g and J is then employed, controlled by the conditions g/D. Scientists have long sought a unifying explanation for the peculiar electrical behaviour observed in high-temperature superconductors, materials that promise revolutionary advances in energy transmission and computing. The challenge lies in understanding the ‘strange metal’ phase these materials exhibit, a state where electrical resistance increases linearly with temperature, a behaviour defying conventional metallic models. This linear resistance, coupled with a similar dependence on magnetic field, has been a persistent puzzle, hinting at a deeper, quantum-critical origin but lacking a clear microscopic mechanism. Detailed experimental work on lanthanum strontium copper oxide reveals this behaviour is remarkably consistent across a range of doping levels, strengthening the case for a universal underlying principle. What makes this work notable is not simply the confirmation of these linear relationships, but the proposed theoretical framework linking them to a specific type of quantum criticality involving ‘Kondo-like’ charge fluctuations. This elegantly connects the temperature and field dependencies, suggesting they both stem from the same fundamental physics, a local disruption of electron behaviour driven by interactions. While previous theories have touched on aspects of this, a unified explanation bridging both phenomena has remained elusive. However, the picture is not yet complete; the theoretical model relies on specific assumptions about the material’s electronic structure, and further investigation is needed to confirm its validity across different cuprate compounds. Moreover, the precise connection between this strange metal phase and the emergence of superconductivity at lower temperatures remains a key question. Future research will likely focus on refining the theoretical model, exploring other materials, and probing the interplay between these quantum fluctuations and the superconducting state itself, potentially paving the way for designing materials with even higher superconducting transition temperatures.