Universality of linear in temperature and linear in field Planckian scattering rate in high temperature cuprate superconductors

One of the long standing puzzles in strongly correlated materials is the microscopic origin of the quantum critical Planckian strange metal phase with universal linear in temperature scattering rate from which unconventional superconductivity directly emerges by lowering temperatures. Recently, the linear in temperature and linear in field resistivity have been simultaneously observed in high temperature cuprate superconductors, manifested by the universal field to temperature scaling in magnetoresistivity. To date, there has been a lack of coherent and unified understanding of these coexisting linear behaviors and their possible link to quantum criticality. In this work, we establish the universality in linear in temperature and linear in field Planckian behaviors in underdoped LSCO near optimal doping. Experimentally, we observe the linear in field Planckian scattering rate and its relation to its linear in temperature counterpart. Theoretically, we propose a spin based common microscopic mechanism based on Kondo-like charge fluctuations near local quantum criticality of heavy fermion formulated tJ model subject to a Zeeman term. Similar to frequency to temperature scaling near quantum criticality, we find the magnetic field here effectively introduces a Zeeman energy, reminiscent of an external energy in the quantum critical regime, leading to field to temperature scaling. Our analytically predicted universal field to temperature scaling in isotropic scattering rate and the relation between the linear in temperature and linear in field Planckian coefficients, unifies these two phenomena over an extended doping range, pointing toward a unified quantum-critical origin of Planckian transport in cuprates.

💡 Research Summary

The paper addresses a long‑standing puzzle in strongly correlated materials: the microscopic origin of the “Planckian” strange‑metal phase, characterized by a universal linear‑in‑temperature (T‑linear) scattering rate that exceeds the Mott‑Ioffe‑Regel limit and from which unconventional superconductivity emerges upon cooling. Recent experiments have revealed that, in high‑Tc cuprates, the resistivity is simultaneously linear in temperature and linear in magnetic field (B‑linear), and that the magnetoresistance obeys a universal B/T scaling. However, a coherent theoretical framework that unifies these two linear behaviors has been lacking.

Experimental Findings
The authors focus on La₂₋ₓSrₓCuO₄ (LSCO) with doping p≈0.19, close to optimal doping. Using pulsed magnetic fields up to >60 T and temperatures down to 2 K, they measure the in‑plane resistivity ρ(B,T). The data separate cleanly into a temperature‑only part ρ₀(T)=c₀+c₁T and a combined field‑temperature contribution that can be written as

ρ(B,T)=ρ₀(T)+k_B T μ_B Φ(μ_B B/k_B T),

with the scaling function Φ(x)=x γ coth(ζ x/2). The parameters γ and ζ are obtained from fits; γ controls the high‑field slope (∂ρ/∂B) and ζ determines the crossover from T‑linear to B‑linear regimes. In the high‑field limit (μ_B B≫k_B T) the magnetoresistance becomes linear in B with a coefficient α_B≈1, while in the zero‑field limit the resistivity is linear in T with a coefficient α_T≈2.5. Crucially, the same scaling function describes the entire dataset, demonstrating a robust B/T scaling that violates the conventional Kohler’s rule (which predicts a quadratic B dependence).

Theoretical Framework
To explain these observations, the authors adopt a recently developed heavy‑fermion formulation of the t‑J model, expressed in slave‑boson language. In this picture, the physical electron fractionalizes into a charge‑neutral spinon and a spinless holon (slave boson). The hopping term t becomes an effective Kondo‑like hybridization between a disordered slave boson field and the spinon band, while the antiferromagnetic exchange J generates resonating‑valence‑bond (RVB) spin‑liquid correlations. Near a local quantum‑critical point (QCP) associated with Kondo‑breakdown, charge fluctuations of the slave boson become critical and produce a self‑energy that is essentially coupling‑independent (a “local” marginal Fermi‑liquid form).

The key insight is that, in the strange‑metal regime, the orbital effect of a magnetic field is negligible (ω_c τ≪1). Instead, the Zeeman splitting of the spinon and holon bands dominates. The Zeeman energy μ_B B therefore plays the same role as an external frequency ω in the usual ω/T scaling of quantum critical systems. By performing a conformal mapping of the zero‑field self‑energy to finite temperature and finite Zeeman field, the authors derive an analytic expression for the field‑dependent scattering rate:

ℏ/τ_B – ℏ/τ₀(T) = 2π k_B T