The scaled-invariant Planckian metal and quantum criticality in Ce$_{1-x}$Nd$_x$CoIn$_5$

Abstract: Perfect $T$-linear resistivity associated with universal scattering rate: $1/\tau =\alpha k_B T/\hbar$ with $\alpha \sim 1$, so-called Planckian metal state, has been observed in the normal state of a variety of strongly correlated superconductors close to a quantum critical point. However, the microscopic origin of this intriguing phenomena and its link to quantum criticality still remains an outstanding open problem. In this work, we observe the quantum-critical $T/B$-scaling of the Planckian metal state in the resistivity and heat capacity of heavy-electron superconductor Ce$_{1-x}$Nd$_x$CoIn$_5$ in magnetic fields near the edge of antiferromagnetism, driven by critical Kondo hybridization at the critical doping $x_c \sim 0.03$. We further provide the first microscopic mechanism to account for the Planckian state in a quantum critical system based on the critical charge fluctuations near Kondo breakdown transition at $x_c$ within the quasi-two-dimensional Kondo-Heisenberg lattice model. This mechanism simultaneously captures the observed universal Planckian scattering rate as well as the quantum-critical scaling and power-law divergence in thermodynamic observables near criticality. Our mechanism is generic to Planckian metal states in a variety of quantum critical superconductors near Kondo destruction.