Strange Metal in Magic-Angle Graphene with near Planckian Dissipation

Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. Here we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems—a broad regime of $T$-linear resistivity above a small density-dependent crossover temperature—for a range of fillings near the correlated insulator. This behavior is reminiscent of similar behavior in other strongly correlated systems, often denoted “strange metals,” such as cuprates, iron pnictides, ruthenates, and cobaltates, where the observations are at odds with expectations in a weakly interacting Fermi liquid. We also extract a transport “scattering rate,” which satisfies a near Planckian form that is universally related to the ratio of $(k_{B}T/\hslash )$. Our results establish magic-angle bilayer graphene as a highly tunable platform to investigate strange metal behavior, which could shed light on this mysterious ubiquitous phase of correlated matter.

Figure 1

Transport in MABLG. (a) Device schematic and four-probe transport measurement configuration (left). (Top right) Side view of the device structure, consisting of bilayers of graphene twisted by $\theta$ relative to each other, sandwiched by hBN on the top and bottom. The carrier density is tuned using the metal gates at the top and bottom. (Bottom right) Schematic MABLG moiré pattern. (b) A schematic phase diagram for MABLG as a function of temperature and filling $\nu$. The strange metal behavior with $T$-linear resistivity is primarily restricted to fillings near $\nu =\pm 2$. Orange regions denote superconductivity. Light blue regions denote the correlated insulator region. The color bars indicate the approximate filling ranges investigated and shown in (c) and (d). (c) Resistivity ($\rho$) as a function of temperature for device MA1 ($\theta =1.16^{\mathrm{°}}$) for gate-induced densities from $-1.96\times {10}^{12}$ (blue) to $-1.22\times {10}^{12}{\mathrm{cm}}^{-2}$ (red); see horizontal color bar near $\nu =-2$ in (b). (d) $\rho (T)$ for device MA4 ($\theta =1.18^{°}$) for gate-induced densities ranging from $1.23\times {10}^{12}$ (blue) to $1.89\times {10}^{12}{\mathrm{cm}}^{-2}$ (red); see horizontal color bar near $\nu =+2$ in (b). (Inset) Traces for the same device at low temperatures. The solid smooth lines have been obtained by using a Gaussian-weighted filter.

Figure 2

$T$-linear resistivity near $\nu =\pm 2$ in MABLG. (a) Resistivity ($\rho$) as a function of temperature for device MA3 ($\theta ={1.09}^{°}$) and MA4 ($\theta ={1.18}^{°}$) at a gate-tuned density of $-1.46\times {10}^{12}{\mathrm{cm}}^{-2}$ ($\nu =-2-\delta$) and $1.19\times {10}^{12}{\mathrm{cm}}^{-2}$ ($\nu =2-\delta$), respectively. (Inset) $\rho (T)$ in $\mathrm{\Omega }/\mathrm{K}$ for MLG on ${\mathrm{SiO}}_2$ (green) and hBN (blue), respectively (data from [33, 34]). (b) The slopes $A=d\rho /dT$ obtained at the fillings near $\nu =\pm 2\pm \delta$ with optimal superconducting $T_c$ for six different devices (MA1–MA6) as a function of respective twist angles. Orange (cyan) markers denote fillings with $\nu >0$ ($\nu <0$), while solid (empty) symbols denote deviations, $\delta >0$ ($\delta <0$), away from the correlated insulators at $\nu =\pm 2$. (Inset) Extrapolated resistivity ${\rho }_0$ for the same devices. (c) $\rho (T)$ for device MA4 near $\nu =-1/2$ for gate-induced densities $-0.51\times {10}^{12}{\mathrm{cm}}^{-2}$ (blue) to $-0.29\times {10}^{12}{\mathrm{cm}}^{-2}$ (red). The data look similar near $\nu =+1/2$. (Inset) $\rho (T)$ for the same device near $\nu =0$ and densities between $-0.13\times {10}^{12}{\mathrm{cm}}^{-2}$ (blue) and $0.13\times {10}^{12}{\mathrm{cm}}^{-2}$ (red). (d) $\rho (T)$ for device MA4 near $\nu =-3/2$ for gate-induced densities from $-1.28\times {10}^{12}{\mathrm{cm}}^{-2}$ (blue) to $-1.08\times {10}^{12}{\mathrm{cm}}^{-2}$ (red). (Inset) $\rho (T)$ for device MA4 near $\nu =+3/2$ from $1.08\times {10}^{12}{\mathrm{cm}}^{-2}$ (blue) to $1.28\times {10}^{12}{\mathrm{cm}}^{-2}$ (red).

Figure 3

Planckian scattering in magic-angle bilayer graphene. (a) Resistivity as a function of temperature for device MA2 ($\theta ={1.03}^{°}$) near $\nu =-2$ for gate-tuned densities from $-1.539\times {10}^{12}{\mathrm{cm}}^{-2}$ (blue) to $-1.113\times {10}^{12}{\mathrm{cm}}^{-2}$ (red). The correlated insulator at $\nu =-2$ is approximately located near $-1.3\times {10}^{12}{\mathrm{cm}}^{-2}$. The solid smooth lines have been obtained by using a Gaussian-weighted filter. (b) (Left axis) Slope of resistivity as a function of filling above 8K for the same device evaluated using a linear fit. (Right axis) The coefficient $C$ of the scattering rate $\mathrm{\Gamma }=C{k}_{B}T/\hslash$ for the same range of fillings.