Phonons and Quantum Criticality Revealed by Temperature Linear Resistivity in Twisted Double Bilayer Graphene

Twisted double bilayer graphene (TDBG) is an electric-field-tunable moiré system, exhibiting electron correlated states and related temperature linear (T-linear) resistivity. The displacement field provides a new knob to in-situ tune the relative strength of electron interactions in TDBG, yielding not only a rich phase diagram but also the ability to investigate each phase individually. Here, we report a study of carrier density (n), displacement field (D) and twist angle (θ) dependence of T-linear resistivity in TDBG. For a large twist angle (θ > 1.5°) where correlated insulating states are absent, we observe a T-linear resistivity (order of 10Ω/K) over a wide range of carrier density and its slope decreases with increasing of n before reaching the van Hove singularity, in agreement with acoustic phonon scattering model. The slope of T-linear resistivity is non-monotonically dependent on displacement field, with a single peak structure closely connected to single-particle van Hove Singularity (vHS) in TDBG. For an optimal twist angle of ~ 1.23° in the presence of correlated states, the slope of T-linear resistivity is found maximum at the boundary of the correlated halo regime (order of 100Ω/K), resulting a ‘M’ shape displacement field dependence. The observation is beyond the phonon scattering model from single particle picture, and instead it suggests a strange metal behavior. We interpret the observation as a result of symmetry-breaking instability developed at quantum critical points where electron degeneracy changes. Our results demonstrate that TDBG is an ideal system to study the interplay between phonon and quantum criticality, and might help to map out the evolution of the order parameters for the ground states.