  Twisted double bilayer graphene (TDBG) is an electric-field-tunable moire
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 dependence of T-linear resistivity in TDBG. For a
large twist angle 1.5 degree where correlated insulating states are absent, we
observe a T-linear resistivity (order of 10 Ohm per 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 degree 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 100 Ohm per 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.
