  The introduction of 'twist' or relative rotation between two atomically thin
van der Waals (vdW) membranes gives rise to periodic Moire potential, leading
to a substantial altercation of the band structure of the planar assembly.
While most of the recent experiments primarily focus on the electronic-band
hybridization by probing in-plane transport properties, here we report
out-of-plane thermoelectric measurements across the van der Waals gap in
twisted bilayer graphene (tBLG), which exhibits an interplay of twist-dependent
inter-layer electronic and phononic hybridization. We show that at a large
twist angle, the thermopower is entirely driven by a novel phonon drag effect
at the sub-nanometer scale, while the electronic component of the thermopower
is recovered only when the misorientation between the layers is reduced to less
than two degrees. Our experiment shows that cross-plane thermoelectricity at a
low angle is exceptionally sensitive to the nature of band dispersion and may
provide fundamental insights into the coherence of electronic states in twisted
bilayer graphene.
