  Twisted bilayer graphene (tBLG) devices with ion gel gate dielectrics are
studied using Raman spectroscopy in the twist angle regime where a resonantly
enhanced G band can be observed. We observe prominent splitting and intensity
quenching on the G Raman band when the carrier density is tuned away from
charge neutrality. This G peak splitting is attributed to asymmetric charge
doping in the two graphene layers, which reveals individual phonon self-energy
renormalization of the two weakly-coupled layers of graphene. We estimate the
effective interlayer capacitance at low doping density of tBLG using an
interlayer screening model. The anomalous intensity quenching of both G peaks
is ascribed to the suppression of resonant interband transitions between the
two saddle points (van Hove singularities), that are displaced in the momentum
space by gate-tuning. In addition, we observe a softening (hardening) of the R
Raman band, a superlattice-induced phonon mode in tBLG, in electron (hole)
doping. Our results demonstrate that gate modulation can be used to control the
optoelectronic and vibrational properties in tBLG devices.
