  Twisted van der Waals bilayers provide an ideal platform to study the
electron correlation in solids. Of particular interest is the 30 degree twisted
bilayer honeycomb lattice system, which possesses an incommensurate moire
pattern and uncommon electronic behaviors may appear due to the absence of
phase coherence. Such system is extremely sensitive to further twist and many
intriguing phenomena will occur. In this work, based on first-principles
calculations we show that, for further twist near 30 degree, there could induce
dramatically different dielectric behaviors of electron between left and right
twisted cases. Specifically, it is found that the left and right twists show
suppressed and amplified dielectric response under vertical electric field,
respectively. Further analysis demonstrate that such exotic dielectric property
can be attributed to the stacking dependent charge redistribution due to twist,
which forms twist-dependent pseudospin textures. We will show that such
pseudospin textures are robust under small electric field. As a result, for the
right twisted case, there is almost no electric dipole formation exceeding the
monolayer thickness when the electric field is applied. Whereas for the left
case, the system could even demonstrate negative susceptibility, i.e. the
induced polarization is opposite to the applied field, which is very rare in
the nature. Such findings not only enrich our understanding on moire systems
but also open an appealing route toward functional 2D materials design for
electronic, optical and even energy storage devices.
