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.
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