Robust insensitivity of heterogeneous charge distribution and interlayer friction to strong external electric fields in twisted graphene bilayers

Twisted graphene bilayers exhibit rich physical phenomena under external fields, yet the coupled effect of electric fields and interlayer sliding on their charge distribution remains elusive. By combining first-principles calculations with a machine learning technique, we systematically investigate interlayer sliding-induced charge transfer and redistribution in both twisted and AB-stacked graphene bilayers under vertical electric fields. Unlike the homogeneous charge distribution observed in AB-stacked bilayers, the heterogeneous charge distribution in certain twisted graphene bilayers exhibits robust insensitivity to applied electric fields, even under strong fields up to 2 V/nm. This field insensitivity enables such twisted bilayers to maintain ultralow interlayer friction under extreme bias conditions. To quantitatively describe the coupled effect of interlayer sliding and electric fields on interlayer charge transfer and friction, we develop a charge-modified registry index (RI_CM) model for graphene bilayers. The revealed electric-field insensitivity in specific twisted configurations can be mainly attributed to the inherently small variation in the maximum registry index change (∆RI_CM) under bias, providing a simple descriptor for designing low-friction interfaces in electrically gated graphene devices.