Electron transport properties of order-disorder separated two-dimensional bilayer systems

Abstract

In the framework of the electronic tight-binding model of order-disorder separated (ODS) bilayer square lattice (BSL) and by calculating the density of states (DOS), participation number of eigen-wavefunctions and quantum diffusion, we systematically study the effects of stacking interface structure, strength of interlayer coupling and degree of disorder on the electron transport properties of order-disorder separated two-dimensional bilayer systems. Our results show that for the ODS-BSL of <i>AA</i>-stacking in the regime of weak coupling, the ODS-BSL always possesses a single energy band with localized states in its band tail, and extended states or critical states similar to the extended ones in the band center region with persistent metal-insulator transitions and associated mobility edges under strong disorder. In the regime of strong coupling, weak disorder leads the critical states to exist in its band tails and extended states to occur in the band center regions, while strong disorder results in the formation of a single band due to the overlapping of the coupling-induced two bands with localized states in the band tails and critical states in the band center region with increasing participation numbers as disorder increases. The ODS-BSL of <i>AB</i>-stacking always possesses a single band and supports extended states and critical states in its band center region, regardless of the strengths of interlayer coupling and disorder. In both ODS-BSL systems of <i>AA</i>- and <i>AB</i>- stackings, quantum diffusion undergoes an anomalous transition from weakening to enhancing behaviors as disorder increases. In the <i>AA</i>-stacking ODS-BSL of weak coupling, <i>AA</i>-stacking ODS-BSL of weak disorder and the <i>AB</i>-stacking ODS-BSL, quantum diffusion exhibits super-diffusion due to the contribution of extended states and the critical states similar to extended ones. In the <i>AA</i>-stacking ODS-BSL of strong coupling, quantum diffusion undergoes sub-diffusion under strong disorder due to the existence of critical states. The numerical results also show that the order-disorder separated (ODS) bilayer hexagonal lattice exhibits the same behaviors as those revealed in ODS-BSL systems.