▎ 摘　　要

The preparation of an atomically thin sheet of graphene/h-BN (GBN) hybrid with lack of defects is almost unachievable as in three dimensional crystals. Here, we first discussed the stability and electronic properties of GBN hybrid nanosheet which is formed by implanting a diamond shaped graphene (G) island into the hexagonal boron nitride (h-BN) layout. We further investigated the effects of mono vacancy on the electronic and magnetic properties of defective GBN nanosheet. The band gap of pristine hybrid decreases with growing G island as expected and the island induces flat (dispersionless) energy bands near the Fermi energy of the h-BN nanosheet. We searched for the energetics of 7 distinct C, B and N mono vacancies created at various places such as h-BN region, G region and interface of the optimized pristine hybrid. The G-BN interface is found as the energetically most favourable place for vacancy formation. Depending on the size of the graphene island, the C vacancy is the most favourable defect type in our DFT calculations. The N vacancy is energetically preferred over the B vacancy due to its lower formation energy with the exception of biggest G island. Although pristine hybrids are non-magnetic semiconductors, the GBN hybrid can become magnetic with a reasonable amount of magnetic moment depending on the type of vacancy and vacancy site. The vacancy defected hybrids also show the properties of semiconductor except for the hybrid involving the smallest size island with the B vacancy in the hBN layout (VBL). Defected hybrids involving the smallest G island have the highest amount of band gaps due to high ratio of carbon atoms at the interface to the island interior. Accordingly, the band gap tends to decrease with expanding G island. However, the band gap of VBL defected structures broadens with increasing size of island interestingly. Moreover, this defected hybrid introduces the greatest amount of magnetic moment (3 mu B) as the island expands. The C vacancies in the G island and around the N atom introduce a magnetic moment of 2 mu B as the G island expands as well. The magnetic moment of the N vacancy defected hybrid is 1 mu B irrespective of island size. The vacancy defect leads local in-plane/out-of-plane distortions rather than structural reconstructions in our calculations. In general, no correlation was observed between the island size and the magnetic moment of a defective hybrid.