  We propose a guideline for exploring substrates that stabilize the monolayer
honeycomb structure of silicene and germanene while simultaneously preserve the
Dirac states: in addition to have a strong binding energy to the monolayer, a
suitable substrate should be a large-gap semiconductor with a proper
workfunction such that the Dirac point lies in the gap and far from the
substrate states when their bands align. We illustrate our idea by performing
first-principles calculations for silicene and germanene on the Al-terminated
(0001) surface of Al2O3 . The overlaid monolayers on Al-terminated Al2O3(0001)
retain the main structural profile of the low-buckled honeycomb structure via a
binding energy comparable to the one between silicene and Ag(111). Unfolded
band structure derived from the k-projection method reveals that gapped Dirac
cone is formed at the K point due to the structural distortion and the
interaction with the substrate. The gaps of 0.4 eV and 0.3 eV respectively for
the supported silicene and germanene suggest that they may have potential
applications in nanoelectronics.
