Intrinsic semimetallicity of graphene and silicene largely limits their applications in functional devices. Mixing carbon and silicon atoms to form two-dimensional (2D) silicon carbide (SixC1-x) sheets is promising to overcome this issue. Using first-principles calculations combined with the cluster expansion method, we perform a comprehensive study on the thermodynamic stability and electronic properties of 2D SixC1-x monolayers with 0 ≤ x ≤ 1. Upon varying the silicon concentration, the 2D SixC1-x presents two distinct structural phases, a homogeneous phase with well dispersed Si (or C) atoms and an in-plane hybrid phase rich in SiC domains. While the in-plane hybrid structure shows uniform semiconducting properties with widely tunable band gap from 0 to 2.87 eV due to quantum confinement effect imposed by the SiC domains, the homogeneous structures can be semiconducting or remain semimetallic depending on a superlattice vector which dictates whether the sublattice symmetry is topologically broken. Moreover, we reveal a universal rule for describing the electronic properties of the homogeneous SixC1-x structures. These findings suggest that the 2D SixC1-x monolayers may present a new "family" of 2D materials, with a rich variety of properties for applications in electronics and optoelectronics.

Doped, substituted, or alloyed graphene is an attractive candidate for use as a tunable element of future nanomechanical and optoelectronic devices. Here we use the density functional theory, density functional tight binding, cluster expansion, and molecular dynamics to investigate the thermal stability and electronic properties of a binary 2D alloy of graphitic carbon and nitrogen (C(1-x)N(x)). The stability range naturally begins from graphene and must end before x = 1, where pure nitrogen rather forms molecular gas. This poses a compelling question of what highest x < 1 still permits stable 2D hexagonal lattice. Such upper limit on the nitrogen concentration that is achievable in a stable alloy can be found based on the phonon and molecular dynamics calculations. The stability switchover is predicted to between x = 1/3 (33.3%) and x = 3/8 (37.5%), and no stable hexagonal lattice two-dimensional CN alloys can exist at the N concentration of x = 3/8 (37.5%) and higher.