  Solid solubility (SS) is one of the most important features of alloys, which
is usually difficult to be largely tuned in the entire alloy concentrations by
external approaches. Some alloys that were supposed to have promising physical
properties could turn out to be much less useful because of their poor SS,
e.g., the case for monolayer BNC [(BN)1-x(C2)x] alloys. Until now, an effective
approach on significantly enhancing SS of (BN)1-x(C2)x in the entire x is still
lacking. In this article, a novel mechanism of selective orbital coupling
between high energy wrong-bond states and surface states mediated by the
specific substrate has been proposed to stabilize the wrong-bonds and in turn
significantly enhance the SS of (BN)1-x(C2)x alloys. Surprisingly, we
demonstrate that five ordered alloys, exhibiting variable direct quasi-particle
bandgaps from 1.35 to 3.99 eV, can spontaneously be formed at different x when
(BN)1-x(C2)x is grown on hcp-phase Cr. Interestingly, the optical transitions
around the band edges in these ordered alloys, accompanied by largely tunable
exciton binding energies of ~1 eV at different x, are significantly strong due
to their unique band structures. Importantly, the disordered (BN)1-x(C2)x
alloys, exhibiting fully tunable bandgaps from 0 to ~6 eV in the entire x, can
be formed on Cr substrate at the miscibility temperature of ~1200 K, which is
greatly reduced compared to that of 4500~5600 K in free-standing form or on
other substrates. Our discovery not only may resolve the long-standing SS
problem of BNC alloys, but also could significantly extend the applications of
BNC alloys for various optoelectronic applications.
