Two-dimensional (2D) carbon allotropes, together with their binary and ternary counterparts, have attracted substantial research interest due to their peculiar geometries and properties. Among them, grapheneplus, a derivative of penta-graphene, has been proposed to exhibit unusual mechanical and electronic behaviour. In this work, we perform a comprehensive first-principles study on its isoelectronic and isostructural analogue, a grapheneplus-like BCN (gp-BCN) monolayer. It is found that this gp-BCN system exhibits robust structural stability from energetic, dynamic, thermal, and mechanical perspectives. A remarkable anisotropy is observed in its mechanical behaviour, which even presents in-plane auxeticity with a high negative Poisson's ratio of -0.3. Different from the semimetallic grapheneplus one, the gp-BCN monolayer is a semiconductor with a direct band gap of 3.23 eV. High electron mobilities up to 103 cm2 V-1 s-1 appear in the gp-BCN system, which are one to two orders of magnitude greater than the hole mobilities. Furthermore, due to the breaking of inversion symmetry, the gp-BCN monolayer exhibits spontaneous out-of-plane polarization, yielding prominent out-of-plane piezoelectric responses that are comparable to those of Janus MoSSe, WSSe and H-decorated BN systems. Our study demonstrates that the BCN analogue of grapheneplus possesses promising mechanical, electronic, and piezoelectric properties, rendering it promising for applications in nanoelectronics and mechanical nanosensors.

Promising mechanical, electronic and piezoelectric properties of grapheneplus-like BCN monolayer: insights from first-principles