  Carbon-based bilayer van der Waals (vdW) materials are attracting much
attention due to their predicted interesting physical properties. Here, we
theoretically investigate electronic and optical properties of C$_3$B/C$_3$N
vdW heterostructure (HTS) under external magnetic field and mechanical strain.
The tight-binding model of the system is constructed to include the
strain-induced modification of the hopping interactions. The influence of a
uniform perpendicular magnetic field is included by using the Peierls
substitution method. We observe the intriguing electronic and optical
characteristics of the HTS under mechanical strain, covering the band
inversion, alteration of band gap and optical gap, distortion of band-edge
states, as well as significant enhancement of optical absorption. Furthermore,
the interplay between external magnetic field and biaxial strain leads to
exotic features of quantization and optical spectra. This work provides
important information for the comprehension of the engineering of materials by
external effects. Our study suggests that C$_3$B/C$_3$N vdW HTS is a promising
candidate for next-generation electronic and optoelectronic devices.
