Valleytronics is a promising paradigm to explore the emergent degree of freedom for charge carriers on the energy band edges. Using ab initio calculations, we reveal that the honeycomb boron nitride (h-BN) monolayer shows a pair of inequivalent valleys in the vicinities of the vertices of hexagonal Brillouin zone even without the protection of the C symmetry. The inequivalent valleys give rise to a 2-fold degree of freedom named the valley pseudospin. The valley pseudospin with a tunable bandgap from deep ultraviolet to far-infrared spectra can be obtained by doping h-BN monolayer with carbon atoms. For a low-concentration carbon periodically doped h-BN monolayer, the subbands with constant valley Hall conductance are predicted due to the interaction between the artificial superlattice and valleys. In addition, the valley pseudospin can be manipulated by visible light for high-concentration carbon doped h-BN monolayer. In agreement with our calculations, the circularly polarized photoluminescence spectra of the BNC sample show a maximum valley-contrasting circular polarization of 40% and 70% at room temperature and 77 K, respectively. Our work demonstrates a class of valleytronic materials with a controllable bandgap.

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