  For a long time, two-dimensional (2D) hexagonal MoS2 was proposed as a
promising material for valleytronic system. However, the limited size of growth
and low carrier motilities in MoS2 restrict its further application. Very
recently, a new kind of hexagonal 2D MXene, MoSi2N4, was successfully
synthesized with large size, excellent ambient stability, and considerable hole
mobility. In this paper, based on the first-principles calculations, we predict
that the valley-contrast properties can be realized in monolayer MoSi2N4 and
its derivative MoSi2As4. Beyond the traditional two-level valleys, the valleys
in monolayer MoSi2As4 are multiple-folded, implying a new valley dimension.
Such multiple-folded valleys can be described by a three-band low-power
Hamiltonian. This study presents the theoretical advance and the potential
applications of monolayer MoSi2N4 and MoSi2As4 in valleytronic devices,
especially multiple information processing.
