  Valleytronics is a rising topic to explore the emergent degree of freedom for
charge carriers in energy band edges and has attracted a great interest due to
many intriguing quantum phenomena and potential application in information
processing industry. Creation of permanent valley polarization, i.e. unbalanced
occupation at different valleys, is a chief challenge and also urgent question
to be solved in valleytronics. Here we predict that the spin-orbit coupling and
magnetic ordering allow spontaneous valley Zeeman-type splitting in pristine
monolayer of VAgP2Se6 by using first-principles calculations. The Zeeman-type
valley splitting can lead to permanent valley polarization after suitable
doping. The Zeeman-type valley splitting is similar to the role of spin
polarization in spintronics and is a vital requirement for practical devices in
valleytronics. The nonequivalent valleys of VAgP2Se6 monolayer can emit or
absorb circularly polarized photons with opposite chirality, and thus this
material shows a great potential to work as a photonic spin filter and
circularly-polarized-light resource. A valley pseudospin field effect
transistor (VPFET) is designed based on the monolayer VAgP2Se6 akin to the spin
field effect transistors. Beyond common transistors, VPFETs carry information
of not only the electrons but also the valley pseudospins.
