Independent degrees of freedom in two-dimensional materials

In hexagonal two-dimensional (2D) materials such as graphene, hexagonal boron nitride, or transition metal dichalcogenides, electrons possess intrinsic degrees of freedom (DOFs): sublattice pseudospin, spin, and valley. Independent polarization of the DOFs for carrying information can be harnessed in future semiconductor industry. Here we propose a general Hamiltonian based on the Haldane model with spin-orbit coupling (SOC) which realizes the independence of all the DOFs that can tune optical absorption spectra as a function of the SOC. The present result suggests a new 2D material or a new 2D electronic device which offers any combination of pseudospintronics, spintronics, and valleytronics applications.