Valleytronics

Valleys at corners of the Brillouin zone connected by the time-reversal symmetry operation and constitutes a binary index for low energy carriers. The breaking of inversion symmetry and high spin-orbit coupling leads to valley contrasting features in the spin splitting, Berry curvatures, and optical circular dichroism. Thus valley polarization can be controlled by optical, transport, and magnetic interactions. Note that valleys may be connected through other symmetries (for example, mirror or rotation), and therefore can host potential valleytronics applications.