Paper Title

In 2D hexagonal materials such as graphene, two degenerate but inequivalent band structure valleys (K, K’) exist resulting ina novel ‘valley’degree of freedom with potential for electronics. Electron valley is similar to electron spinandcarries magnetic moment with opposite signs for opposite valleys.Previous studies have been focused on homogeneous structures and treated the moment as an integrated quantity, with the well known result that the moment can interact with a uniform out of-plane magnetic field, resulting in valley Zeeman splitting and a corresponding carrier population differential between opposite valleys useful for valley-based electronics. Our work extends previous studies to cases of inhomogeneous structures and magnetic fields. The concept of ‘local valley magnetic moment’is introduced to address such cases, withthe moment beingthe corresponding spatial distribution of the integrated moment and shown to be the suitable quantity to express valley Zeeman energy. For numerical demonstration, the tight binding model is applied to two graphene structures, namely, a Q1D lateral barrier-channel-barrier structure in gapped graphene and a zigzag nanoribbon in gapless graphene, in vanishing, uniform, or strip confined magnetic fields. Local valley magnetic moments of several electron states in the two structures are presented.