The role of the strain induced population imbalance in Valley polarization of graphene: Berry curvature perspective

Tohid Farajollahpour, Arash Phirouznia

Published 2017-01-23Version 1

Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points ($K$ and $K'$) of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, the strain alone could not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since in this case there is not any imbalance between the population of the valley points. In other words each of gauges alone could not induce any topological valley polarization in system at zero Fermi energy. Meanwhile at non-zero Fermi energies population imbalance can be generated as a result of the external strain even at zero magnetic field. Within the linear response regime the valley polarization (both magnetic free polarization, $\Pi_0$, and field dependent response function, $\chi_\alpha$) in different values of gauge fields of lattice deformation has been obtained. Furthermore, in the context of the Berry curvature calculations in different parametric spaces, which give rise to different physical quantities, magnetic field and deformation induced electromotive force and topological charge pumping are studied. The obtained electromotive force for time dependent deformation and magnetic field, is a good evidence for the synthetic electric field that is required to enhance the value of topological valley Hall current. In addition modified density of states has been investigated using the Berry curvature of phase space.