Pseudospin lifetime in relaxed-shape armchair graphene nanoribbons due to in-plane phonon modes

Abstract

We study the influence of ripple waves on the band structures of strained armchair graphene nanoribbons. We argue that the Zeeman pseudospin (p-spin) splitting energy induced by ripple waves might not be neglected for smaller widths of armchair graphene nanoribbons (GNRs). We show that the p-spin splitting energy breaks the symmetry of degeneracy due to the ripple-induced Zeeman effect in GNRs, originating from electromechanical coupling. We estimate the p-spin lifetime in strained armchair GNRs caused by in-plane phonon modes for possible applications in straintronics and quantum information processing. By considering higher order terms in the strain tensor expansion, we also demonstrate that highly asymmetric band structures of GNRs induce asymmetric phonon-mediated p-spin relaxation. Such asymmetric p-spin relaxation is not possible for unstrained armchair and zigzag GNRs. In particular, we report that the p-spin transition rate decreases like ${B}_{0}^{5}$ (as a function of p-magnetic fields), ${L}^{\ensuremath{-}9}$ (as a function of GNR width) and ${\ensuremath{\tau}}_{e}^{\ensuremath{-}1}$, where ${\ensuremath{\tau}}_{e}$ is the externally applied tensile edge stress.