Valley quantum Hall effect meets strain: Subgap formation and large increment of the Hall conductivity

We consider the effect of the uniaxial strain applied to a graphene monolayer with a realized quantum valley Hall state, for which we use a version of the Haldane model. In its specific point, the latter model has two spectral valleys: the gapless one and the gapped one. Using analytical and numerical arguments, we show that this state is unstable against mechanical deformations of the lattice, which influences the energy spectrum, the density of states, and the conductivity tensor. In particular, the Hall conductivity in the near-DC regime may surpass largely the known plateau value along with the simultaneous sign change. Above effects pave the way to the applied graphene strain engineering or straintronics. Namely, they can be used in quantum logical gates utilizing a controllable strain manipulation for reversing or on-and off-switching of the Hall current.