Valley Hall effect and nonlocal transport in strained graphene

Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of pseudo-Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley Hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only parameters characterizing the transport theory. Using the theory, we compute the nonlocal resistance of a Hall bar device in the diffusive regime. Our theory is also relevant for the study of moderate strain effects in the (nonlocal) transport properties of other two-dimensional materials and van der Walls heterostructures.