Temperature and local strain-controlled electron transport in few-layer graphene: a lattice mechanics and quantum transport theory

We develop a theory to describe temperature and local strain-dependent out-of-plane electron tunneling in graphene and few-layer graphene (FLG) stacks. Out-of-plane electron transport occurs through a phonon amplitude-enhanced tunneling mechanism that is exponentially enhanced by temperature. Tunneling current is also exponentially sensitive to the local strain distribution in few-layer graphene stacks. Temperature and strain effects are coupled since phonon mode stiffening at higher local strains decreases the temperature sensitivity of conductivity. A theory is developed to describe the three-dimensional current and strain distribution in a few-layer graphene stack that is locally indented by a current-carrying scanning probe tip. The degrees of electronic coupling between the tip, sample, and substrate can influence the contact resistance and measured conductivity of nanoscale graphene samples. It is shown that metal/graphene contact resistance has an activated character that is qualitatively different from intrinsic out-of-plane phonon amplitude-enhanced tunneling in FLG. Electrical resistance is primarily contact-dominated for small samples and approaches intrinsic values for thicker samples. For bulk graphitic samples, an in-plane shorting mechanism is also relevant.