Scaling and Interaction-Assisted Transport in Graphene with One-Dimensional Defects

We analyze the scattering from one-dimensional defects in intrinsic graphene. The Coulomb repulsion between electrons is found to be able to induce singularities of such scattering at zero temperature as in one-dimensional conductors. In striking contrast to electrons in one space dimension, however, repulsive interactions here can enhance transport. We present explicit calculations for the scattering from vector potentials that appear when strips of the material are under strain. There the predicted effects are exponentially large for strong scatterers.

Figure 1

A vector potential $A_y$ in a narrow strip (dark blue) forms a tunneling barrier in a sheet of graphene (light blue [light gray] with contacts in green [dark gray]). $A_y$ may be induced by strain or by current-carrying wires (brown [medium gray]). Inset: bound state (amplitude in $z$ direction). Transport enhancement: an electron (red circles) may virtually occupy the bound state through the exchange interaction and traverse the barrier without tunneling.

Figure 2

Normalized resistance $G_r^{-1}$ at $\tilde{\chi }=5$ and $T<v\mathrm{sech}\tilde{\chi }/a$, when $G_r$ is renormalized by bound states, as a function of $\Delta l=\ln (v\mathrm{sech}\tilde{\chi }/Ta)$.