Electronic transport in bent carbon nanotubes

We study the electronic transport through uniformly bent carbon nanotubes. For this purpose, we describe the nanotube with the tight-binding model and calculate the local current flow by employing nonequilibrium Green's functions (NEGF) in the Keldysh formalism. In addition, we describe the low-energy excitations using an effective Dirac equation in curved space with a strain-induced pseudomagnetic field, which can be solved analytically for the torus geometry in terms of the Mathieu functions. We obtain a perfect quantitative agreement with the NEGF results. For nanotubes with an armchair edge, already a weak bending of $1%$ substantially changes the electronic properties. Depending on the valley, the current of the zero mode flows either on the outer or the inner side of the torus and, therefore, can be used as a valley splitter. In contrast, the zigzag nanotubes are largely unaffected by the bending. Our findings are of importance for nanoelectronic applications of carbon nanotubes and open new possibilities for valleytronics.