Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

作者：Miserev D S^*

来源：Journal of Experimental and Theoretical Physics, 2016, 122(6): 1070-1083.

DOI：10.1134/S1063776116060066

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincar, index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p (y) of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.

• 出版日期2016-6