English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The problem of localized states in 1D systems with the relativistic spectrum,namely, graphene stripes and carbon nanotubes, has been analytically studied.The bound state as a superposition of two chiral states is completely describedby their relative phase which is the foundation of the variable phase method(VPM) developed herein. Basing on our VPM, we formulate and prove therelativistic Levinson theorem. The problem of bound state can be reduced to theanalysis of closed trajectories of some vector field. Remarkably, the Levinsontheorem appears as the Poincare indices theorem for these closed trajectories.The reduction of the VPM equation to the non-relativistic and semi-classicallimits has been done. The limit of the small momentum $p_y$ of the transversequantization is applicable to arbitrary integrable potential. In this case theonly confined mode is predicted.

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