Журнал Экспериментальной и Теоретической Физики
НАЧАЛО | ПОИСК | ДЛЯ АВТОРОВ | ПОМОЩЬ      e
Общая информация о журнале
Золотые страницы
Адреса редакции
Содержание журнала
Сообщения редакции
Правила для авторов
Загрузить статью
Проверить статус статьи


ЖЭТФ, Том 149, Вып. 6, стр. 1233 (Июнь 2016)
(Английский перевод - JETP, Vol. 122, No 6, p. 1070, June 2016 доступен on-line на www.springer.com )

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: the variable phase method and the relativistic Levinson theorem
Miserev D.S.

Поступила в редакцию: 2 Августа 2015

DOI: 10.7868/S0044451016060134

PDF (343.1K)

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 Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum py of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.

 
Сообщить о технических проблемах