Effective masses for zigzag nanotubes in magnetic fields

TL;DR

This paper analyzes the spectral properties of Schrödinger operators modeling zigzag carbon nanotubes in magnetic fields, deriving identities and estimates related to effective masses and energy gaps.

Contribution

It introduces new identities and a priori estimates for effective masses and gap lengths in the spectrum of nanotube models under magnetic fields.

Findings

Spectral spectrum includes continuous parts and infinite multiplicity eigenvalues.

Derived identities linking effective masses and gap lengths.

Provided estimates for spectral properties of the nanotube models.

Abstract

We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of zigzag single-wall carbon nanotubes in magnetic field. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We obtain identities and a priori estimates in terms of effective masses and gap lengths.