Spiral symmetry and general Bloch's theorem

TL;DR

This paper explores spiral symmetry in cylindrical coordinates and introduces a generalized Bloch's theorem, which is particularly useful for analyzing properties of single-walled carbon nanotubes.

Contribution

It presents a new form of Bloch's theorem derived from spiral symmetry, extending its applicability to cylindrical structures like nanotubes.

Findings

Generalized Bloch's theorem applicable to spiral symmetry

Enhanced understanding of electronic properties in nanotubes

Potential applications in nanomaterials analysis

Abstract

In this paper, spiral symmetry in cylindrical coordinate and general Bloch's theorem induced from it are discussed. This general Bloch's theorem is useful for considering the properties related to single-walled carbon nanotubes.