Electronic properties of the 1D Frenkel-Kontorova model

TL;DR

This paper investigates the electronic energy spectra and quantum diffusion in a one-dimensional incommensurate Frenkel-Kontorova model, revealing distinct behaviors in different regimes and their relation to known models.

Contribution

It provides a numerical analysis of spectral and dynamical properties in the FK model, highlighting differences between invariance circle and Cantorus regimes.

Findings

Spectral and dynamical behaviors differ significantly between regimes.

Invariance circle regime resembles the Harper model.

Cantorus regime exhibits properties similar to the Fibonacci model.

Abstract

The energy spectra and quantum diffusion of an electron in a 1D incommensurate Frenkel-Kontorova (FK) model are studied numerically. We found that the spectral and dynamical properties of electron display quite different behaviors in invariance circle regime and in Cantorus regime. In the former case, it is similar to that of the Harper model, whereas in the latter case, it is similar to that of the Fibonacci model. The relationship between spectral and transport properties is discussed.