Persistent current in an almost staggered Harper model

TL;DR

This study investigates the persistent current in a nearly staggered Harper model near half-filling, revealing that even in the metallic regime, the current exhibits insulating behavior due to the nature of the central band states.

Contribution

It uncovers the non-metallic persistent current behavior in the Harper model despite its metallic regime, highlighting the impact of band state hybridization.

Findings

Persistent current does not show metallic behavior in the Harper model's metallic regime.

Insulating behavior of persistent current occurs when superlattice is incommensurate with system length.

Central band states are hybridized Gaussian states localized at superlattice points.

Abstract

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model, which is a quasi-periodic system, is different than other one dimensional systems with uncorrelated disorder in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as in an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.