Re-parameterization Invariance in Fractional Flux Periodicity

TL;DR

This paper investigates how fractional flux periodicity in 2D systems can be understood through re-parameterization of quantum numbers, revealing differences between exact and approximate periodicities.

Contribution

It introduces the concept that fractional flux can be absorbed into quantum number re-parameterization, clarifying the nature of fractional flux periodicity.

Findings

Exact fractional periodicity involves all electronic states in re-parameterization.

Approximate periodicity near the Fermi level involves only states close to it.

Re-parameterization explains the fractional flux effects in 2D systems.

Abstract

We analyze a common feature of a nontrivial fractional flux periodicity in two-dimensional systems. We demonstrate that an addition of fractional flux can be absorbed into re-parameterization of quantum numbers. For an exact fractional periodicity, all the electronic states undergo the re-parameterization, whereas for an approximate periodicity valid in a large system, only the states near the Fermi level are involved in the re-parameterization.