On the geometrical description of fractional Chern insulators based on static structure factor calculations

TL;DR

This paper analytically examines the static structure factor of fractional Chern insulators, linking it to the Fubini Study metric, and explores conditions for Laughlin-like behavior and state persistence through exact diagonalization.

Contribution

It provides analytical forms for the static structure factor in fractional Chern insulators and relates the Fubini Study metric to long-distance behavior, highlighting conditions for Laughlin-like states.

Findings

Static structure factor analyzed in the long-distance limit.

Fubini Study metric influences effective filling factor.

Fractional Chern insulator state persists under certain metric deviations.

Abstract

We study the static structure factor of the fractional Chern insulator Laughlin-like state and provide analytical forms for this quantity in the long-distance limit. In the course of this we identify averaged over Brillouin zone Fubini Study metric as the relevant metric in the long-distance limit. We discuss under which conditions the static structure factor will assume the usual behavior of Laughlin-like fractional quantum Hall system i.e. the scenario of Girvin, MacDonald, and Platzman [Phys. Rev. B 33, 2481 (1986)]. We study the influence of the departure of the averaged over Brillouin zone Fubini Study metric from its fractional quantum Hall value which appears in the long-distance analysis as an effective change of the filling factor. According to our exact diagonalization results on the Haldane model and analytical considerations we find persistence of fractional Chern insulator state even in this region of the parameter space.