Comparative Study of the Insulator-Hall Liquid-Insulator Transitions: Composite Boson Picture vs Composite Fermion Picture

TL;DR

This paper compares insulator-Hall liquid transitions in high and low magnetic fields using composite boson and fermion models, explaining symmetries, energy scales, and temperature behaviors with experimental support.

Contribution

It extends the composite fermion picture to analyze low-field transitions and compares it with the composite boson approach, providing a unified understanding of the phenomena.

Findings

Reflection symmetries explained by gapful excitation symmetry

Different energy scales linked to critical filling factors and effective masses

Opposite temperature-dependence of resistivities understood through particle statistics

Abstract

Based on a newly advanced phenomenological understanding of the high-field insulator- Hall liquid transition in a composite fermion picture, we extend its composite boson counterpart to the analysis of the low-field insulator-Hall liquid transition. We thus achieve a comparative study of these two transitions. In this way, the similar reflection symmetries in filling factors in both transitions are understood consistently as due to the symmetry of the gapful excitations which dominate $\sigma_{xx}$ across the transitions, and the abrupt change in $\sigma_{xy}$ at the transitions. The substantially different characteristic energy scales involved in these two transitions can be attributed to the differences in critical filling factors $\nu_c$ and the effective masses. The opposite temperature-dependences of the critical longitudinal resistivities are also well-understood, which can be traced to the opposite statistical natures of the composite fermion and the composite boson. We also give a tentative discussion of the zero-temperature dissipative conductivity. The above results are supported by a recent experiment (cond-mat/9708239).