Fractional charges and quantum phase transitions in imbalanced bilayer quantum Hall systems

TL;DR

This paper extends the Composite Boson theory to analyze imbalanced bilayer quantum Hall systems, revealing continuous fractional charge variation and two quantum phase transitions, aligning with experimental and microscopic results.

Contribution

It introduces an extended theoretical framework for imbalanced bilayer quantum Hall systems, detailing fractional charge behavior and phase transitions.

Findings

Fractional charges vary continuously with imbalance.

Two quantum phase transitions identified: commensurate to incommensurate PSDW, then to superfluid.

Theory aligns with experimental and microscopic data.

Abstract

We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $ U(1) $ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing fractional charges. In the translational symmetry breaking pseudo-spin density wave (PSDW) side, there are two quantum phase transitions from the commensurate PSDW to an in-commensurate PSDW and then to the excitonic superfluid state. We compare our theory with experimental data and also the previous microscopic calculations.