Broken symmetry, excitons, gapless modes and topological excitations in Trilayer Quantum Hall systems

TL;DR

This paper investigates the properties of trilayer quantum Hall systems at total filling factor 1, revealing quantized resistivities, gapless modes, novel excitations, and broken symmetries, using multiple theoretical approaches.

Contribution

It introduces a comprehensive analysis of TLQH systems, highlighting the superiority of the CB approach and classifying new excitation spectra and phase transitions.

Findings

Quantized Hall and Hall drag resistivities at h/e^2

Identification of two neutral gapless modes with velocities ratio close to √3

Discovery of charge neutral bosonic and fermionic bound states and multiple KT transitions

Abstract

We study the interlayer coherent incompressible phase in Trilayer Quantum Hall systems (TLQH) at total filling factor $ \nu_{T}=1 $ from three approaches: Mutual Composite Fermion (MCF), Composite Boson (CB) and wavefunction approach. Just like in Bilayer Quantum Hall system, CB approach is superior than MCF approach in studying TLQH with broken symmetry. The Hall and Hall drag resistivities are found to be quantized at $ h/e^{2} $. Two neutral gapless modes with linear dispersion relations are identified and the ratio of the two velocities is close to $ \sqrt{3} $. The novel excitation spectra are classified into two classes: Charge neutral bosonic 2-body bound states and Charge $ \pm 1 $ fermionic 3-body bound states. In general, there are two 2-body Kosterlize-Thouless (KT) transition temperatures and one 3-body KT transition. The Charge $ \pm 1 $ 3-body fermionic bound states may be the main dissipation source of transport measurements. The broken symmetry in terms of $ SU(3) $ algebra is studied. The structure of excitons and their flowing patterns are given. The coupling between the two Goldstone modes may lead to the broadening in the zero-bias peak in the interlayer correlated tunnelings of the TLQH. Several interesting features unique to TLQH are outlined. Limitations of the CB approach are also pointed out.