Broken symmetry, excitons, gapless modes, and topological excitations in trilayer quantum Hall systems

We study the interlayer coherent incompressible phase in trilayer quantum Hall systems (TLQH) at total filling factor ν_T=1 from three approaches: Mutual composite fermion (MCF), composite boson (CB), and wave function 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∕e². Two neutral gapless modes with linear dispersion relations are identified and the ratio of the two velocities is close to √3. The excitation spectra are classified into two classes, charge neutral bosonic two-body bound states and charge ±1 fermionic three-body bound states. In general, there are two two-body Kosterlize-Thouless (KT) transition temperatures and one three-body KT transition. The charge ±1 three-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 will 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.