The study of Goldstone modes in ν = 2 bilayer quantum Hall systems

Abstract

At the filling factor ν=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase. PACS. 73.21.-b Collective excitations in nanoscale systems -73.43.Nq Phase transitions quantum Hall effects

Nambu–Goldstone modes and the Josephson supercurrent in the bilayer quantum Hall system

“…We have first reproduced the perturbative results on the dispersions and coherence lengths obtained in Ref. [19]. We have then presented the effective theory describing the interlayer coherence in the bilayer QH system at ν = 1, 2.…”

“…The nonperturbative analysis was beyond the scope of Ref. [19]. It has been argued [3] that the interlayer coherence is due to the Bose-Einstein condensation of composite bosons, which are single electrons bound to magnetic flux quanta.…”

“…We have recently analyzed the full details of these NG modes in each phase [19]. The CAF phase is most interesting, where one of the NG modes becomes gapless and has a linear dispersion relation [19] as the tunneling interaction vanishes (∆ SAS → 0). It is an urgent and intriguing problem what kind of phase coherence this NG mode develops.…”

“…The CP 3 field emerges when composite bosons undergo Bose-Einstein condensation [3]. We first make a perturbative analysis of the NG modes and reproduce the same results as obtained in [19]. We next analyze the nonperturbative phase coherent phenomena developed by the NG mode having linear dispersion, where the phase field ϑ(x) is essentially classical and may become very large, which is necessary to analyze the associated Josephson supercurrent.…”

Spin supercurrent in the canted antiferromagnetic phase

“…[17,18]. We have recently analyzed the full details of these Goldstone modes in each phase [19]. The CAF phase is the most interesting, where the spins are canted coherently and making antiferromagnetic correlations between the two layers.…”