Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems

Abstract

We present an effective theory for the bulk Fractional Quantum Hall states in spin-polarized bilayer and spin-1/2 single layer two-dimensional electron gases (2DEG) in high magnetic fields consistent with the requirement of global gauge invariance on systems with periodic boundary conditions. We derive the theory for the edge states that follows naturally from this bulk theory. We find that the minimal effective theory contains two propagating edge modes that carry charge and energy, and two non-propagating topological modes responsible for the statistics of the excitations. We give a detailed description of the effective theory for the spin-singlet states, the symmetric bilayer states and for the (m, m, m) states. We calculate explicitly, for a number of cases of interest, the operators that create the elementary excitations, their bound states, and the electron. We also discuss the scaling behavior of the tunneling conductances in different situations: internal tunneling, tunneling between identical edges and tunneling into a FQH state from a Fermi liquid.

Quasiparticle Tunneling across an Exciton Condensate

“…We obtain a clear zero bias peak in the tunnel conductance of a quantum point contact (QPC). The peak and its temperature dependence fit well to the theoretical formula derived for weak quasiparticle tunneling in a single layer [44], confirming the theoretically predicted correspondence between the bilayer QHS and the single layer states [19]. Interestingly, the extracted quasiparticle charge is only a few percent of the free electron charge, presumably reflecting a distinct type of interaction between the quasiparticle on the edge and the excitonic condensate in the bulk [20].…”

“…We fit simultaneously the peaks (dotted lines) at ten temperature points with e à , g, A, and g ∞ as the four fitting parameters. The experimental results can be satisfactorily described by the weak tunneling formula, as expected from the Lopez-Fradkin theory [19]. The extracted interaction constant is g ¼ 0.30.…”

“…A meron carries an electrical charge of AEðe=2Þ but tends to bind a second meron with opposite vorticity. Immediately following the early excitement on the quantum Hall bilayer experiments [18], Lopez and Fradkin [19] constructed an effective field theory for the edge states. They showed that the edge in a ðm; m; mÞ Halperin multicomponent QHS is largely analogous to that of the 1=m Laughlin QHS itself (m is an integer), but there exists leakage from the edge to the bulk due to the presence of gapless excitations [20] [inset of Fig.…”

“…1(a)]. It was proposed that an interedge tunneling experiment should be carried out to verify the theory and shed light on the edgebulk interactions [19].…”

“…Interestingly, the extracted quasiparticle charge is only a few percent of the free electron charge, presumably reflecting a distinct type of interaction between the quasiparticle on the edge and the excitonic condensate in the bulk [20]. The presence of gapless excitations in the bulk [15] allows for leakage from the edge [19] and this process should be taken into account for a complete theory of quasiparticle tunneling [44] in bilayers.…”