Influence of device geometry on tunneling in theν=52quantum Hall liquid

Abstract

Two recent experiments [I. P. Radu et al., Science 320, 899 (2008) and X. Lin et al., Phys. Rev. B 85, 165321 (2012)] measured the temperature and voltage dependence of the quasiparticle tunneling through a quantum point contact in the ν = 5/2 quantum Hall liquid. The results led to conflicting conclusions about the nature of the quantum Hall state. In this paper, we show that the conflict can be resolved by recognizing different geometries of the devices in the experiments. We argue that in some of those geometries there is significant unscreened electrostatic interaction between the segments of the quantum Hall edge on the opposite sides of the point contact. Coulomb interaction affects the tunneling current. We compare experimental results with theoretical predictions for the Pfaffian, SU (2)2, 331 and K = 8 states and their particle-hole conjugates. After Coulomb corrections are taken into account, measurements in all geometries agree with the spin-polarized and spin-unpolarized Halperin 331 states.

Experimental constraints and a possible quantum Hall state atν=5/2

“…It was argued that the measured exponents are affected by long-range electrostatic forces [10]. Their effect depends on the sample geometry and in all cases increases the observed g. Thus, all tunneling data are compatible with the 331 state [10].At the same time, the 331 state is incompatible with the observation [12] of an upstream neutral mode. This means that no proposed ground state wave function fits…”

“…9 and 10). At the same time, one can also construct Abelian states with the same filling factor, such as the Halperin 331, K = 8 and anti-331 states [9,10].Most above-mentioned states were invented before experimental information beyond the existence of the 5/2 QHE plateau and the value of its energy gap became available. This made it impossible to select the correct theory of the 5/2-liquid.…”

Probing theν=52quantum Hall state with electronic Mach-Zehnder interferometry

“…A collection of non-Abelian quasiparticles span a degenerate ground state manifold which may be useful for topological quantum computation 12,13 . Such non-Abelian models [3][4][5][6][7]10 include the Pfaffian state, the SU (2) 2 state, the anti-Pfaffian state and the anti-SU (2) 2 state. At the same time, models [8][9][10] predicting "ordinary" Abelian quasiparticles, such as the Halperin 331 state, the K = 8 state and their particle-hole dual states, were also constructed.…”

“…The fact that the filling factor has an even denominator indicates the possibility of electron pairing. Along this line, a number of models [3][4][5][6][7][8][9][10][11] were proposed to explain the ν = 5/2 FQH state (see Ref. 10 for an overview of the proposed models).…”

“…The predictions of the 113 state and the 331 state are quite close in the tunneling experiments, whose difference lies within experimental uncertainty. 10,24 The measurements of spin polarization [25][26][27][28] are controversial and do not help, since the 113 state and the 331 state allow both zero and full spin polarizations 10,11,24 . Data of bulk thermopower measurement 29 showed features that may be associated with non-Abelian quasiparticles, 30 but the 113 and 331 states may exhibit similar features if they host different quasiparticle species that are degenerate in energy.…”