Subband engineering even-denominator quantum Hall states

Proposed even-denominator fractional quantum Hall effect (FQHE) states suggest the possibility of excitations with non-Abelian braid statistics. Recent experiments on wide square quantum wells indicate even-denominator FQHE even under electrostatic tilt. We theoretically analyze these structures and develop a procedure to accurately test proposed quantum Hall wave functions. We find that tilted wells favor partial subband polarization to yield Abelian even-denominator states. Our results show that tilting quantum wells effectively engineers different interaction potentials allowing exploration of a wide variety of even-denominator states.

Figure 1

(Color online) Top: confinement energy plotted as function of subband polarization for parameters corresponding to tilted wide well samples of Ref. 15. The right axis shows Coulomb units in terms of the fixed magnetic length, $\overline{l}$, obtained for $\nu =1/2$ and $\rho =1.72\times {10}^{11}{\text{cm}}^{-2}$. Bottom: the same but for the subband energy difference (dashed) and the chemical potential offset (solid). The dotted line plots the $B=0$ subband energy difference. Inset: schematic showing partial subband occupancy captured by an effective chemical potential.

Figure 2

(Color online) In-plane correlation energies of several states, Eqs. (3, 4), at $\gamma =0.5$ plotted versus the intersubband interaction parameter $R$. The arrow indicates the parameter relevant for the tilted well samples of Ref. 15, where the $\left(3/7,1/5\mid 1\right)$ state is shown to have the lowest correlation energy at $\gamma =0.5$. Inset: normalized lowest (solid) and first (dashed) subband wave functions plotted versus position in the tilted quantum well for several $\gamma$ between 0 and 1. In the limit $\gamma \to 0$ the subbands localize to mimic layer states.