Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells

Abstract

The nature of the fractional quantum Hall effect at $\nu =1/2$ observed in wide quantum wells almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the assumption that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We hope that this will motivate further experimental studies of this state.

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Cited by in corpus (11)

• Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Composite fermion pairing induced by Landau level mixing
• Revisiting excitation gaps in the fractional quantum Hall effect
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Fixed-phase diffusion Monte Carlo study of the activation gap and the skyrmion excitation of $\nu =1$ system in the presence of charged impurities
• Edge reconstruction of compressible Quantum Hall fluid in the filling fraction range 1/3 to 2/3
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene