Title: Non-abelian to abelian transition of the 1/2 fractional quantum Hall state

Speaker: Siddharth K. Singh, Princeton University

Abstract: The ground state at ν=1/2 in the lowest (N = 0) Landau level in two-dimensional electrons confined to wide GaAs quantum wells transitions from composite fermion Fermi sea to a fractional quantum Hall state (FQHS) and finally to a bilayer Wigner crystal as the density (n) is raised. In wide wells, the electron system has a bilayer charge distribution because of which the nature of the 1/2 FQHS has been a subject of debate. Here, we report the evolution of the 1/2 FQHS in a 72.5 nm wide quantum well as a function of density, from 1.0 to 1.59×10^11 cm^(-2) while keeping the charge distribution symmetric by appropriately biasing the front- and back-gates. The transport energy gap of the 1/2 FQHS shows an upward cusp with a maximum value of about 6 K at n=1.37×10^11 cm^(-2) and monotonically decreases to zero as the density is changed in either direction. We find qualitative agreement with theoretical calculations of the energy gap of the 1/2 FQHS where the upward cusp in the energy gap is identified to be due to a transition between the 1-component Pfaffian (Pf) and the 2-component Halperin-331 (Ψ_331) states as the density is increased from a small to high value. Interestingly, the Hall plateau at ν=1/2 remains strongly quantized in this entire range of densities. At n=1.37×10^11 cm^(-2) and slightly lower densities, when the 1/2 FQHS is sufficiently strong we also observe the daughter states of the 1/2 FQHS at ν=8/17 and 7/13, whose positions are consistent with the daughter states of the Pf state. At higher densities, evidence for the 2-component nature of the electron system can be observed with the emergence of the bilayer Wigner crystal and the destruction of odd-numerator FQHSs. We also show that several of these transitions occur at the same value of interlayer tunneling in units of the Coulomb energy. The continuous transition of the 1/2 FQHS from the non-abelian Pf state to the abelian Ψ_331 state can potentially be useful for experiments in topological quantum computing and quantum criticality.