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Fractional Quantum Hall Hierarchy and the Second Landau Level
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We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.
Forward citations
Cited by 2 Pith papers
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Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies
An order-five Sp(4,Z) duality acts projectively on 3d U(1)^2 theories, and its hierarchy operations generate candidate bilayer quantum Hall states at 3/8+3/8 and 5/12+5/12.
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Topological phase transitions between bosonic and fermionic quantum Hall states near even-denominator filling factors
The transition between Jain and daughter quantum Hall states is mapped to an E8 to trivial transition and predicted to split into at least eight transitions with intermediate topological phases.
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