Hierarchical Nature of the Quantum Hall Effects

Abstract

I demonstrate that the wavefunction for a nu = n+ tilde{nu} quantum Hall state with Landau levels 0,1,...,n-1 filled and a filling fraction tilde{nu} quantum Hall state with 0 < tilde{nu} \leq 1 in the nth Landau level can be obtained hierarchically from the nu = n state by introducing quasielectrons which are then projected into the (conjugate of the) tilde{nu} state. In particular, the tilde{nu}=1 case produces the filled Landau level wavefunctions hierarchically, thus establishing the hierarchical nature of the integer quantum Hall states. It follows that the composite fermion description of fractional quantum Hall states fits within the hierarchy theory of the fractional quantum Hall effect. I also demonstrate this directly by generating the composite fermion ground-state wavefunctions via application of the hierarchy construction to fractional quantum Hall states, starting from the nu=1/m Laughlin states.