Hierarchical Nature of the Quantum Hall Effects

TL;DR

This paper reveals the hierarchical structure of quantum Hall wavefunctions, showing how integer and fractional states can be constructed from simpler states using a hierarchy approach, unifying different descriptions of quantum Hall effects.

Contribution

It introduces a hierarchical method to derive quantum Hall wavefunctions, linking integer and fractional states and integrating the composite fermion theory within the hierarchy framework.

Findings

Hierarchical construction of quantum Hall wavefunctions from simpler states.

Unified view of integer and fractional quantum Hall effects.

Generation of composite fermion wavefunctions via hierarchy methods.

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.