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Nuclear Physics B

Hierarchy of quantized Hall states in double-layer electron systems

Martin Greiter, Ian A. McDonald

Published Dec 1, 1993• 9 citations
Publisher
DOI
10.1016/0550-3213(93)90527-v

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An analytically solvable few-electron model of a double-layer electron system is presented which includes mixing with all Landau levels. Inter-layer correlations are found to give rise to novel ground states which differ fundamentally from previously suggested Jastrow-like wavefunctions for double layer N-electron systems. Comparison with experimental data suggests that these states may represent small-N precursors of recently observed fractional quantum Hall states in double-layer (large-N) systems.

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Unified Integer and Fractional Quantum Hall Effects from Boundary-Induced Edge-State Quantization

Pedro Pereyra

Despite the success of Landau-level theory and edge-state transport formalisms, a direct microscopic link between bulk quantization and the observed hierarchy of quantum Hall plateaus has not been established. In particular, no unified microscopic mechanism accounting simultaneously for integer and fractional sequences has been derived within standard quantum mechanics. Here we show that boundary-induced quantization of edge states provides this missing bridge. Starting from the Landau problem in laterally confined two-dimensional electron systems, we demonstrate that the imposition of Dirichlet, Neumann, and mixed (Robin) boundary conditions discretizes both the guiding-center coordinate and the longitudinal momentum of chiral edge states. The resulting boundary-dependent spectra generate families of edge channels with well-defined multiplicities that couple to electronic transport. When incorporated into an edge-state transport description, this boundary quantization reproduces the integer Hall sequence and simultaneously yields a structured hierarchy of fractional filling factors without invoking separate microscopic mechanisms. We further show that a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum while leaving the bulk Landau levels intact. This controlled symmetry breaking enhances edge-state multiplicities at small Landau indices and stabilizes the fractional plateaus observed at strong magnetic fields. The quantized Hall response thus emerges from the interplay between Landau quantization and boundary-induced guiding-center discretization, which together determine the spectrum and occupation of chiral edge channels. These results establish boundary-induced quantization as the microscopic origin of quantum Hall transport and provide a unified description of both integer and fractional regimes within conventional quantum mechanics.

cond-mat.mes-hallCross-listedarXiv:2603.04652•Mar 6, 2026
An analytically solvable few-electron model of a double-layer electron system is presented which includes mixing with all Landau levels. Inter-layer correlations are found to give rise to novel ground states which differ fundamentally from previously suggested Jastrow-like wavefunctions for double layer N-electron systems. Comparison with experimental data suggests that these states may represent small-N precursors of recently observed fractional quantum Hall states in double-layer (large-N) systems.
Despite the success of Landau-level theory and edge-state transport formalisms, a direct microscopic link between bulk quantization and the observed hierarchy of quantum Hall plateaus has not been established. In particular, no unified microscopic mechanism accounting simultaneously for integer and fractional sequences has been derived within standard quantum mechanics. Here we show that boundary-induced quantization of edge states provides this missing bridge. Starting from the Landau problem in laterally confined two-dimensional electron systems, we demonstrate that the imposition of Dirichlet, Neumann, and mixed (Robin) boundary conditions discretizes both the guiding-center coordinate and the longitudinal momentum of chiral edge states. The resulting boundary-dependent spectra generate families of edge channels with well-defined multiplicities that couple to electronic transport. When incorporated into an edge-state transport description, this boundary quantization reproduces the integer Hall sequence and simultaneously yields a structured hierarchy of fractional filling factors without invoking separate microscopic mechanisms. We further show that a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum while leaving the bulk Landau levels intact. This controlled symmetry breaking enhances edge-state multiplicities at small Landau indices and stabilizes the fractional plateaus observed at strong magnetic fields. The quantized Hall response thus emerges from the interplay between Landau quantization and boundary-induced guiding-center discretization, which together determine the spectrum and occupation of chiral edge channels. These results establish boundary-induced quantization as the microscopic origin of quantum Hall transport and provide a unified description of both integer and fractional regimes within conventional quantum mechanics.