Anomalous structure in the single particle spectrum of the fractional quantum Hall effect

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Abstract

The two-dimensional electron system is a powerful laboratory for investigating the physics of interacting particles. Application of a large magnetic field produces massively degenerate quantum levels known as Landau levels; within a Landau level the kinetic energy of the electrons is suppressed, and electron–electron interactions set the only energy scale1. Coulomb interactions break the degeneracy of the Landau levels and can cause the electrons to order into complex ground states. Here we observe, in the high energy single particle spectrum of this system, salient and unexpected structure that extends across a wide range of Landau level filling fractions. The structure appears only when the two-dimensional electron system is cooled to very low temperatures, indicating that it arises from delicate ground state correlations. We characterize this structure by its evolution with changing electron density and applied magnetic field, and present two possible models for understanding these observations. Some of the energies of the features agree qualitatively with what might be expected for composite fermions, which have proven effective for interpreting other experiments in this regime. At the same time, a simple model with electrons localized on ordered lattice sites also generates structure similar to that observed in the experiment. Neither of these models alone is sufficient to explain the observations across the entire range of densities measured. The discovery of this unexpected prominent structure in the single particle spectrum of an otherwise thoroughly studied system suggests that there exist core features of the two-dimensional electron system that have yet to be understood.

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Figure 1: High field TDCS spectra show ‘sash’ features: bright and dark diagonal lines across the spectrum.
Figure 2: A energy dependence indicates that the sashes originate with electron–electron interactions within the lowest Landau levels.
Figure 3: From the viewpoint of a composite quasiparticle, sweeping the density in a quantum well also sweeps the effective magnetic field.
Figure 4: The ν = 1 sash features are emphasized by taking an additional derivative of the data, easing comparison with simulated spectra from a model of electrons localized on a lattice.

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Acknowledgements

We are grateful to A. MacDonald and Y. Meir, who independently suggested the identification of sash features with nearby localized states that formed the basis for the lattice model. We thank P. Lee, L. Levitov and B. Halperin for discussions regarding the interpretation of our results. This work was sponsored by the Office of Science of the US Department of Energy.

Author Contributions O.E.D. built the apparatus and performed measurements and analysis. R.C.A. supervised the work and performed analysis. O.E.D. and R.C.A. prepared the manuscript. L.N.P. and K.W.W. performed the crystal growth.

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Correspondence to O. E. Dial or R. C. Ashoori.

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Supplementary Information

This file contains Supplementary Figures 1- 6 with legends, Supplementary Material 1-5 and Supplementary References. (PDF 806 kb)

Supplementary Movie 1

This brief video shows the typical results from annealing the electron locations in the semi-classical model. Each frame shows the approximate ground state at a single density in a manner similar to that of supplemental figure 5d; the grey hexagons are empty lattice sites, shown using their Wigner-Seitz cells. Red sites are singly occupied, while yellow sites are doubly occupied. The solution is periodic with a 20 site period in each lattice direction. A single period is highlighted for clarity, and repeated in darker colours to demonstrate how the boundary conditions are met. For this calculation, the disorder was 0.2% of the Coulomb energy, and the setback was 2 magnetic lengths. (MOV 4629 kb)

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Dial, O., Ashoori, R., Pfeiffer, L. et al. Anomalous structure in the single particle spectrum of the fractional quantum Hall effect. Nature 464, 566–570 (2010). https://doi.org/10.1038/nature08941

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