Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Nature volume 464, pages 566–570 (2010)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

  1. Jain, J. K. Composite Fermions (Cambridge Univ. Press, 2007)

    Book  Google Scholar 

  2. Dial, O. E., Ashoori, R. C., Pfeiffer, L. N. & West, K. W. High-resolution spectroscopy of two-dimensional electron systems. Nature 448, 176–179 (2007)

    Article  CAS  ADS  Google Scholar 

  3. Chan, H. B., Glicofridis, P. I., Ashoori, R. C. & Melloch, M. R. Universal linear density of states for tunneling into the two-dimensional electron gas in a magnetic field. Phys. Rev. Lett. 79, 2867–2870 (1997)

    Article  CAS  ADS  Google Scholar 

  4. Luhman, D. R., Tsui, D. C., Pfeiffer, L. N. & West, K. W. Electronic transport studies of a systematic series of GaAs/AlGaAs quantum wells. Appl. Phys. Lett. 91, 072104 (2007)

    Article  ADS  Google Scholar 

  5. Ashoori, R. C., Lebens, J. A., Bigelow, N. P. & Silsbee, R. H. Equilibrium tunneling from the 2-dimensional electron-gas in GaAs — evidence for a magnetic-field-induced energy-gap. Phys. Rev. Lett. 64, 681–684 (1990)

    Article  CAS  ADS  PubMed  Google Scholar 

  6. Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Coulomb barrier to tunneling between parallel two-dimensional electron systems. Phys. Rev. Lett. 69, 3804–3807 (1992)

    Article  CAS  ADS  PubMed  Google Scholar 

  7. Ashoori, R. C., Lebens, J. A., Bigelow, N. P. & Silsbee, R. H. Energy gaps of the two-dimensional electron gas explored with equilibrium tunneling spectroscopy. Phys. Rev. B 48, 4616–4628 (1993)

    Article  CAS  ADS  Google Scholar 

  8. Yang, S.-R. E. & Macdonald, A. H. Coulomb gaps in a strong magnetic field. Phys. Rev. Lett. 70, 4110–4113 (1993)

    Article  CAS  ADS  PubMed  Google Scholar 

  9. Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Compressibility of the two-dimensional electron gas: measurements of the zero-field exchange energy and fractional quantum Hall gap. Phys. Rev. B 50, 1760–1778 (1994)

    Article  CAS  ADS  Google Scholar 

  10. Khrapai, V. S. et al. Direct measurements of fractional quantum Hall effect gaps. Phys. Rev. Lett. 99, 086802 (2007)

    Article  CAS  ADS  PubMed  Google Scholar 

  11. Sondhi, S. L., Karlhede, A., Kivelson, S. A. & Rezayi, E. H. Skyrmions and the crossover from integer to fractional quantum Hall effect at small Zeeman energies. Phys. Rev. B 47, 16419–16426 (1993)

    Article  CAS  ADS  Google Scholar 

  12. Barret, S. E., Dabbagh, G., Pfeiffer, L. N., West, K. W. & Tycko, R. Optically pumped NMR evidence for finite-size skyrmions in GaAs quantum wells near Landau level filling ν = 1. Phys. Rev. Lett. 74, 5112–5115 (1995)

    Article  ADS  Google Scholar 

  13. Schmeller, A., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for skyrmions and single spin flips in the integer quantized Hall effect. Phys. Rev. Lett. 75, 4290–4293 (1995)

    Article  CAS  ADS  PubMed  Google Scholar 

  14. Gallais, Y., Yan, J., Pinczuk, A., Pfeiffer, L. N. & West, K. W. Soft spin wave near ν = 1: evidence for a magnetic instability in skyrmion systems. Phys. Rev. Lett. 100, 086806 (2008)

    Article  ADS  PubMed  Google Scholar 

  15. Halperin, B. I., Lee, P. A. & Read, N. Theory of the half-filled Landau level. Phys. Rev. B 47, 7312–7343 (1993)

    Article  CAS  ADS  Google Scholar 

  16. Hirjibehedin, C. F., Pinczuk, A., Dennis, B. S., Pfeiffer, L. N. & West, K. W. Crossover and coexistence of quasiparticle excitations in the fractional quantum Hall regime at ν≤1/3. Phys. Rev. Lett. 91, 186802 (2003)

    Article  CAS  ADS  PubMed  Google Scholar 

  17. Peterson, M. R. & Jain, J. K. Flavor altering excitations of composite fermions. Phys. Rev. Lett. 93, 046402 (2004)

    Article  ADS  PubMed  Google Scholar 

  18. Morf, R. & d'Ambrumenil, N. Stability and effective masses of composite fermions in the first and second Landau level. Phys. Rev. Lett. 74, 5116–5119 (1995)

    Article  CAS  ADS  PubMed  Google Scholar 

  19. Park, K., Meskini, N. & Jain, J. K. Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness. J. Phys. Condens. Matter 11, 7283–7299 (1999)

    Article  CAS  ADS  Google Scholar 

  20. Leadley, D. R., van der Burgt, M., Nicholas, R. J., Foxon, C. T. & Harris, J. J. Pulsed-magnetic-field measurements of the composite-fermion effective mass. Phys. Rev. B 53, 2057–2063 (1996)

    Article  CAS  ADS  Google Scholar 

  21. Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989)

    Article  CAS  ADS  PubMed  Google Scholar 

  22. Fogler, M. M., Koulakov, A. A. & Shklovskii, B. I. Ground state of a two-dimensional electron liquid in a weak magnetic field. Phys. Rev. B 54, 1853–1871 (1996)

    Article  CAS  ADS  Google Scholar 

  23. Ando, T. & Uemura, Y. Theory of oscillatory g factor in a MOS inversion layer under strong magnetic fields. J. Phys. Soc. Jpn 37, 1044–1052 (1974)

    Article  CAS  ADS  Google Scholar 

  24. Pikus, F. G. & Efros, A. L. Coulomb gap in a two-dimensional electron gas with a close metallic electrode. Phys. Rev. B 51, 16871–16877 (1995)

    Article  CAS  ADS  Google Scholar 

Download references

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.

Author information

Author notes

  1. L. N. Pfeiffer & K. W. West

    Present address: Present address: Princeton University, Princeton, New Jersey 08544, USA.,

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA ,

    O. E. Dial & R. C. Ashoori

  2. Alcatel-Lucent Bell Laboratories, Murray Hill, New Jersey 07974, USA ,

    L. N. Pfeiffer & K. W. West

Authors
  1. O. E. Dial
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. C. Ashoori
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. N. Pfeiffer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. W. West
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

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)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature08941

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing