We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level (index $N\ensuremath{\ge}2$) half filled by electrons. Strong and sharp peaks are found in the wave-vector dependence of both the static density susceptibility and the equal-time density-density correlation function, in finite-size systems with up to twelve electrons. Qualitatively different from the partially filled lowest ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ ) Landau level, these results are suggestive of a tendency toward charge-density-wave ordering in these systems. The ordering wave vector is found to decrease with increasing $N$ .We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level (index $N\ensuremath{\ge}2$) half filled by electrons. Strong and sharp peaks are found in the wave-vector dependence of both the static density susceptibility and the equal-time density-density correlation function, in finite-size systems with up to twelve electrons. Qualitatively different from the partially filled lowest ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) Landau level, these results are suggestive of a tendency toward charge-density-wave ordering in these systems. The ordering wave vector is found to decrease with increasing $N$.

arXiv:cond-mat/9903258Physical Review LettersAug 9, 1999140 citations

QUANTUM PHASES IN PARTIALLY FILLED LANDAU LEVELS

M. O. Goerbig, Pascal Lederer, C. Morais Smith

International Conference on High Magnetic Fields in Semiconductor Physics (HMF)May 1, 20050 citations

Wigner crystals in the lowest Landau level at low-filling factors

Kun Yang, F. D. M. Haldane, Edward H. Rezayi

We report on results of finite-size numerical studies of partially filled lowest Landau level, at low electron filling factors. We find convincing evidence suggesting that electrons form Wigner crystals at sufficiently low filling factors, and the critical filling factor is ${\ensuremath{\nu}}_{c}\ensuremath{\approx}1/7.$ At $\ensuremath{\nu}=1/7$ we find the system undergoes a phase transition from the Wigner crystal to the incompressible Laughlin state when the short-range part of the Coulomb interaction is modified slightly. This transition is either continuous or very weakly first order.We report on results of finite-size numerical studies of partially filled lowest Landau level, at low electron filling factors. We find convincing evidence suggesting that electrons form Wigner crystals at sufficiently low filling factors, and the critical filling factor is ${\ensuremath{\nu}}_{c}\ensuremath{\approx}1/7.$ At $\ensuremath{\nu}=1/7$ we find the system undergoes a phase transition from the Wigner crystal to the incompressible Laughlin state when the short-range part of the Coulomb interaction is modified slightly. This transition is either continuous or very weakly first order.

arXiv:cond-mat/0105170Physical review. B, Condensed matterAug 2, 200187 citations

Landau Fermi‐Liquid Theory

Gordon Baym, C. J. Pethick

Wiley eBooksDec 16, 1991704 citations

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

) Landau level, these results are suggestive of a tendency toward charge-density-wave ordering in these systems. The ordering wave vector is found to decrease with increasing

N