Dynamics of electrons in quantum Hall bubble phases

Abstract

In Landau levels N > 1, the ground state of the two-dimensional electron gas (2DEG) in a perpendicular magnetic field evolves from a Wigner crystal for small filling ν * of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as ν * increases, to a modulated stripe state near ν * = 0.5. In this work, we show that these first-order phase transitions between the bubble states lead to measurable discontinuities in several physical quantities such as the density of states and the magnetization of the 2DEG. We discuss in detail the behavior of the collective excitations of the bubble states and show that their spectra have higher-energy modes besides the pinned phonon mode. The frequencies of these modes, at small wavevector k, have a discontinuous evolution as a function of filling factor that should be measurable in, for example, microwave absorption experiments.

Depinning transition of bubble phases in a high Landau level

“…Similar sliding behaviors in RIQHE have been observed in a wide range of temperatures and in certain magnetic field regime, for both samples. These observations conform to the characteristics of a large class of CDW [1,2,[4][5][6][8][9][10][11][12][13][36][37][38][39] in solids, where metastability and hysteresis are commonly observed at low temperatures [1,2].…”

“…Here the precise filling factors of RIQHE are determined by the position of the minimum conductivity at elevated temperatures, when the bubble phases start to melt. Theoretical calculations suggest that the form factor depends on the partial filling factor [37,38,41]. The one-, two-and three-electron bubble phases and stripe phase are predicted in the N=2 LL by Hartree-Fock theory but three-electron bubbles are not expected by the density matrix renormalization group calculations [41].…”

Spin and Charge Ordering in the Quantum Hall Regime

“…They predict that the electron bubbles arrange in a triangular lattice with a period of roughly 3 · , where = √ 2 /( ) is the cyclotron radius [92,93]. The number of electrons varies according to the partial filling˜with the restriction that the maximum number of electrons per bubble is limited to in the th Landau level (for > 1) [92,98] 1 . The optimal number of electrons per bubble can be well approximated by 3˜ [3,98].…”

“…It can be considered a special case of the bubble phase. For higher˜, the system undergoes a succession of phases separated by first order transitions with an increasing number of electrons per bubble [98].…”

“…The number of electrons varies according to the partial filling˜with the restriction that the maximum number of electrons per bubble is limited to in the th Landau level (for > 1) [92,98] 1 . The optimal number of electrons per bubble can be well approximated by 3˜ [3,98]. Thus, when increasing˜starting from˜= 0, at first only a single electron occupies a bubble site.…”