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arXiv:cond-mat/9810307 · Physical Review Letters

Collective Excitations in the Dilute 2D Electron System

M. A. Eriksson, Aron Pinczuk, B. S. Dennis, Steven H. Simon, Loren N. Pfeiffer, K. W. West

Published Mar 8, 1999• 73 citations
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Abstract

We report inelastic light scattering measurements of dispersive spin and charge density excitations in dilute 2D electron systems reaching densities less than ${10}^{10}{\mathrm{cm}}^{\ensuremath{-}2}$. In the quantum Hall state at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$, roton critical points in the spin inter-Landau level mode show a pronounced softening as ${r}_{s}$ is increased. Instead of a soft mode instability predicted by Hartree-Fock calculations for ${r}_{s}\ensuremath{\sim}3.3$, we find evidence of multiple rotons in the dispersion of the softening spin excitations.

DOI
10.1103/physrevlett.82.2163

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We study the effect of electron-electron interaction on the charge and spin structures at the edge of integer quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems indicates that the low-energy excitations of the $\ensuremath{\nu}=1$ ferromagnetic state are bosonic edge spin waves. Instabilities of the ferromagnetic state with altering confinement strength result from the softening of these edge spin waves and formation of edge spin textures. In the $\ensuremath{\nu}\ensuremath{\lesssim}2$ regime, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appearing between two compact states are their edge spin waves. The initial $\ensuremath{\nu}=2$ instability is toward the compact state with total spin 1. Larger systems are studied using a microscopic trial wave function, and some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit.
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