Regensburg 2000 – wissenschaftliches Programm

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HL: Halbleiterphysik

HL 17: Symposium: Der Quanten-Hall-Effekt wird 20 (II)

HL 17.7: Vortrag

Dienstag, 28. März 2000, 18:15–18:30, H15

Umklapp scattering at quantum-Hall edges — •U. Zülicke — Institut für Theoretische Festkörperphysik, Universität Karlsruhe

The sharp edge of a quantum-Hall sample at filling factor ν=1 supports a single branch of chiral one-dimensional (1D) excitations. However, if the confining potential is just not sharp enough to stabilize a single compact quantum-Hall droplet against electrostatic repulsion, a transition occurs to a new configuration where a satellite lump of electronic charge surrounds a smaller compact droplet [1,2]. This new reconstructed state supports three branches of chiral 1D edge excitations, one of which having chirality opposite to the other two. We have studied the low-energy, long-wave-length edge excitations of a reconstructed quantum-Hall sample and find that, in addition to forward scattering between the three edge branches, Coulomb interactions give rise to a new type of Umklapp scattering which has not been discussed before. As Umklapp processes do not conserve particle number in each edge branch separately, they cannot be accounted for within an effective Tomonaga-Luttinger description. Rather, a chiral version of the familiar Sine-Gordon model is obtained, which we are able to solve exactly using a refermionization trick [3]. Calculating electronic correlation functions, we find that Umklapp scattering suppresses Luttinger-liquid behavior below a certain energy scale.