Effects of Quantum Hall Edge Reconstruction on Momenum-Resolved Tunneling

Abstract

Received DAY MONTH YEAR Revised DAY MONTH YEARDuring the reconstruction of the edge of a quantum Hall liquid, Coulomb interaction energy is lowered through the change in the structure of the edge. We use theory developed earlier by one of the authors [K. Yang, Phys. Rev. Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a reconstructed edge, and study the consequences of the edge reconstruction for the momentum-resolved tunneling into the edge. It is found that additional excitation modes that appear after the reconstruction produce distinct features in the energy and momentum dependence of the spectral function, which can be used to detect the presence of edge reconstruction. Keywords: Quantum Hall Effect; Edge Reconstruction; TunnelingThe paradigm of the Quantum Hall effect (QHE) edge physics is based on an argument due to Wen, 1 according to which the low-energy edge excitations are described by a chiral Luttinger liquid (CLL) theory. One attractive feature of this theory is that due to the chirality, the interaction parameter of the CLL is often tied to the robust topological properties of the bulk and is independent of the details of electron interaction and edge confining potential; studying the physics at the edge thus offers an important probe of the bulk physics. It turns out, however, that the CLL ground state may not always be stable.2,3 On the microscopic level, the instability is driven by Coulomb interactions and leads to the change of the structure of the edge. This effect has been termed "edge reconstruction". One of its manifestations is the appearance of new low-energy excitations of the edge not present in the original CLL theory.Previous numerical studies 4,5 have suggested that the phenomenon of edge reconstruction can be understood as an instability of the original edge mode described by the CLL theory. This instability occurs as a result of increasing curvature of the edge spectrum as the edge confining potential softens. The spectrum curves down at high values of momenta until it touches zero at the transition point. This signals

Universality of the Edge-Tunneling Exponent of Fractional Quantum Hall Liquids

“…This suggests that the true asymptotic behavior in the reconstructed case can only be observed at a larger length scale. Such behavior agrees qualitatively with the edge reconstruction corrections to α at short distances: δα ∝ v φ /v 2 [16,23], where v φ and v are of neutral and charge modes, respectively. The significant drop in α for ν = 1/3 in the case of hard edges corroborates the previous results for long-range interaction [19,20,21].…”