Reconstruction of Fractional Quantum Hall Edges

Abstract

We study the interplay of interaction, confining potential and effects of finite temperature at the edge of a quantum Hall liquid. Our exact diagonalization calculation indicates that edge reconstruction occurs in the fractional quantum Hall regime for a variety of confining potential, including ones that correspond to a "sharp" edge. Our finite temperature Hartree-Fock calculation for integer quantum Hall edges indicates that reconstruction is suppressed above certain temperature. We discuss the implication of our results on recent edge tunneling and microwave absorption experiments. 73.40.Hm, 71.10.Pm The physics of the quantum Hall edge states is important for a number of reasons. When the system is in a quantum Hall state, the bulk is incompressible and the edge carries the dissipationless current. In addition, the edge states also provide a unique arena to study correlated electrons in one-dimension, where the Fermi liquid theory breaks down. Indeed, the edge electrons have been argued [1] to form the so-called chiral Luttinger liquid (CLL) in this case, with many properties determined solely by the robust bulk topological order of the system, and independent of the details of the edge potential. For example it was predicted [1] that in the tunneling between a Fermi liquid and a quantum Hall edge, the current-voltage relation follows a power-law I ∼ V α , with universal exponents α for simple edges like that of bulk filling ν = 1/3. While such power-law behavior has been observed in experiments indicating non-Fermi liquid behavior [2], detailed studies of the bulk filling factor as well as sample dependence of α have found important differences from the predictions of CLL theory [3][4][5].In the CLL theory [1], one assumes that there is a single boundary separating the incompressible quantum Hall liquid from the electron vacuum, and for simple edges like those of ν = 1 and ν = 1/3, the only low-energy excitations are the shape fluctuations of the boundary, which form a single branch of chiral bosons. On the other hand it is known that for integer quantum Hall edges, the competition between electron-electron Coulomb interaction and edge confining potential can lead to edge reconstruction [6,7], when the edge confining potential is smooth enough. At the reconstructed edge, the electron density oscillates and there are more than one chiral boson modes, which do not propagate in the same direction [7]. Thus edge reconstruction can change the physics at the edge qualitatively.Motivated by the edge tunneling puzzle, as well as a recent microwave absorption measurement in which the presence of artificial edge channels leads to absorption enhancement [8], we examine in this work the possibility of edge reconstruction when the bulk filling is fractional. We find numerical evidence from exact diagonalization studies suggesting that edge reconstruction can occur when the bulk filling is fractional as well, for a variety of edge confining potentials (including those we believe properly describe a sharp cleaved edge)...

Identification of the fractional quantum Hall edge modes by density oscillations

“…35,41 The results in Fig.1(b) shows that the energies of the edge spectrum from the Jacks are consistent with the exact diagonalization with a high accuracy. The largest leakage is in the order of 10…”

“…42 One possible reason of this discrepancy is electronic density reconstruction at the edge of FQH liquid. 41,43 The edge reconstruction introduces additional non-chiral edge modes that do not correspond to the bulk topology which break down the universality. From a simple electrostatic analysis of the 2DEG in semiconductor heterostructure as did in Ref.…”

Electron interactions in an antidot in the integer quantum Hall regime

“…The edge reconstruction is also important in the fractional regime as it is determined by the interplay of electron-electron interaction in the fractional regime, the single-particle electrostatic edge potential (or antidot potential), and effects of finite temperature. A recent numerical prediction [110] on edge reconstruction in the fractional regime has been linked to experimental results [111] on the microwave conductivity of two-dimensional electron systems with an array of antidots. More systematic studies on the edge reconstruction are required to understand excitations of an antidot in both the integer and fractional regimes.…”

Effects of Quantum Hall Edge Reconstruction on Momenum-Resolved Tunneling

“…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.…”