Edge reconstructions in fractional quantum Hall systems

Abstract

Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges of the incompressible quantum Hall regions, where gapless excitations are present. We present a microscopic calculation of the edge states in the fractional quantum Hall systems at various filling factors using the extended Hamiltonian theory of the fractional quantum Hall effect. We find that at ν = 1/3 the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors, such as ν = 2/5, 3/7, are robust against reconstruction. We present the results for the dependence of the edge states on various system parameters such as temperature, functional form and range of electron-electron interactions, and the confining potential. Our results have implications for the tunneling experiments into the edge of a fractional quantum Hall system.

Nonequilibrated Counterpropagating Edge Modes in the Fractional Quantum Hall Regime

“…The latter one was recently observed via shot noise measurements [16][17][18] and also by heating a narrow constriction [16,[19][20][21]. Noting that for a sufficiently shallow confining potential near the edge, edge reconstruction was predicted to take place also in a variety of non-hole-conjugate fractional states [22][23][24][25][26][27][28][29] (neutral modes had been recently found in electronlike fractional states [18]) and even in integer fillings [30].…”

Aharonov–Bohm interference of fractional quantum Hall edge modes

“…[40]. We mention that a sharp confining potential may also be beneficial for measuring interference at the ν = 1/3 state by preventing edge reconstruction and the proliferation of neutral edge modes [20,47,48] which may cause dephasing [49,50]; neutral modes have been detected at ν = 1/3 and numerous other fractional quantum Hall states in standard GaAs structures without screening wells [51].…”

Charge and Statistics of Quasiparticles in Fractional Quantum Hall Effect

“…It is found that at ν = 1/3 the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors are robust against reconstruction. 10 Since the edge physics at ν = 1/3 is not confined to the boundary but extends to the bulk, we should consider our results within a specific range. 11 However, as the size of the droplet varies as R ∼ √ N, it is expected that the situation will improve for large N .…”