Probing theν=23fractional quantum Hall edge by momentum-resolved tunneling

Abstract

The nature of the fractional quantum Hall state with filling factor ν = 2/3 and its edge modes continues to remain an open problem in low-dimensional condensed matter physics. Here, we suggest an experimental setting to probe the ν = 2/3 edge by tunnel-coupling it to a ν = 1 integer quantum Hall edge in another layer of a two-dimensional electron gas (2DEG). In this double-layer geometry, the momentum of tunneling electrons may be boosted by an auxiliary magnetic field parallel to the two planes of 2DEGs. The threshold behavior of the current as a function of bias voltage and the boosting magnetic field yields information about the spectral function of the ν = 2/3 edge, and in particular about the nature of the chiral edge modes. Our theoretical analysis accounts also for the effects of Coulomb interaction and disorder.Introduction. In the conditions of quantum Hall effect, the compressible regions remain only at the edges of a sample and are known as edge states [1,2]. Edges of fractional Hall states are strongly-correlated chiral electron liquids [3]. The situation becomes even more intriguing for systems with filling factors different from those of Laughlin states, for which ν = 1/m with odd integer m > 0. Here we consider the particular case of a quantum Hall system with filling factor ν = 2/3.A prominent conjecture [4,5] considers the ν = 2/3 edge [6,7] as composed of two spatially separated edge channels: an outer channel with filling factor ν = 1 and an inner counter-propagating one corresponding to a ν = 1/3 liquid of hole states. Coulomb interactions between the two channels and backscattering off disorder enrich the physical picture and in the low-energy limit drive the system into a state with universal twoterminal and Hall conductance G = 2e 2 /3h [8]. Theory [8] predicts two effective edge modes, a charge-carrying mode and a counter-propagating neutral one. Recent shot noise measurements at a quantum point contact [9] have provided indirect evidence for the existence of such a neutral mode and a mechanism of upstream heating by neutral currents [9][10][11]. However, two observations put the picture of two counter-propagating modes in question and favor the possibility of two co-propagating ν = 1/3 modes as alternatively suggested long ago [12]. One is the observation of a G = e 2 /3h plateau [13,14] in the conductance through quantum point contacts. The second is the effective charge, detected through shot noise measurements [14], which crosses over from e/3 at higher temperature to 2e/3 at lower ones. A "unified" theory has recently [15] been proposed in terms of a four-channel model for a reconstructed edge. In this situation of competing theories, direct experimental evidence about the internal structure of the ν = 2/3 edge is called for.In this paper, we are suggesting a bilayer experiment to investigate the spectral function and, in particular, the nature of the chiral modes of the ν = 2/3 edge. In this experiment, the fractional quantum Hall edge is probed by momentum-resolved tunneling into o...

Charge equilibration in integer and fractional quantum Hall edge channels in a generalized Hall-bar device

“…5(h). The inter-channel distance a ′ is determined by the interaction 17,53 and may be affected by the edge potential and the energy gap 54 . Therefore, a ′ can be very short comparable to the magnetic length 46,55 and shorter than a for ν G = 4/3.…”

Abelian origin of $ν=2/3$ and $2+2/3$ fractional quantum Hall effect

“…In this section we will study the bulk properties of both ν = 1/3, 2/3 state. The nature of ν = 2/3 state is thought to be the particle-hole conjugation of Laughlin ν = 1/3 state 73,74 , but the discussion on ν = 2/3 state revives recently 27,28,30 , mainly due to experimental identification complex edge structures that is beyond the previous description [9][10][11] . We also study the ν = 2/3 state in the second Landau level(SLL), i.e.…”

“…The spin polarized ν = 2/3 FQH state is usually regarded as a particle-hole-conjugated Laughlin ν = 1/3 state or, equivalently, a hole 1/3 state embedded in the integer quantum Hall ν = 1 background 14 . This is the simplest example with counter-propagating edge modes, thus the nature of 2/3 state has been widely studied both theoretically and experimentally [14][15][16][17][18][19][20][21][22][23][24][25][26] .Especially, the upstream neutral edge mode has recently been identified in experiments [9][10][11][12][13] , together with a more delicate indication of edge reconstruction [27][28][29][30] . One of our motivation is to provide clear evidence of possible edge reconstruction of 2/3 state and uncover its connection with the experimental observations 9,10 .…”

Topological dephasing in theν=2/3fractional quantum Hall regime

“…Neutral modes have attracted much attention, as they are charge neutral and carry energy. They have been recently detected through shot noise measurements 6 , and their properties such as energy and decay length have been extensively studied [7][8][9][10][11][12][13][14][15][16][17][18][19][20] .…”