Momentum-resolved tunneling into fractional quantum Hall edges

Zülicke, U.; Shimshoni, Efrat; Governale, Michele

doi:10.1103/physrevb.65.241315

Cited by 26 publications

(36 citation statements)

References 31 publications

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“…While this is a convenient approximation for theoretical investigations that has been often assumed in previous works, 5,6,7,8 it needs to be further justified. Tunneling into multimode 1D wires was considered in Ref.…”

Section: Appendix A: Independent-mode Approximationmentioning

confidence: 99%

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

et al. 2003

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We present theoretical calculations and experimental measurements which reveal the Luttingerliquid (LL) nature of elementary excitations in a system consisting of two quantum wires connected by a long narrow tunnel junction at the edge of a GaAs/AlGaAs bilayer heterostructure. The boundaries of the wires are important and lead to a characteristic interference pattern in measurements on short junctions. We show that the experimentally observed modulation of the conductance oscillation amplitude as a function of the voltage bias can be accounted for by spin-charge separation of the elementary excitations in the interacting wires. Furthermore, boundaries affect the LL exponents of the voltage and temperature dependence of the tunneling conductance at low energies. We show that the measured temperature dependence of the conductance zero-bias dip as well as the voltage modulation of the conductance oscillation pattern can be used to extract the electron interaction parameters in the wires.

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Section: Appendix A: Independent-mode Approximationmentioning

confidence: 99%

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

et al. 2003

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“…In the context of the quantum Hall effect, similar settings using momentum-conserved tunneling have been discussed in Refs. [18][19][20][21]. Bilayer settings like the one we are suggesting are to be distinguished from tunnel-coupled lateral quantum Hall systems [22].…”

mentioning

confidence: 69%

“…2 /2 and µ − n = 3/2 [18]. The exponent µ + n of the non-analytic line defined by u − is smallest for n = 0 and −1.…”

mentioning

confidence: 93%

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

Meier¹,

Gefen²,

Glazman³

2014

Phys. Rev. B

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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...

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“…We note that such perturbative calculations have been done in various tunneling situations and are a valuable tool to perform spectroscopy of reduced dimensionality samples [17,23,24,25,27] in the quantum Hall regime.…”

Section: The Geometry and Kinematics Of Tunnelingmentioning

confidence: 99%

Tunneling in fractional quantum Hall line junctions

2005

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We study the tunneling current between two counterpropagating edge modes described by chiral Luttinger liquids when the tunneling takes place along an extended region. We compute this current perturbatively by using a tunnel Hamiltonian. Our results apply to the case of a pair of different two-dimensional electron gases in the fractional quantum Hall regime separated by a barrier, e. g. electron tunneling. We also discuss the case of strong interactions between the edges, leading to nonuniversal exponents even in the case of integer quantum Hall edges. In addition to the expected nonlinearities due to the Luttinger properties of the edges, there are additional interference patterns due to the finite length of the barrier.

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Momentum-resolved tunneling into fractional quantum Hall edges

Cited by 26 publications

References 31 publications

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

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

Tunneling in fractional quantum Hall line junctions

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