Observability of counterpropagating modes at fractional quantum Hall edges

Zülicke, U.; MacDonald, Allan H.; Johnson, Michael D.

doi:10.1103/physrevb.58.13778

Cited by 15 publications

(15 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and 20) where ϑ 1 and ϑ 2 are the elliptic theta functions 22,23 . In the following equations we define…”

Section: A Phase Field Correlation Functionsmentioning

confidence: 99%

“…(16)], the result can be obtained using also Eqs. (19) and (20). In both of these terms space coordinates appear in the combinations z ± +z ± , z ′ ± +z ′ ± , and z ± +z ′ ± , z ± + z ′ ± , which are not translational invariant.…”

Section: A Phase Field Correlation Functionsmentioning

confidence: 99%

“…IV we discuss our results, comparing some predictions of this model with the predictions of more realistic models that must be solved numerically. We also discuss the possible roles of edge reconstruction and of the incompressible strip formation 19,20 on the properties of experimental systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Edge state tunneling in a split Hall bar model

Papa

MacDonald

2005

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.

show abstract

“…and 20) where ϑ 1 and ϑ 2 are the elliptic theta functions 22,23 . In the following equations we define…”

Section: A Phase Field Correlation Functionsmentioning

confidence: 99%

Section: A Phase Field Correlation Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Edge state tunneling in a split Hall bar model

Papa

MacDonald

2005

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…We focus here on the experimentally realistic case when inner and outer edges are strongly coupled and the normal modes correspond to the familiar [30] charged and neutral edge-density waves [36]. In this limit, we have [30,31] …”

mentioning

confidence: 99%

Momentum-resolved tunneling into fractional quantum Hall edges

2002

Self Cite

View full text Add to dashboard Cite

Tunneling from a two-dimensional contact into quantum-Hall edges is considered theoretically for a case where the barrier is extended, uniform, and parallel to the edge. In contrast to previously realized tunneling geometries, details of the microscopic edge structure are exhibited directly in the voltage and magnetic-field dependence of the differential tunneling conductance. In particular, it is possible to measure the dispersion of the edge-magnetoplasmon mode, and the existence of additional, sometimes counterpropagating, edge-excitation branches could be detected. PACS numbers: 73.43.Jn, 73.43.Cd, 71.10.Pm The quantum Hall (QH) effect[1] arises due to incompressibilities developing in two-dimensional electron systems (2DES) at special values of the electronic sheet density n 0 and perpendicular magnetic field B for which the filling factor ν = 2πhc n 0 /|eB| is equal to an integer or certain fractions. The microscopic origin of incompressibilities at fractional ν is electron-electron interaction. Laughlin's trial-wave-function approach [2] successfully explains the QH effect at ν = ν 1,p ≡ 1/(p + 1) where p is a positive even integer. Our current microscopic understanding of why incompressibilities develop at many other fractional values of the filling factor, e.g., ν m,p ≡ m/(mp + 1) with nonzero integer m = ±1, is based on hierarchical theories [3,4,5].The underlying microscopic mechanism responsible for creating charge gaps at fractional ν implies peculiar properties of low-energy excitation in a finite quantum-Hall sample which are localized at the boundary [6]. For ν = ν m,p , m branches of such edge excitations [7,8,9,10] are predicted to exist which are realizations of strongly correlated chiral one-dimensional electron systems called chiral Luttinger liquids (χLL). Extensive experimental efforts were undertaken recently to observe χLL behavior because this would yield an independent confirmation of our basic understanding of the fractional QH effect. In all of these studies [11,12,13,14,15,16], current-voltage characteristics yielded a direct measure of the energy dependence of the tunneling density of states for the QH edge. This quantity generally contains information on global dynamic properties as, e.g., excitation gaps and the orthogonality catastrophe, but lacks any momentum resolution. Power-law behavior consistent with predictions from χLL theory was found [11,12,15] for the edge of QH systems at the Laughlin series of filling factors, i.e., for ν = ν 1,p . However, at hierarchical filling factors, i.e., when ν = ν m,p with |m| > 1, predictions of χLL theory are, at present, not supported by experiment [13,14]. This discrepancy inspired theoretical works, too numerous to cite here, from which, however, no generally accepted resolution emerged. Current experiments [16] suggest that details of the edge potential may play a crucial Two mutually perpendicular two-dimensional electron systems are realized, e.g., in a semiconductor heterostructure. An external magnetic field is applied such tha...

show abstract

“…The d 2=3 to zero edge itself has counterpropagating modes which leads to a disorder-dependent edge structure. The clean 2=3 edge has an outer 1 mode and an inner (counterpropagating) ÿ1=3 mode [7,17]. But as Ref.…”

mentioning

confidence: 99%

Universal Periods in Quantum Hall Droplets

2007

View full text Add to dashboard Cite

Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states. . Here we will focus only on the Abelian quantum Hall states, but we will make use of their topological properties to reveal universal periodicities (as a function of magnetic flux through the droplet) in the ground-state energy and edge properties of a quantum Hall droplet inside a surrounding Hall fluid of a different filling factor. The universal periodicities in the groundstate properties can generically be used to probe the quantum Hall edge states in equilibrium settings.Our work is motivated in part by a series of beautiful experiments done on quantum Hall interferometers where superperiods and fractional statistics have purportedly been observed [4]. Several theoretical studies have already addressed these experiments [5], but a complete picture, particularly in the fractional quantum Hall regime, is still lacking. In this Letter we study the universal properties of a finite size quantum Hall droplet inside a quantum Hall fluid of a different filling factor (Fig. 1). For most geometries and droplet filling factors we find that the ground-state energy of the system has a periodicity with magnetic flux through the inner droplet that is determined only by the two filling fractions in the limit that the charging energy of the surrounding fluid edge tends to zero. However, edges such as that of the 2=3 state (which have counterpropagating modes and disorder-influenced excitations [6]) require a special degree of consideration, as we discuss below.Consider a droplet of filling factor d surrounded by a fluid of filling factor s , which itself may be inside an outer fluid of filling o (Fig. 1). As magnetic flux is adiabatically threaded through the inner droplet, its ground-state energy and its radius oscillate with a universal periodicity. This periodicity reveals important information about the microscopic structure of the droplet edge itself, thus providing a mechanism by which theoretical edge models can be directly tested experimentally. We concentrate on two important special cases:General filling fractions with Abelian statistics follow one of the two cases above. While disorder does not play a central role in the physics of the edge in case (i), in case (ii) disorder determines the nature of the edge excitations [6], by causing counterpropagating modes of th...

show abstract

Observability of counterpropagating modes at fractional quantum Hall edges

Cited by 15 publications

References 40 publications

Edge state tunneling in a split Hall bar model

Edge state tunneling in a split Hall bar model

Momentum-resolved tunneling into fractional quantum Hall edges

Universal Periods in Quantum Hall Droplets

Contact Info

Product

Resources

About