Transport evidence for phase separation into spatial regions of different fractional quantum Hall fluids near the boundary of a two-dimensional electron gas

Anomalous quantized plateaus in two-dimensional electron gas with gate confinement

Quantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer.

Spin-Selective Equilibration among Integer Quantum Hall Edge Channels

The equilibration between quantum Hall edge modes is known to depend on the disorder potential and the steepness of the edge. Modern samples with higher mobilities and setups with lower electron temperatures call for a further exploration of the topic. We develop a framework to systematically measure and analyze the equilibration of many (up to 8) integer edge modes. Our results show that spin-selective coupling dominates even for non-neighboring channels with parallel spin. Changes in magnetic field and bulk density let us control the equilibration until it is almost completely suppressed and dominated only by individual microscopic scatterers. This method could serve as a guideline to investigate and design improved devices, and to study fractional and other exotic states.

Magnetic-Field-Dependent Equilibration of Fractional Quantum Hall Edge Modes

Fractional conductance is measured by partitioning a ν=1 edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the ν=1 plateau, respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance e^{2}/3h arising from edge reconstruction. The results reveal a remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing magnetic field.

Spontaneous Breakdown of Topological Protection in Two Dimensions

Because of time-reversal symmetry, two-dimensional topological insulators support counterpropagating helical edge modes. Here we show that, unlike the infinitely sharp edge potential utilized in traditional calculations, an experimentally more realistic smooth edge potential gives rise to edge reconstruction and, consequently, spontaneous time-reversal symmetry breaking. Such edge reconstruction may lead to breaking of the expected perfect conductance quantization, to a finite Hall resistance at zero magnetic field, and to a spin current. This calculation underpins the fragility of the topological protection in realistic systems, which is of crucial importance in proposed applications.

Coulomb blockade with neutral modes

We study transport through a quantum dot in the fractional quantum Hall regime with filling factors ν=2/3 and ν=5/2, weakly coupled to the leads. We account for both injection of electrons to or from the leads, and quasiparticle rearrangement processes between the edge and the bulk of the quantum dot. The presence of neutral modes introduces topological constraints that modify qualitatively the features of the Coulomb blockade (CB). The periodicity of CB peak spacings doubles and the ratio of spacing between adjacent peaks approaches (in the low temperature and large dot limit) a universal value: 2∶1 for ν=2/3 and 3∶1 for ν=5/2. The corresponding CB diamonds alternate their width in the direction of the bias voltage and allow for the determination of the neutral mode velocity, and of the topological numbers associated with it.

Edge reconstruction in the ν=2/3 fractional quantum Hall state

The edge structure of the ν=2/3 fractional quantum Hall state has been studied for several decades, but recent experiments, exhibiting upstream neutral mode(s), a plateau at a Hall conductance of 1/3(e2/h) through a quantum point contact, and a crossover of the effective charge, from e/3 at high temperature to 2e/3 at low temperature, could not be explained by a single theory. Here we develop such a theory, based on edge reconstruction due to a confining potential with finite slope, that admits an additional ν=1/3 incompressible strip near the edge. Renormalization group analysis of the effective edge theory due to disorder and interactions explains the experimental observations.

Quantization of the diagonal resistance: density gradients and the empirical resistance rule in a 2D system

We have observed quantization of the diagonal resistance, R(xx), at the edges of several quantum Hall states. Each quantized R(xx) value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R(xy). Peaks in R(xx) occur at different positions in positive and negative magnetic fields. Practically all R(xx) features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R(xx) is determined by R(xy) and unrelated to the diagonal resistivity rho(xx). Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.