We investigate dynamic nuclear polarization in quantum point contacts (QPCs) in the integer and fractional quantum Hall regimes. Following the application of a dc bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, ν=1/2, suggesting an interpretation in terms of composite fermions. Polarizing and detecting at different filling factors indicates that Zeeman energy is reduced by the induced nuclear polarization. Mapping effects from integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of magnetic induction, chemical potential and temperature. The Hall resistance function contains a single-electron energy spectrum, which has phenomenological perturbation terms with three tunable parameters. The formula yields 12 plateaus that are consistent with the experiment. The perturbations can be interpreted as precession or nutation of a Landau orbital in…
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. Especially, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
在分数量子霍尔效应下，我们测量了门控GaAs/Al $_{x}$ Ga $_{1-x}$ As异质结中二维电子系统（2DES）的对角（$ρ_{xx}$）和霍尔（$ρ_{xy}$）磁阻张量分量，以及2DES与门极之间的电容.我们在相当低的磁场下观察到了1/3和2/3分数量子霍尔效应，此时相应的量子态密度的分数极小值已经消失，表明准粒子能隙被完全抑制。
We report a simple route to generate magnetotransport data that results in fractional quantum Hall plateaus in the conductance. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that th…
Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. We point out that optical probes are enabled by the periodic potentials produced by a moiré pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moiré-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on $f-$sum rule considerations supplemented by a perturbative analysis of the influence of the moiré potential on many-body states.
We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\pm e/3$ at fractional fillings of $ν= \pm 1/3$. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against thermal excitation. The capability of localizing fractional quasiparticles on QH antidots brings promising opportunities for realizing anyon braiding and novel quantum electronics.
The fractional quantum hall effect (FQHE) is a milestone of modern day physics, its disovery paved the way for the study of fractional charges which do not obey abelian physics. However, all FQHE require an external magnetic field in order for there to be fractionally charged electrons. This work shows a theoretical study of strongly interaction electrons in the Kagome lattice with magnetism. Under optimal conditions, a band gap opens on the surface of the material which hosts fractional Fermions. These fractional Fermions form composite quasi-electrons without the need for external magnetic f…
We study the linear thermoelectric response of a quantum dot embedded in a constriction of a quantum Hall bar with fractional filling factors nu=1/m within Laughlin series. We calculate the figure of merit ZT for the maximum efficiency at a fixed temperature difference. We find a significant enhancement of this quantity in the fractional filling in relation to the integer-filling case, which is a direct consequence of the fractionalization of the electron in the fractional quantum Hall state. We present simple theoretical expressions for the Onsager coefficients at low temperatures, which expl…
Hole-conjugate states of the fractional quantum Hall effect host counter-propagating edge channels which are thought to exchange charge and energy. These exchanges have been the subject of extensive theoretical and experimental works; in particular, it is yet unclear if the presence of integer quantum Hall edge channels stemming from fully filled Landau levels affects heat equilibration along the edge. In this letter, we present heat transport measurements in quantum Hall states of graphene demonstrating that the integer channels can strongly equilibrate with the fractional ones, leading to ma…
Fractional charge and statistics are hallmarks of low-dimensional interacting systems such as fractional quantum Hall (QH) systems. Integer QH systems are regarded noninteracting, yet they can have fractional charge excitations when they couple to another interacting system or time-dependent voltages. Here, we notice Abelian fractional mutual statistics between such a fractional excitation and an electron, and propose a setup for detection of the statistics, in which a fractional excitation is generated at a source and injected to a Mach-Zehnder interferometer (MZI) in the integer QH regime. I…
The possibility of realizing fractional quantum Hall liquids in photonic systems has attracted a great deal of interest of late. Unlike electronic systems, interactions in photonic systems must be engineered from non-linear elements and are thus subject to positional disorder. The stability of the topological liquid relies on repulsive interactions. In this paper we investigate the stability of fractional quantum Hall liquids to impurities which host attractive interactions. We find that for sufficiently strong attractive interactions these impurities can destroy the topological liquid. Howeve…
Moire driven edge reconstruction in Fractional quantum anomalous Hall states
The Hong Kong University of Science and Technology（香港科技大学）；Center for Theoretical Condensed Matter Physics, The Hong Kong University of Science and Technology（香港科技大学理论凝聚态物理中心）
Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect
受分数量子霍尔效应中极低能量集体模式的发现的启发（Kang，Pinczuk { \em et al.}），在低于塞曼能量的情况下，我们从理论上研究了分数量子霍尔态在$ν=2/5$和3/7的自旋反转激发，发现了与$ν=1/3$不同的性质。我们发现，一个低能量，电荷中性的“自旋回旋子”，与自旋反转激发，涉及在复合费米子朗道能级指数的变化，具有合理的协议与实验的能量。
