Controllable point junctions between different quantum Hall phases are a necessary building block for the development of mesoscopic circuits based on fractionally-charged quasiparticles. We demonstrate how particle-hole duality can be exploited to realize such point-contact junctions. We show an implementation for the case filling factors $ν=1$ and $ν^*\le1$ in which both the fractional filling $ν^*$ and the coupling strength can be finely and independently tuned. A peculiar crossover from insulating to conducting behavior as $ν^*$ goes from 1/3 to 1 is observed. These results highlight the key role played on inter-edge tunneling by local charge depletion at the point contact.
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
We discuss anomalous fractional quantum Hall effect that exists without external magnetic field. We propose that excitations in such systems may be described effectively by non-interacting particles with the Hamiltonians defined on the Brillouin zone with a branch cut. Hall conductivity of such a system is expressed through the one-particle Green function. We demonstrate that for the Hamiltonians of the proposed type this expression takes fractional values times Klitzing constant. Possible relation of the proposed construction with degeneracy of ground state is discussed as well.
We study the $ν={\pm}1/2$ fractional quantum Hall states in graphene observed by Zibrov et al. [Nat. Phys. 14, 930 (2018)]. The parton construction is employed to provide a valley unpolarized trial wave function for these states. The lattice scale valley anisotropic terms in the Hamiltonian soften the repulsion between electrons in different valleys to favor the valley unpolarized state. The validity of our proposal is corroborated by numerical calculations.
We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $ν=n/(2n+1)$ has a striking {\it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson loca…
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 study the time-dependent dynamical phase of fractional quasiparticles in quantum Hall states using Ramsey interferometry. A Ramsey two-pulse voltage modulation generates an interference term in the current noise of a quantum point contact oscillating with the dynamical phase. We show that the interference pattern probes the Green's function of the fractional quasi-particles in the time domain and reveals the fractional charge. We address both the case of a point-like tunnel junction and the case of momentum-resolved tunneling which also provides information on the speed of those quasipartic…
Magnetic Induction Dependence of Hall Resistance in Fractional Quantum Hall Effect
通过分析[J. P. Eisenstein和H. L. Stormer，{Science} { \bf 248}，1510（1990）]。该公式是作为磁感应强度、化学势和温度的函数给出的。霍尔电阻函数包含一个单电子能谱，它具有三个可调参数的唯象微扰项。该公式产生了与实验一致的12个平台。这些扰动可以解释为三维空间中朗道轨道的岁差或章动。
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。
