A theoretical calculation is presented of current noise which is due charge fractionalization, in two interacting edge channels in the integer quantum Hall state at filling factor $ν=2$. Because of the capacitive coupling between the channels, a tunneling event, in which an electron is transferred from a biased source lead to one of the two channels, generates propagating plasma mode excitations which carry fractional charges on the other edge channel. When these excitations impinge on a quantum point contact, they induce low-frequency current fluctuations with no net average current. A perturbative treatment in the weak tunneling regime yields analytical integral expressions for the noise as a function of the bias on the source. Asymptotic expressions of the noise in the limits of high and low bias are found.
Fractionalization is a phenomenon where an elementary excitation partitions into several pieces. This picture explains non-trivial transport through a junction of one-dimensional edge channels defined by topologically distinct quantum Hall states, for example, a hole-conjugate state at Landau-level filling factor $ν$ = 2/3. Here we employ a time-resolved scheme to identify an elementary fractionalization process; injection of charge q from a non-interaction region into an interacting and scattering region of one-dimensional channels results in the formation of a collective excitation with char…
One remarkable feature of strongly correlated systems is the phenomenon of fractionalization where quasiparticles carry only a fraction of the charge or spin of the elementary constituents. Such quasiparticles often present anyonic statistics in two dimensions and lie at the heart of the fractional quantum Hall effect. We discuss the observation of fractionalization and anyonic statistics already in the integer quantum Hall effect coupled to a metallic island. A continuous fractional emitter is proposed, which sends dilute beams of non-integer charges, and its full counting statistics is obtai…
We study dephasing in electron transport through a large quantum dot (a Fabry-Perot interferometer) in the fractional quantum Hall regime with filling factor $2/3$. In the regime of sequential tunneling, dephasing occurs due to electron fractionalization into counterpropagating charge and neutral edge modes on the dot. In particular, when the charge mode moves much faster than the neutral mode, and at temperatures higher than the level spacing of the dot, electron fractionalization combined with tje fractional statistics of the charge mode leads to the dephasing selectively suppressing $h/e$ A…
We study the problem of injecting single electrons into interacting one-dimensional quantum systems, a fundamental building block for electron quantum optics. It is well known that such injection leads to charge and energy fractionalization. We elucidate this concept by calculating the nonequilibrium electron distribution function in the momentum and energy domains after the injection of an energy-resolved electron. Our results shed light on how fractionalization occurs via the creation of particle-hole pairs by the injected electron. In particular, we focus on systems with a pair of counterpr…
Fractional charges in emergent neutral modes at the integer quantum Hall effect
在低维相互作用电子系统中，电荷分裂是一种可能的激发。一个已知的例子是在分数量子霍尔效应（Fractional Hall effect，HHE）机制中的分数电荷，这是电子之间的强库仑相互作用的结果，电子的动能被强磁场淬灭。或者，整数QHE（IQHE），其中电子在朗道能级（LL）中主要表现为独立粒子，缺乏这种分馏。然而，对于填充v=2，3，.电子在共同传播的相邻手性边缘沟道中传播，从而相互作用并改变非相互作用的LL。例如，在v=2时，选择性地注入到单个非相互作用（裸）边缘沟道中的电子预期在相互作用区域中分解成“快”模式和“慢”模式;每个模式携带在两个裸沟道之间共享的部分电荷。在这里，我们报告我们的灵敏的散粒噪声测量，确认存在这样的细分在v=2。注入分区电流到一个“热”边缘通道导致低频散粒噪声在相邻的无电流的“冷”边缘通道后，它已被分区。控制热通道和冷通道的划分允许确定两个通道中的部分电荷以及通道的速度差。这种方法可以很容易地扩展到研究在二维系统的拓扑结构支配边缘通道输运的相互作用。
Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. Here we advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids, and uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL). We show the first exact analytic computation of the quasielectron Berry con…
Coulomb interaction has a striking effect on electronic propagation in one dimensional conductors. The interaction of an elementary excitation with neighboring conductors favors the emergence of collective modes which eventually leads to the destruction of the Landau quasiparticle. In this process, an injected electron tends to fractionalize into separated pulses carrying a fraction of the electron charge. Here we use two-particle interferences in the electronic analog of the Hong-Ou-Mandel experiment in a quantum Hall conductor at filling factor 2 to probe the fate of a single electron emitte…
We show that correlated two-particle backscattering can induce fractional charge oscillations in a quantum dot built at the edge of a two-dimensional topological insulator by means of magnetic barriers. The result nicely complements recent works where the fractional oscillations were obtained employing of semiclassical treatments. Moreover, since by rotating the magnetization of the barriers a fractional charge can be trapped in the dot via the Jackiw-Rebbi mechanism, the system we analyze offers the opportunity to study the interplay between this noninteracting charge fractionalization and th…
We study nonequilibrium transport through a charge Kondo device realizing the two-channel Kondo critical point in a recent experiment by Iftikhar et al. By computing the current and shot noise at low voltages near the critical point, we obtain a universal Fano factor $e^*/e=1/2$. We identify elementary transport processes as weak scattering of emergent fermions carrying half-integer charge quantum numbers. This forms an experimental fingerprint for fractionalization in a non-Fermi liquid, which, compared to spin-Kondo devices, could be observed at elevated temperatures.
Fractional charge (and statistics) in Luttinger liquids
电荷分馏是多粒子系统中准粒子激发相对于基本电荷单位呈现非整数值的现象。从场论模型和从物理实现已知这样的系统的示例。近年来，人们对Luttinger液体理论描述的一维体系中的电荷分馏产生了兴趣。这些都是无隙系统，这就产生了一个问题，即非整数电荷是否应该被视为与有隙系统中相同意义的尖锐电荷。在这次演讲中，我首先介绍了电荷分馏作为一种效应在带隙系统，并讨论在什么意义上的电荷分馏效应是发现在无隙Luttinger液体。该演讲基于Mats Horsdal和Thors Hans Hansson最近的一篇论文。
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…
Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that …
Universal fractionalization of quantum transport characteristics in Majorana quantum dot devices is expected to emerge for well separated Majorana bound states. We show that the Majorana universality of the differential shot noise $\partial S^>/\partial V$ and conductance $\partial I/\partial V$ at low bias voltages $V$ arises only in ideal setups with only one Majorana mode entangled with the quantum dot. In realistic devices, where both Majorana modes are entangled with the quantum dot, $\partial S^>/\partial V$ and $\partial I/\partial V$ become very sensitive to tunneling phases and their …
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.
We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $σ_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $σ_{xy} = \pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with $σ_{xy} = 0$ can be realized at the band center, hence restoring fully a conventional integer QHE with particle-ho…
Fractionalization from Kinetic Frustration in Doped Two-Dimensional SU(4) Quantum Magnets
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）
Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance standards by means of the integer quantum Hall effect. We propose modifications of samples displaying the integer quantum Hall effect which render the tunability of the Fermi velocity possible by external control parameters such as gate voltages. In this way, so far unexplored possibilities arise to realize devices such as tunable delay lines and interferometers.
The quest to realize novel phases of matter with topological order is an important pursuit with implications for strongly correlated physics and quantum information. Utilizing ideas from state-of-the-art coherent control of artificial quantum systems such as superconducting circuits, we present a proposal to realize bosonic fractional quantum Hall physics on small lattices by creating nearly flat topological bands using staggered flux patterns. Fingerprints of fractionalization through charge pumping can be observed with nearly perfect quantization using as few as 24 lattice sites (two photons…
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…
