Thermopower as a Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall States

Thermoelectric response of fractional quantized Hall and re-entrant insulating states in the N=1 Landau level

Detailed measurements of the longitudinal thermopower of two-dimensional electrons in the first excited Landau level are reported. Clear signatures of numerous fractional quantized Hall states, including those at $ν= 5/2$ and 7/3, are observed in the magnetic field and temperature dependence of the thermopower. An abrupt collapse of the thermopower is observed below about $T= 40$ mK at those filling factors where re-entrant insulating electronic states have been observed in conventional resistive transport studies. The thermopower observed at $ν= 5/2$ is discussed in the context of recent theo…

Anomalous conductivity, Hall factor, magnetoresistance, and thermopower of accumulation layer in $\text{SrTiO}_3$

We study the low temperature conductivity of the electron accumulation layer induced by the very strong electric field at the surface of $\text{SrTiO}_3$ sample. Due to the strongly nonlinear lattice dielectric response, the three-dimensional density of electrons $n(x)$ in such a layer decays with the distance from the surface $x$ very slowly as $n(x) \propto 1/x^{12/7}$. We show that when the mobility is limited by the surface scattering the contribution of such a tail to the conductivity diverges at large $x$ because of growing time electrons need to reach the surface. We explore truncation …

Thermopower of Two-Dimensional Electrons at $ν$ = 3/2 and 5/2

The longitudinal thermopower of ultra-high mobility two-dimensional electrons has been measured at both zero magnetic field and at high fields in the compressible metallic state at filling factor $ν= 3/2$ and the incompressible fractional quantized Hall state at $ν= 5/2$. At zero field our results demonstrate that the thermopower is dominated by electron diffusion for temperatures below about $T = 150$ mK. A diffusion dominated thermopower is also observed at $ν= 3/2$ and allows us to extract an estimate of the composite fermion effective mass. At $ν= 5/2$ both the temperature and magnetic fie…

Low-field diffusion magneto-thermopower of a high mobility two-dimensional electron gas

The low magnetic field diffusion thermopower of a high mobility GaAs-heterostructure has been measured directly on an electrostatically defined micron-scale Hall-bar structure at low temperature (T = 1.6 K) in the low magnetic field regime (B < 1.2 T) where delocalized quantum Hall states do not influence the measurements. The sample design allowed the determination of the field dependence of the thermopower both parallel and perpendicular to the temperature gradient, denoted respectively by Sxx (longitudinal thermopower) and Syx (Nernst-Ettinghausen coefficient). The experimental data show cl…

Quantum Hall Effect under Rotation and Mass of the Laughlin Quasiparticles

We consider the quantum Hall effect induced by magnetic field and rotation, which can drive the Hall samples into the quantum Hall regime and induce fractional excitations. Both the mass and the charge of the Laughlin quasiparticles are predicted to be fractionally quantized. The observable effects induced by rotation are discussed. Based on the usual Hall samples under rotation, we propose an experimental setup for detecting the macroscopic quantization phenomena and the fractional mass of the Laughlin quasiparticles.

Anomalous growth of thermoelectric power in gapped graphene

There exist experiments indicating that at certain conditions, such as an appropriate substrate, a gap of the order of 10 meV can be opened at the Dirac points of a quasiparticle spectrum of graphene. We demonstrate that the opening of such a gap can result in the appearance of a fingerprint bump of the Seebeck signal when the chemical potential approaches the gap edge. The magnitude of the bump can be up to one order higher than the already large value of the thermopower occurring in graphene. Such a giant effect, accompanied by the nonmonotonous dependence on the chemical potential, is relat…

Thermopower and thermophase in a $d$-wave superconductor

In an unconventional superconductor, the interplay of scattering off impurities and Andreev processes may lead to different scattering times for electronlike and holelike quasiparticles. Such electron-hole asymmetry appears when the impurity scattering phase shift is intermediate between the Born and unitary limits and leads to an expectation for large thermoelectric effects. Here, we examine the thermoelectric response of a $d$-wave superconductor connected to normal-metal reservoirs under a temperature bias using a fully self-consistent quasiclassical theory. The thermoelectrically induced q…

Scaling dimension of quantum Hall quasiparticles from tunneling current noise measurements

Determination of properties of quasiparticle excitations is an important task in the experimental investigation of the fractional quantum Hall effect (FQHE). We propose a model-independent method for finding the scaling dimension of FQHE quasiparticles from measurements of the electric current tunneling between two FQHE edges and its noise. In comparison to the commonly used method based on measuring the tunneling current only, the proposed method is less prone to the errors due to non-universal physics of tunnel junctions.

The Evolution of Quasiparticle Charge in the Fractional Quantum Hall Regime

The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the nu=1/3 FQH state, a charge smoothly evolving from e*=e/3 for t=1 to e*=e for t<<1 was determined, agreeing with chiral Luttinger liquid theory. In the nu=2/5 FQH state the quasiparticle charge evolves smoothly from e*=e/5 at t=1 to a maximum charge less than e*=e/3 at t<<1. Thus it appears that quasiparticles with an approximate charge e/5 pass a barrier they see as almost opaque.

Signatures of fractional Hall quasiparticles in moments of current through an antidot

The statistics of tunneling current in a fractional quantum Hall sample with an antidot is studied in the chiral Luttinger liquid picture of edge states. A comparison between Fano factor and skewness is proposed in order to clearly distinguish the charge of the carriers in both the thermal and the shot limit. In addition, we address effects on current moments of non-universal exponents in single-quasiparticle propagators. Positive correlations, result of propagators behaviour, are obtained in the shot noise limit of the Fano factor, and possible experimental consequences are outlined.

Superperiods in interference of e/3 Laughlin quasiparticles encircling filling 2/5 fractional quantum Hall island

We report experiments in a large, 2.5 micron diameter Fabry-Perot quantum Hall interferometer with two tunneling constrictions. Interference fringes are observed as conductance oscillations as a function of applied magnetic field (the Aharonov-Bohm flux through the electron island) or a global backgate voltage (electronic charge in the island). Depletion is such that in the fractional quantum Hall regime, filling 1/3 current-carrying chiral edge channels pass through constrictions when the island filling is 2/5. The interferometer device is calibrated with fermionic electrons in the integer qu…

Microscopic theory of fractional excitations in gapless bilayer quantum Hall states: semi-quantized quantum Hall states

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…

Single quasiparticle and electron nano-emitter in the fractional quantum Hall regime

We propose a device consisting in an antidot periodically driven in time by a magnetic field as a fractional quantum Hall counterpart of the celebrated mesoscopic capacitor-based single electron source. We fully characterize the setup as an ideal emitter of individual quasiparticles and electrons into fractional quantum Hall edge channels of the Laughlin sequence. Our treatment relies on a master equation approach and identifies the optimal regime of operation for both types of sources. The quasiparticle/quasihole emission regime involves in practice only two charge states of the antidot, allo…

Fractional statistics in the fractional quantum Hall effect

A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $ν=1/3$ and $ν=2/5$ by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discu…

Quantized Thermoelectric Hall Effect Induces Giant Power Factor in a Topological Semimetal

Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric H…

相互作用常数为 $K = 1/2$ 的含杂质 Tomonaga-Lüttinger 液体：热电粒子输运相关的热电势研究、熵变和热容密度

Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant $K = 1/2$: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport

针对含杂质的 Tomonaga-Lüttinger 液体（$K=1/2$），利用玻色化和再费米化精确推导热电势，揭示低温下类 Mott 行为，并建立与熵和热容密度的联系，应用于分数量子霍尔点接触等系统。

Thermopower and thermoelectric power factor of ${\mathbb Z}_k$ parafermion quantum dots

Using the conformal field theory approach to the thermoelectric characteristics of fractional quantum Hall states, previously developed in Nucl. Phys. B 894 (2015) 284, we show that the thermoelectric power factor of Coulomb-blockaded islands, realized by point contacts in Fabry--Pérot interferometers in the $\mathbb{Z}_k$ parafermion Hall states, could give reliable signatures for distinguishing the topological orders of different quantum Hall states having identical electric properties. For example, while the conductance peak patterns in the Coulomb blockade regime for such states are practi…

分数量子霍尔效应中的光辅助电流作为准粒子算符标度维数的探针

Photo-assisted current in the fractional quantum Hall effect as a probe of the quasiparticle operator scaling dimension

本文提出通过量子点接触中光辅助电流二次谐波的相移，直接探测分数量子霍尔态中Laughlin准粒子的标度维数，从而诊断其统计性质。

NMR Evidence for Spin-Pseudospin Intermixing in Quantum Hall Skyrmions

We investigate quasiparticles in bilayer quantum Hall systems around total filling factor nu =1 by current-pumped and resistively detected NMR. The measured Knight shift reveals that the spin component in the quasiparticle increases continuously with $Δ_{SAS}$. Combined with results for the pseudospin component obtained by activation gap measurements, this demonstrates that both spin and pseudospin are contained in a quasiparticle at intermediate $Δ_{SAS}$, providing evidence for the existence of the spin-pseudospin intermixed SU(4) skyrmion. Nuclear spin relaxation measurements show that the …

Transport in the Laughlin quasiparticle interferometer: Evidence for topological protection in an anyonic qubit

We report experiments on temperature and Hall voltage bias dependence of the superperiodic conductance oscillations in the novel Laughlin quasiparticle interferometer, where quasiparticles of the 1/3 fractional quantum Hall fluid execute a closed path around an island of the 2/5 fluid. The amplitude of the oscillations fits well the quantum-coherent thermal dephasing dependence predicted for a two point-contact chiral edge channel interferometer in the full experimental temperature range 10.2<T<141 mK. The temperature dependence observed in the interferometer is clearly distinct from the behav…

$ν=1/3$ 分数量子霍尔区域中的准粒子 Andreev 散射

Quasiparticle Andreev scattering in the $ν=1/3$ fractional quantum Hall regime

本研究在分数量子霍尔区域中观察到准粒子的类Andreev反射现象，即$e/3$准粒子反射为$-2e/3$空穴并伴随$e$准电子透射，揭示了分数量子粒子的非常规散射行为，为新型准粒子和非局域纠缠的产生提供了启示。

Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra

In the pattern-of-zeros approach to quantum Hall states, a set of data {n;m;S_a|a=1,...,n; n,m,S_a in N} (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data {n;m;S_a} corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the patterns of zeros alone does not completely characterize the quantum Hall states. In thi…

Transport of fractional Hall quasiparticles through an antidot

Current statistics of an antidot in the fractional quantum Hall regime is studied for Laughlin's series. The chiral Luttinger liquid picture of edge states with a renormalized interaction exponent $g$ is adopted. Several peculiar features are found in the sequential tunneling regime. On one side, current displays negative differential conductance and double-peak structures when $g<1$. On the other side, universal sub-poissonian transport regimes are identified through an analysis of higher current moments. A comparison between Fano factor and skewness is proposed in order to clearly distinguis…

Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge $Q$ and scaling dimension $Δ$. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase $θ=2πΔ$). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for des…

Transport of Dirac quasiparticles in graphene: Hall and optical conductivities

The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical potential and applied field which is caused by the fact that the quasiparticle excitations in graphene are Dirac-like. One of the most striking effects observed in graphene is the odd integer quantum Hall effect. We argue that it is caused by the anomalous properties of the Dirac quasiparticles from the lowest Landau level. Other quantities such as Hall angle …

Electron and Quasiparticle Exponents of Haldane-Rezayi state in Non-abelian Fractional Quantum Hall Theory

The quasiparticle propagator of Haldane-Rezayi(HR) fractional quantum Hall (FQH) state is calculated, based on a chiral fermion model (or a Weyl fermion model) equipped with a hidden spin SU(2) symmetry. The spectrum of the chiral fermion model for each total spin and total momentum is shown to be identical to that of the SU(2) c = -2 model introduced to describe the edge spectrum of the HR state.

Nature of quasiparticle excitations in the fractional quantum Hall effect

We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau levels. In particular, the composite-fermion wave function for a single quasiparticle has 15% lower energy than the trial wave function suggested by Laughlin, and for two quasiparticles, the composite fermion theory also gives new qualitative structures.

Localizing fractional quasiparticles on graphene quantum hall antidots

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.

Antidot tunneling between Quantum Hall liquids with different filling factors

We consider tunneling through two point contacts between two edges of Quantum Hall liquids of different filling factors $ν_{0,1}=1/ (2m_{0,1}+1)$ with $m_0-m_1\equiv m>0$. Properties of the antidot formed between the point contacts in the strong-tunneling limit are shown to be very different from the $ν_0 =ν_1$ case, and include vanishing average total current in the two contacts and quasiparticles of charge $e/m$. For $m>1$, quasiparticle tunneling leads to non-trivial $m$-state dynamics of effective flux through the antidot which restores the regular ``electron'' periodicity of the current i…

ν=2/3 分数量子霍尔系统中量子点接触内的非常规准粒子和隧穿电导

Unusual quasiparticles and tunneling conductance in quantum point contacts in $ν=2/3$ fractional quantum Hall systems

该研究精确求解了ν=2/3分数量子霍尔系统中量子点接触的隧穿问题，发现电导随电压饱和于e²/2h，并出现由电荷e/2准粒子携带的反向散射，提出了揭示边缘态性质的实验方案。

体准粒子诱导的量子霍尔流体边缘自旋分数化

Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles

该研究定义了存在体准粒子的量子霍尔态边缘的可测量自旋，揭示其分数值源自体准粒子的分数自旋，提出不依赖波函数全局对称性的几何图像，并通过矩阵乘积态计算验证了结果。

Large enhancement of thermopower at low magnetic field in compensated semimetals

The thermoelectric properties of conductors with low electron density can be altered significantly by an applied magnetic field. For example, recent work has shown that Dirac/Weyl semimetals with a single pocket of carriers can exhibit a large enhancement of thermopower when subjected to a sufficiently large field that the system reaches the extreme quantum limit, in which only a single Landau level is occupied. Here we study the magnetothermoelectric properties of compensated semimetals, for which pockets of electron- and hole-type carriers coexist at the Fermi level. We show that, when the c…

Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of the fractional quantum Hall liquids near fillings $1/m$ ($m$ odd) at low temperature are studied in the approximation of generalized ideal gas. The existence of hierarchical states in the fractional quantum Hall effect is shown to be a manif…

整数量子霍尔态中任意子统计的特征信号

Signature of anyonic statistics in the integer quantum Hall regime

本研究突破分数量子霍尔态的实验局限，在整数量子霍尔态中利用通道间库仑相互作用产生类阿贝尔任意子的分数电荷，通过负互相关信号验证其编织统计特性，为任意子研究提供了新的稳定平台。

Thermal activation of exclusonic quasiparticles in the fractional quantum Hall effect

Quasiparticles of the fractional quantum Hall systems obey fractional (including mutual) exclusion statistics. In this note we study the effects of exclusion statistics on thermal activation of quasiparticle pairs in the approximation of generalized ideal gas. The distribution function for thermally activated quasiparticles is found explicitly for the statistics matrix given by the composite fermion picture and the thermodynamic consequences are discussed analytically. In particular, at low temperatures, there is a quasielectron-quasihole duality in the description of the system between two ad…

Integral charge quasiparticles in a fractional quantum Hall liquid

Starting from a collective description of the incompressible fractional quantum Hall liquid as an elastic medium that supports gapped neutral excitations I show that the one-electron spectral function of this system exhibits a sharp peak at the lowest available excitation energy, well separated from the continuum spectrum at higher energy. I interpret this peak as the signature of the integral charge quasiparticle recently predicted by Peterson and Jain\cite{Jain05}, and calculate its spectral weight for different filling factors.

Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect

It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian during which the gap does not close. We show in this article that, at least for finite systems, as the interaction is changed from a model three body interaction to Coulomb, the ground state at filling factor $ν=2/5$ evolves continuously from the so-called Gaffnian wave function to the composite fermion wave function, but the quasiholes alter their character…

Statistics of Quasiparticles in Fractional Quantum Hall States

We have considered here the statistics parameter for quasiparticles in FQH states from an analysis of these states in the framework of chiral anomaly and Berry phase. It is shown that we have a generalized relation such that the statistical phase of a quasiparticle for FQH states at $ν=p/q$ with $p(q)$ even or odd, is given by $e^{iπθ}$ with $θ=p/q $ and the charge is $-e \frac{p}{q}$. The statistics parameter for a quasihole is identical with that of a quasiparticle and the charge is of opposite sign.

Cross-Correlation Investigation of Anyon Statistics in the $ν=1/3$ and $2/5$ Fractional Quantum Hall States

Recent pioneering works have set the stage for exploring anyon braiding statistics from negative current cross-correlations along two intersecting quasiparticle beams. In such a dual-source - analyzer quantum point contact setup, also referred to as 'collider', the anyon exchange phase of fractional quantum Hall quasiparticles is predicted to be imprinted into the cross-correlations characterized by an effective Fano-factor $P$. In the case of symmetric incoming quasiparticle beams, conventional fermions result in a vanishing $P$. In marked contrast, we observe signatures of anyon statistics i…

反常粒子在分数量子霍尔效应的Laufflin分数中的Andreev反射

Quasiparticle Andreev reflection in the Laughlin fractions of the fractional quantum Hall effect

本文研究了在分数量子霍尔效应中，通过两个量子点接触的设置，分析了Andreev反射现象，利用玻色化方法和非平衡Keldysh格林函数技术，计算了输出电流的相关性，并验证了实验观测结果。

偶极表示中的量子霍尔双层

Quantum Hall bilayer in dipole representation

本文利用偶极表示研究填充因子 $ν=1$ 的量子霍尔双层，发现在大范围层间距内，偶极准粒子的 Cooper $s$ 波配对（即 BEC 凝聚）胜过 $p$ 波与激子配对，支持发生奇异相变而非存在独立相的图景。

Thermal and Tunneling Pair Creation of Quasiparticles in Quantum Hall Systems

We make a semiclassical analysis of thermal pair creations of quasiparticles at various filling factors in quantum Hall systems. It is argued that the gap energy is reduced considerably by the Coulomb potential made by impurities. It is also shown that a tunneling process becomes important at low temperature and at strong magnetic field. We fit typical experimental data excellently based on our semiclassical results of the gap energy.

Generalized Random-Phase Approximation Theory of Quasiparticle Spectral Functions: Application to Bilayer Quantum Hall Ferromagnets

We present a microscopic theory of ground-state spectral function of bilayer quantum Hall systems that includes interactions between Hartree-Fock quasiparticles and quantum fluctuations of the order parameter field. The collective modes in these systems are properly described only when fluctuations in direct and exchange particle-hole channels are taken into account. Using an auxiliary field functional integral approach, we present a generalization of the random phase approximation \emph{for quasiparticle self-energy} which captures fluctuations in both channels. We discuss its relationship to…

Quasiparticle spin from adiabatic transport in quantum Hall trial wavefunctions

Quasiparticle spin (in the spacetime sense) couples to curvature of space. Here this fact is used to calculate the spin of quasiholes in trial quantum Hall states by adiabatically dragging them around on a sphere, for trial states given by conformal blocks in some conformal field theory. The spin is found to agree with the conformal weight of the corresponding field. The result completes a recent argument that constructions using blocks from non-unitary theories that contain negative quantum dimensions produce contradictions that prevent them from describing topological (gapped) phases of matt…

Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state

We have experimentally identified fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact (QPC) in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T1(1 ? T1) over a wide range of T1, where T1 is the transmission probability of the IQH edge channel. This binomial distribution indicates …

Magnetothermoelectric transport properties in phosphorene

We numerically study the electrical and thermoelectric transport properties in phosphorene in the presence of both a magnetic field and disorder. The quantized Hall conductivity is similar to that of a conventional two-dimensional electron gas, but the positions of all the Hall plateaus shift to the left due to the spectral asymmetry, in agreement with the experimental observations. The thermoelectric conductivity and Nernst signal exhibit remarkable anisotropy, and the thermopower is nearly isotropic. When a bias voltage is applied between top and bottom layers of phosphorene, both thermopowe…

Evidence for non-linear quasiparticle tunneling between fractional quantum Hall edges

Remarkable nonlinearities in the differential tunneling conductance between fractional quantum Hall edge states at a constriction are observed in the weak-backscattering regime. In the $ν$ = 1/3 state a peak develops as temperature is increased and its width is determined by the fractional charge. In the range $2/3 \le ν\le 1/3$ this width displays a symmetric behavior around $ν$ = 1/2. We discuss the consistency of these results with available theoretical predictions for inter-edge quasiparticle tunneling in the weak-backscattering regime.

Telegraph Noise and Fractional Statistics in the Quantum Hall Effect

We study theoretically nonequilibrium noise in the fractional quantum Hall regime for an Aharonov Bohm ring which has a third contact in the middle of the ring. We show that as a consequence of their fractional statistics the tunneling of a Laughlin quasiparticle between the inner and outer edge of the ring changes the effective Aharonov Bohm flux experienced by quasiparticles going around the ring, leading to a change in the conductance across the ring. A small current in the middle contact therefore gives rise to fluctuations in the current flowing across the ring which resemble random teleg…

Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes

The pseudopotentials describing the interactions of quasiparticles in fractional quantum Hall (FQH) states are studied. Rules for the identification of incompressible quantum fluid ground states are found, based upon the form of the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where n and p are integers, appear to be the only incompressible states in the thermodynamic limit, although other FQH hierarchy states occur for finite size systems. This explains the success of the composite Fermion picture.

Local Charge of the nu=5/2 Fractional Quantum Hall State

Electrons in two dimensions and strong magnetic fields effectively lose their kinetic energy and display exotic behavior dominated by Coulomb forces. When the ratio of electrons to magnetic flux quanta in the system is near 5/2, the unique correlated phase that emerges is predicted to be gapped with fractionally charged quasiparticles and a ground state degeneracy that grows exponentially as these quasiparticles are introduced. Interestingly, the only way to transform between the many ground states would be to braid the fractional excitations around each other, a property with applications in …

分数量子霍尔态的高分辨率隧道谱学

High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States

研究通过高分辨率隧道谱学揭示双层石墨烯中分数量子霍尔态的特性，发现非阿贝尔分数态的能量间隙显著大于其他系统，并指出其在拓扑量子计算中的潜力。

量子霍尔准粒子的实空间成像

Real-space Imaging of Quantum Hall Quasiparticles

利用扫描隧道谱学在石墨烯中成像量子霍尔准粒子，通过缺陷势诱导的朗道能级分裂和局域激发特征，在分数量子霍尔态下观测到任意子的光谱指纹。

Quasiparticles in quantum Hall effect: Smet's fractional charge

It has been pointed out by Smet that there are fractional-charge values which do not fit with their formula of composite fermions. We find that our formula predicts these fractional charges very well and in fact there exists a relationship between spin and charge of a quasiparticle.

Quasiparticle Tunneling in the Fractional Quantum Hall State at ν= 5/2

Theory predicts that quasiparticle tunneling between the counter-propagating edges in a fractional quantum Hall state can be used to measure the effective quasiparticle charge e* and dimensionless interaction parameter g, and thereby characterize the many-body wavefunction describing the state. We report measurements of quasiparticle tunneling in a high mobility GaAs two dimensional electron system in the fractional quantum Hall state at nu=5/2 using a gate-defined constriction to bring the edges close together. We find the dc-bias peaks in the tunneling conductance at different temperatures c…