Dynamics of neutral modes for fractional quantum Hall states is investigated for a quantum point contact geometry in the weak-backscattering regime. The effective field theory introduced by Fradkin-Lopez for edge states in the Jain sequence is generalized to the case of propagating neutral modes. The dominant tunnelling processes are identified also in the presence of non-universal phenomena induced by interactions. The crossover regime in the backscattering current between tunnelling of single-quasiparticles and of agglomerates of p-quasiparticles is analysed. We demonstrate that higher order cumulants of the backscattering current fluctuations are a unique resource to study quantitatively the competition between different carrier charges. We find that propagating neutral modes are a necessary ingredient in order to explain this crossover phenomena.
Edges of quantum Hall phases give rise to a multitude of exotic modes supporting quasiparticles of different values of charge and quantum statistics. Among these are neutralons (chargeless anyons with semion statistics), which were found to be ubiquitous in fractional quantum Hall matter. Studying and manipulating the neutral sector is an intriguing and interesting challenge, all the more so since these particles are accessible experimentally. Here we address the limit of strongly-interacting neutralons giving rise to neutralon superconductivity, where pairing is replaced by a quarteting mecha…
Quantum point contact devices are indispensable tools for probing the edge structure of the fractional quantum Hall (FQH) states. Recent observations of quantized conductance plateaus accompanied by shot noise in such devices, as well as suppression of Mach-Zehnder interference, call for theoretical explanations. In this paper, we develop a theory of FQH edge state transport through quantum point contacts, which allows for a generic Abelian edge structure and assumes strong equilibration between edge modes (incoherent transport regime). We find that conductance plateaus are found whenever the …
We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the con…
Integrability of electron dynamics in one dimension is manifested by the non-equilibrium stationary states. They emerge near a point contact coupling two quantum Hall edges with different chemical potentials. I use the non-equilibrium bosonization technique to show that the effective temperature of such states at the fractional quantum Hall edges has a universal linear dependence on the current through the contact. In contrast, the temperature at eventual equilibrium scales as the square root of the power dissipating at the point contact. I propose to use this distinction to detect these intri…
This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the $ν= 2/5$ phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream, and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the elec…
Tracking the energies of one-dimensional subband edges in quantum point contacts using dc conductance measurements
半导体量子点接触一直是一维电子输运研究的焦点。它们的电特性通常使用交流电导方法进行研究，但最近的工作表明，直流电导可用于获得额外的信息，最近报道了密度依赖的Landé有效g因子[T.- M. Chen等人，Phys.Rev.B79，081301（2009）]。我们讨论了以前的量子点接触的直流电导测量，展示了如何有价值的额外信息可以从数据中提取。我们提供了一个全面的和一般的框架，直流电导测量，提供了一个路径，以提高现有数据的准确性，并获得有用的额外数据。一个关键的方面是，直流电导测量可用于直接映射1D子带边缘的能量，从而对自旋分裂1D子带填充时发生的物理现象提供新的见解。通过对Chen等人获得的数据的重新分析，我们得到两个发现。第一个是，2-下子带边缘紧密跟踪源化学势时，它第一次开始填充之前下降得更快的能量。第二个是2-up子带随着子带边缘接近漏极电势而更快速地填充。这第二个发现表明，自旋能隙可能会停止打开，甚至开始再次关闭，因为2-up子带继续填充，与最近的理论计算和实验研究一致。
Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counterpropagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counterpropagating modes, which, by way of mode renormalization, m…
We analyze transport through a quantum point contact in fractional quantum Hall states with counter-propagating neutral edge modes. We show that both the noise (as expected and previously calculated by other authors) and (perhaps surprisingly) the average transmitted current are affected by downstream perturbations within the standard edge state model. We consider two different scenarios for downstream perturbations. We argue that the change in transmitted current should be observable in experiments that have observed increased noise.
Edge-contacted superconductor-graphene-superconductor Josephson junction have been utilized to realize topological superconductivity, which have shown superconducting signatures in the quantum Hall regime. We perform the first-principles calculations to interpret electronic couplings at the superconductor-graphene edge contacts by investigating various aspects in hybridization of molybdenum d orbitals and graphene $π$ orbitals. We also reveal that interfacial oxygen defects play an important role in determining the doping type of graphene near the interface.
We describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode --- i.e. an edge mode that does not carry electric charge. These models consist of two counter-propagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study …
Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. We propose a way to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affe…
Fractional Chern insulators (FCIs) realized in fractional quantum Hall systems subject to a periodic potential are topological phases of matter for which space group symmetries play an important role. In particular, lattice dislocations in an FCI can host topology-altering non-Abelian topological defects, known as genons. Genons are of particular interest for their potential application to topological quantum computing. In this work, we study FCI edges and how they can be used to detect genons. We find that translation symmetry can impose a quantized momentum difference between the edge electr…
Relaxation in driven integer quantum Hall edge states
一个高度非热的电子分布时，产生的量子霍尔边缘态源在不同的电位满足量子点接触。在最近的实验中已经观察到这种分布作为接触下游距离的函数而松弛成静止形式[Phys. Rev. Lett. 105，056803（2010）]。在这里，我们提出了一个精确的治疗的极小模型的系统填充因子为ν=2，与结果，以及帐户的观察。
The bulk-boundary correspondence is a defining feature of topological states of matter. However, for quantum magnets such as spin liquids or topological magnon insulators a direct observation of topological surface states has proven challenging because of the charge-neutral character of the excitations. Here we propose spin-polarized scanning tunneling microscopy as a spin-sensitive local probe to provide direct information about charge neutral topological edge states. We show how their signatures, imprinted in the local structure factor, can be extracted by specifically employing the strength…
We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in two-dimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of Majorana edge modes can be gapped out by an appropriate interaction without spontaneously breaking any one of the protecting symmetries. Hence, the noninteracting classification $\mathbb{Z}$ reduces to $\mathbb{Z}^{\,}_{8}$ when these interactions are present. It is also known that the stability when there are less than eight modes can be understood in terms of th…
