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Register a new userInterference effects in transport across a single incompressible strip at the edge of the fractional quantum Hall system
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We experimentally investigate interference effects in transport across a single incompressible strip at the edge of the quantum Hall system by using a Fabry-Perot type interferometer. We find the interference oscillations in transport across the incompressible strips with local filling factors $ u_c=1, 4/3, 2/3$ even at high imbalances, exceeding the spectral gaps. In contrast, there is no sign of the interference in transport across the principal Laughlin $ u_c=1/3$ incompressible strip. This indicates, that even at fractional $ u_c$, the interference effects are caused by normal electrons. The oscillations period is determined by the effective interferometer area, which is sensitive to the filling factors because of screening effects.
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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 contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter -- playing the role of an effective interaction strength within an idealized model of thermal reservoirs -- is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.
Topological superconductors represent a phase of matter with nonlocal properties which cannot smoothly change from one phase to another, providing a robustness suitable for quantum computing. Substantial progress has been made towards a qubit based on Majorana modes, non-Abelian anyons of Ising ($Z_2$) topological order whose exchange$-$braiding$-$produces topologically protected logic operations. However, because braiding Ising anyons does not offer a universal quantum gate set, Majorana qubits are computationally limited. This drawback can be overcome by introducing parafermions, a novel generalized set of non-Abelian modes ($Z_n$), an array of which supports universal topological quantum computation. The primary route to synthesize parafermions involves inducing superconductivity in the fractional quantum Hall (fqH) edge. Here we use high-quality graphene-based van der Waals devices with narrow superconducting niobium nitride (NbN) electrodes, in which superconductivity and robust fqH coexist. We find crossed Andreev reflection (CAR) across the superconductor separating two counterpropagating fqH edges which demonstrates their superconducting pairing. Our observed CAR probability of the integer edges is insensitive to magnetic field, temperature, and filling, which provides evidence for spin-orbit coupling inherited from NbN enabling the pairing of the otherwise spin-polarized edges. FqH edges notably exhibit a CAR probability higher than that of integer edges once fully developed. This fqH CAR probability remains nonzero down to our lowest accessible temperature, suggesting superconducting pairing of fractional charges. These results provide a route to realize novel topological superconducting phases with universal braiding statistics in fqH-superconductor hybrid devices based on graphene and NbN.
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.
Using charge accumulation imaging, we measure the charge flow across an incompressible strip and follow its evolution with magnetic field. The strip runs parallel to the edge of a gate deposited on the sample and forms at positions where an exact number of integer Landau levels is filled. An RC model of charging fits the data well and enables us to determine the longitudinal resistance of the strip. Surprisingly, we find that the strip becomes more resistive as its width decreases.
Using a time-resolved phonon absorption technique, we have measured the specific heat of a two-dimensional electron system in the fractional quantum Hall effect regime. For filling factors $ u = 5/3, 4/3, 2/3, 3/5, 4/7, 2/5$ and 1/3 the specific heat displays a strong exponential temperature dependence in agreement with excitations across a quasi-particle gap. At filling factor $ u = 1/2$ we were able to measure the specific heat of a composite fermion system for the first time. The observed linear temperature dependence on temperature down to $T = 0.14$ K agrees well with early predictions for a Fermi liquid of composite fermions.
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