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Register a new userDirect measurement of the coherence length of edge states in the Integer Quantum Hall Regime
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We have determined the finite temperature coherence length of edge states in the Integer Quantum Hall Effect (IQHE) regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing to define a coherence length $l_phi$. The variations of $l_phi$ with magnetic field are the same for all samples, with a maximum located at the upper end of the quantum hall plateau. Our results provide the first accurate determination of $l_phi$ in the quantum Hall regime.
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An electronic Mach Zehnder interferometer is used in the integer quantum hall regime at filling factor 2, to study the dephasing of the interferences. This is found to be induced by the electrical noise existing in the edge states capacitively coupled to each others. Electrical shot noise created in one channel leads to phase randomization in the other, which destroys the interference pattern. These findings are extended to the dephasing induced by thermal noise instead of shot noise: it explains the underlying mechanism responsible for the finite temperature coherence time $tau_phi(T)$ of the edge states at filling factor 2, measured in a recent experiment. Finally, we present here a theory of the dephasing based on Gaussian noise, which is found in excellent agreement with our experimental results.
We present an experiment where the quantum coherence in the edge states of the integer quantum Hall regime is tuned with a decoupling gate. The coherence length is determined by measuring the visibility of quantum interferences in a Mach-Zehnder interferometer as a function of temperature, in the quantum Hall regime at filling factor two. The temperature dependence of the coherence length can be varied by a factor of two. The strengthening of the phase coherence at finite temperature is shown to arise from a reduction of the coupling between co-propagating edge states. This opens the way for a strong improvement of the phase coherence of Quantum Hall systems. The decoupling gate also allows us to investigate how inter-edge state coupling influence the quantum interferences dependence on the injection bias. We find that the finite bias visibility can be decomposed into two contributions: a Gaussian envelop which is surprisingly insensitive to the coupling, and a beating component which, on the contrary, is strongly affected by the coupling.
Observation of interference in the quantum Hall regime may be hampered by a small edge state velocity due to finite phase coherence time. Therefore designing two quantum point contact (QPCs) interferometers having a high edge state velocity is desirable. Here, we present a new simulation method for realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. We calculate the filling fraction in the center of the QPC and the velocity of the edge states, and predict structures with high edge state velocity. The 3D Schrodinger equation is split into 1D and 2D parts. Quasi-1D Schrodinger and Poisson equations are solved self-consistently in the IQHE regime to obtain the potential profile near the edges, and quantum transport is used to solve for the edge state wavefunctions. The velocity of edge states is found to be $left< E right> / B$, where $left< E right>$ is the expectation value of the electric field for the edge state. Anisotropically etched trench gated heterostructures with double sided delta doping have the highest edge state velocity among the structures considered.
We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by non-linear transformations to the spectra of quantum Hall edge--states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends BOTH on boundary conditions and the energies of the bulk states.
This review presents experimental results on the inter-edge-state transport in the quantum Hall effect, mostly obtained in the regime of high imbalance. The application of a special geometry makes it possible to perform I-V spectroscopy between individual edge channels in both the integer and the fractional regime. This makes it possible to study in detail a number of physical effects such as the creation of topological defects in the integer quantum Hall effect and neutral collective modes excitation in fractional regime. The while many of the experimental findings are well explained within established theories of the quantum Hall effects, a number of observations give new insight into the local structure at the sample edge, which can serve as a starting point for further theoretical studies.
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