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Register a new userAuger-spectroscopy in quantum Hall edge channels: a possible resolution to the missing energy problem
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Added by
Tobias Stefan Kr\\\"ahenmann
Publication date
2019
fields
Physics
and research's language is
English
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Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle can be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels.
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In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the usual case of photon quantum optics. In particular, it provides a natural playground to understand decoherence and relaxation effects in quantum transport.
Achieving metrological precision of quantum anomalous Hall resistance quantization at zero magnetic field so far remains limited to temperatures of the order of 20 mK, while the Curie temperature in the involved material is as high as 20 K. The reason for this discrepancy remains one of the biggest open questions surrounding the effect, and is the focus of this article. Here we show, through a careful analysis of the non-local voltages on a multi-terminal Corbino geometry, that the chiral edge channels continue to exist without applied magnetic field up to the Curie temperature of bulk ferromagnetism of the magnetic topological insulator, and that thermally activated bulk conductance is responsible for this quantization breakdown. Our results offer important insights on the nature of the topological protection of these edge channels, provide an encouraging sign for potential applications, and establish the multi-terminal Corbino geometry as a powerful tool for the study of edge channel transport in topological materials.
Recent electron quantum optics experiments performed with on-demand single electron sources call for a mixed time/frequency approach to electronic quantum coherence. Here, we present a Wigner function representation of first order electronic coherence and show that is provides a natural visualization of the excitations emitted by recently demonstrated single electron sources. It also gives a unified perspective on single particle and two particle interferometry experiments. In particular, we introduce a non-classicality criterion for single electron coherence and discuss it in the context of Mach-Zenhder interferometry. Finally, the electronic Hanbury Brown and Twiss and the Hong Ou Mandel experiments are interpreted in terms of overlaps of Wigner function thus connecting them to signal processing.
A theoretical study of the single electron coherence properties of Lorentzian and rectangular pulses is presented. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose charge and shape reflects the properties of interactions. We show that the dependence of fractionalization induced electron/hole pair production in the pulses amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses and an Hanbury Brown and Twiss interferometer to measure interaction induced electron/hole pair production and more generally to reconstruct single electron coherence of these excitations before and after their fractionalization.
Charge equilibration between quantum-Hall edge states can be studied to reveal geometric structure of edge channels not only in the integer quantum Hall (IQH) regime but also in the fractional quantum Hall (FQH) regime particularly for hole-conjugate states. Here we report on a systematic study of charge equilibration in both IQH and FQH regimes by using a generalized Hall bar, in which a quantum Hall state is nested in another quantum Hall state with different Landau filling factors. This provides a feasible way to evaluate equilibration in various conditions even in the presence of scattering in the bulk region. The validity of the analysis is tested in the IQH regime by confirming consistency with previous works. In the FQH regime, we find that the equilibration length for counter-propagating $delta u $ = 1 and $delta u $ = -1/3 channels along a hole-conjugate state at Landau filling factor $ u $ = 2/3 is much shorter than that for co-propagating $delta u $ = 1 and $delta u $ = 1/3 channels along a particle state at $ u $ = 4/3. The difference can be associated to the distinct geometric structures of the edge channels. Our analysis with generalized Hall bar devices would be useful in studying edge equilibration and edge structures.
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