Abstract
Motivated by the recent experiment by Marguerite et al. [1] on imaging in graphene samples, we investigate theoretically the dissipation induced by resonant impurities in the quantum Hall regime. The impurity induced forward scattering of electrons at quantum Hall edges leads to an enhanced phonon emission, which reaches its maximum when the impurity state is tuned to resonance by a scanning tip voltage. Our analysis of the effect of the tip potential on the dissipation reveals peculiar thermal rings around the impurities, in consistency with experimental observations. Remarkably, this impurity-induced dissipation reveals non-trivial features that are unique for chiral 1D systems such as quantum Hall edges. First, the dissipation is not accompanied by the generation of resistance. Second, this type of dissipation is highly nonlocal: a single impurity induces heat transfer to phonons along the whole edge.
Highlights
The quantum Hall (QH) effect has been studied for decades, it continues to attract the attention of the community for multiple reasons
We have studied dissipation on a chiral edge of a QH sample in the presence of a resonant impurity
In strong contrast to the expectation that forward scattering is irrelevant to energy dissipation, we have shown that the forward scattering within a single chiral QH channel at a resonant impurity produces a nontrivial dissipation enhancement
Summary
The quantum Hall (QH) effect has been studied for decades, it continues to attract the attention of the community for multiple reasons. It has been shown that even for a clean single chiral channel, energy dissipation is possible through the electron-phonon interaction [13] This effect leads to dissipation (transfer of energy from electrons to phonons) along the quantum Hall edges with a homogeneous power density. It can be considered as an ultimate manifestation of nonlocal dissipation [14,15]. Our theory explains the fascinating features observed in the experiment: the ring-shape structure of the thermal profile as a function of the tip position where a local potential is applied (Fig. 1) This thermal profile is not accompanied by any electrical resistance (additional voltage drop).
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