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Simultaneous voltage and current density imaging of flowing electrons in two dimensions

Abstract

A variety of physical phenomena associated with nanoscale electron transport often results in non-trivial spatial voltage and current patterns, particularly in nonlocal transport regimes. While numerous techniques have been devised to image electron flows, the need remains for a nanoscale probe capable of simultaneously imaging current and voltage distributions with high sensitivity and minimal invasiveness, in a magnetic field, across a broad range of temperatures and beneath an insulating surface. Here we present a technique for spatially mapping electron flows based on a nanotube single-electron transistor, which achieves high sensitivity for both voltage and current imaging. In a series of experiments using high-mobility graphene devices, we demonstrate the ability of our technique to visualize local aspects of intrinsically nonlocal transport, as in ballistic flows, which are not easily resolvable via existing methods. This technique should aid in understanding the physics of two-dimensional electronic devices and enable new classes of experiments that image electron flow through buried nanostructures in the quantum and interaction-dominated regimes.

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Fig. 1: Overview of the nanoscale voltage and current imaging technique.
Fig. 2: Spatial imaging of the voltage drop of flowing electrons in the diffusive and ballistic regimes.
Fig. 3: Extracting local quantities from electrostatic potential maps.
Fig. 4: Imaging the local current density in a graphene device with a bend.
Fig. 5: Imaging nonlocal ballistic voltage drops.

Data availability

The data that support the plots and other analysis in this work are available from the corresponding author upon request.

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Acknowledgements

We thank G. Falkovich, L. Levitov, A. Shytov and A. Stern for discussions and D. Mahalu for electron-beam lithography. We further acknowledge support from the Helmsley Charitable Trust grant, the ISF (grant no. 712539), WIS-UK collaboration grant and the ERC-Cog (See-1D-Qmatter, no. 647413).

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Authors

Contributions

L.E., S.I. and J.A.S. conceived the technique. L.E., A.R., S.I. and J.A.S. created the SETs, performed the measurements and analysed the data. J.B., D.P., J.Z. and M.B.-S. fabricated the graphene devices. K.W. and T.T. supplied the hBN crystals. L.E., S.I. and J.A.S. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Joseph A. Sulpizio.

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The authors declare no competing interests.

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Journal peer review informationNature Nanotechnology thanks Klaus Ensslin and other anonymous reviewer(s) for their contribution to the peer review of this work.

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Ella, L., Rozen, A., Birkbeck, J. et al. Simultaneous voltage and current density imaging of flowing electrons in two dimensions. Nat. Nanotechnol. 14, 480–487 (2019). https://doi.org/10.1038/s41565-019-0398-x

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