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Nanoscale thermal imaging of dissipation in quantum systems


Energy dissipation is a fundamental process governing the dynamics of physical, chemical and biological systems. It is also one of the main characteristics that distinguish quantum from classical phenomena. In particular, in condensed matter physics, scattering mechanisms, loss of quantum information or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Yet the microscopic behaviour of a system is usually not formulated in terms of dissipation because energy dissipation is not a readily measurable quantity on the micrometre scale. Although nanoscale thermometry has gained much recent interest1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, existing thermal imaging methods are not sensitive enough for the study of quantum systems and are also unsuitable for the low-temperature operation that is required. Here we report a nano-thermometer based on a superconducting quantum interference device with a diameter of less than 50 nanometres that resides at the apex of a sharp pipette: it provides scanning cryogenic thermal sensing that is four orders of magnitude more sensitive than previous devices—below 1 μK Hz−1/2. This non-contact, non-invasive thermometry allows thermal imaging of very low intensity, nanoscale energy dissipation down to the fundamental Landauer limit16,17,18 of 40 femtowatts for continuous readout of a single qubit at one gigahertz at 4.2 kelvin. These advances enable the observation of changes in dissipation due to single-electron charging of individual quantum dots in carbon nanotubes. They also reveal a dissipation mechanism attributable to resonant localized states in graphene encapsulated within hexagonal boron nitride, opening the door to direct thermal imaging of nanoscale dissipation processes in quantum matter.

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Figure 1: tSOT characteristics and performance.
Figure 2: Thermal imaging of single-walled CNTs and scanning gate thermometry of quantum dots.
Figure 3: Scanning gate thermometry of dissipation at localized resonant states at graphene edges.

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We thank A. F. Young for discussions, M. V. Costache and S. O. Valenzuela for facilitation of fabrication of permalloy (Py)/copper (Cu) samples that were used in Supplementary Information section S9, D. Shahar, I. Tamir, T. Levinson and S. Mitra for assistance in fabrication of a:In2O3 integrated devices that were used in Supplementary Information section S2, M. E. Huber for SOT readout setup, and M. L. Rappaport for technical assistance. This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 programme (grant no. 655416), by the Minerva Foundation with funding from the Federal German Ministry of Education and Research, and by a Rosa and Emilio Segré Research Award. L.S.L. and E.Z. acknowledge the support of the MISTI MIT-Israel Seed Fund.

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Authors and Affiliations



D.H., J.C. and E.Z. conceived the technique and designed the experiments. D.H. and J.C. performed the measurements. D.H. performed the analysis and theoretical modelling. L.E. constructed the scanning SOT microscope. M.B.S. and A.K.G. designed and provided the graphene sample and contributed to the analyses of the results. N.S. and E.J. fabricated the CNT samples. J.C. fabricated the Cu/Py sample. D.H., H.R.N. and J.S. fabricated the a:In2O3 sample. D.H. and Y.R. designed and fabricated the spatial resolution demonstration sample. H.R.N., Y.A. and A.U. fabricated the tSOT sensors. Y.A. and Y.M. developed the SOT fabrication technique. A.U., Y.M. and D.H. developed the tuning-fork based tSOT height control technique. L.S.L. performed theoretical analysis. D.H., J.C. and E.Z. wrote the manuscript. All authors participated in discussions and writing of the manuscript.

Corresponding authors

Correspondence to D. Halbertal or E. Zeldov.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks I. Maasilta, S. Volz and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-16 and additional references. (PDF 3962 kb)

Scanning gate thermometry of hBN/graphene/hBN device

Video S1 presents a sequence of ac images of the inner aperture of the washer-shaped graphene device acquired by the tSOT as a function of the potential VtSOT between the tip and the sample. The images present the gradient of the local temperature û Tdc(x,y) produced by measuring the ac signal of the tSOT due to the ac vibration of the TF with an rms amplitude of 5 nm along û at 36.694 kHz as described in Supplementary Information section S16. Supplementary Figures S16b,c present two frames from the video. New ring-like structures are formed along the graphene edge and expand as VtSOT is increased as discussed in Supplementary Information sections S13 and S16. (AVI 3111 kb)

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Halbertal, D., Cuppens, J., Shalom, M. et al. Nanoscale thermal imaging of dissipation in quantum systems. Nature 539, 407–410 (2016).

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