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.
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.
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.