Scanning thermal microscopy using electrical measurements

The local temperature and voltage of a quantum system out of equilibrium is defined via a floating probe\footnote{Abhay Shastry and Charles Stafford, Physical Review B 94, 155433 (2016)} operating in the tunneling regime. However, experimental difficulties in thermally isolating the probe have limited the spatial resolution of scanning thermal microscopy. We now propose a method to measure the temperature using only electrical measurements in systems obeying the Wiedemann-Franz law. The method significantly advances the spatial resolution and accuracy of scanning thermal microscopy, bringing it to the previously inaccessible tunneling regime.