Thermometry with Subnanometer Resolution in the Electron Microscope Using the Principle of Detailed Balancing

We measure phonon energy gain and loss down to 20 meV in a single nanostructure using an atom-wide monochromatic electron beam. We show that the bulk and surface, energy loss and energy gain processes obey the principle of detailed balancing in nanostructured systems at thermal equilibrium. By plotting the logarithm of the ratio of the loss and gain bulk/surface scattering as a function of the excitation energy, we find a linear behavior, …