Abstract
The tunnelling current in scanning tunnelling spectroscopy (STS) is typically and often implicitly modelled by a continuous and homogeneous charge flow. If the charging energy of a single-charge quantum sufficiently exceeds the thermal energy, however, the granularity of the current becomes non-negligible. In this quantum limit, the capacitance of the tunnel junction mediates an interaction of the tunnelling electrons with the surrounding electromagnetic environment and becomes a source of noise itself, which cannot be neglected in STS. Using a scanning tunnelling microscope operating at 15 mK, we show that we operate in this quantum limit, which determines the ultimate energy resolution in STS. The P(E)-theory describes the probability for a tunnelling electron to exchange energy with the environment and can be regarded as the energy resolution function. We experimentally demonstrate this effect with a superconducting aluminium tip and a superconducting aluminium sample, where it is most pronounced.
Highlights
Scanning tunneling spectroscopy has evolved into one of the most versatile tools to study the electronic structure in real space with atomic precision [1,2,3]
We show that the energy resolution that can be obtained is principally limited by the electromagnetic interaction of the tunneling electrons with the surrounding environmental impedance as well as the capacitative noise of the junction
In this Letter, we show that the photon exchange of tunneling electrons with the surrounding environment in conjunction with the capacitative junction noise represents a principal limit of the energy resolution in spectroscopic measurements using tunnel junctions
Summary
The effect of the capacitance in the tunnel junction and the interaction of the tunneling electrons with the surrounding environmental impedance has been modeled within the framework of P (E)-theory, where the P (E)-function describes the probability for a tunneling electron to exchange energy with the environment. The P0(E)-function changes the coefficient γ slightly depending on the actual values of the parameters This means that for low enough temperature, the P (E)-broadening will eventually be the dominant contribution to the resolution limit, regardless of whether the tip and/or sample are superconducting or not. We have shown that the interaction of tunneling electrons with the environmental impedance as well as the capacitative junction noise limit the effective energy resolution in spectroscopic measurements of the differential conductance.
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