Observing quantum trapping on MoS2 through the lifetimes of resonant electrons: revealing the Pauli exclusion principle.

We demonstrate that the linewidth of the field emission resonance (FER) observed on the surface of MoS2 using scanning tunneling microscopy can vary by up to one order of magnitude with an increasing electric field. This phenomenon originates from quantum trapping, in which the electron relaxed from a resonant electron in the FER is momentarily trapped in a potential well on the MoS2 surface due to its wave nature. Because the relaxed electron and the resonant electron have the same spin, through the action of the Pauli exclusion principle, the lifetimes of the resonant electrons can be substantially prolonged when the relaxed electrons engage in resonance trapping. The linewidth of the FER is thus considerably reduced to as narrow as 12 meV. The coexistence of the resonant electron and the relaxed electron requires the emission of two electrons, which can occur through the exchange interaction.

Sharpness-induced energy shifts of quantum well states in Pb islands on Cu(111).

We elucidate that the tip sharpness in scanning tunneling microscopy (STM) can be characterized through the number of field-emission (FE) resonances. A higher number of FE resonances indicates higher sharpness. We observe empty quantum well (QW) states in Pb islands on Cu(111) under different tip sharpness levels. We found that QW states observed by sharper tips always had lower energies, revealing negative energy shifts. This sharpness-induced energy shift originates from an inhomogeneous electric field in the STM gap. An increase in sharpness increases the electric field inhomogeneity, that is, enhances the electric field near the tip apex, but weakens the electric field near the sample. As a result, higher sharpness can increase the electronic phase in vacuum, causing the lowering of QW state energies. Moreover, the behaviors of negative energy shift as a function of state energy are entirely different for Pb islands with a thickness of two and nine atomic layers. This thickness-dependent behavior results from the electrostatic force in the STM gap decreasing with increasing tip sharpness. The variation of the phase contributed from the expansion deformation induced by the electrostatic force in a nine-layer Pb island is significantly greater, sufficient to effectively negate the increase of electronic phase in vacuum.

Field enhancement factors and self-focus functions manifesting in field emission resonances in scanning tunneling microscopy.

Field emission (FE) resonance (or Gundlach oscillation) in scanning tunneling microscopy (STM) is a phenomenon in which the FE electrons emitted from the microscope tip couple into the quantized standing-wave states within the STM tunneling gap. Although the occurrence of FE resonance peaks can be semi-quantitatively described using the triangular potential well model, it cannot explain the experimental observation that the number of resonance peaks may change under the same emission current. This study demonstrates that the aforementioned variation can be adequately explained by introducing a field enhancement factor that is related to the local electric field at the tip apex. The peak number of FE resonances increases with the field enhancement factor. The peak intensity of the FE resonance on the reconstructed Au(111) surface varies in the face-center cubic, hexagonal-close-packed, and ridge regions, thus providing the contrast in the mapping through FE resonances. The mapping contrast is demonstrated to be nearly independent of the tip-sample distance, implying that the FE electron beam is not divergent because of a self-focus function intrinsically involved in the STM configuration.