Quantum degeneracy in atomic point contacts revealed by chemical force and conductance

Quantum degeneracy is an important concept in quantum mechanics with large implications to many processes in condensed matter. Here, we show the consequences of electron energy level degeneracy on the conductance and the chemical force between two bodies at the atomic scale. We propose a novel way in which a scanning probe microscope can detect the presence of degenerate states in atomic-sized contacts even at room temperature. The tunneling conductance G and chemical binding force F between two bodies both tend to decay exponentially with distance in a certain distance range, usually maintaining direct proportionality G∝F. However, we show that a square relation G∝F2 arises as a consequence of quantum degeneracy between the interacting frontier states of the scanning tip and a surface atom. We demonstrate this phenomenon on the Si(111)-(7×7) surface reconstruction where the Si adatom possesses a strongly localized dangling-bond state at the Fermi level.