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.

Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center Universidad Autónoma de Madrid 28049 Madrid Spain

Graduate School of Engineering Nagoya University Furo cho Chikusa ku Nagoya 464 8603 Japan

Graduate School of Engineering Osaka University 2 1 Yamada Oka 565 0871 Suita Osaka Japan

Institute of Physics Academy of Sciences of the Czech Republic Cukrovarnická 10 162 00 Prague Czech Republic

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Chemical structure imaging of a single molecule by atomic force microscopy at room temperature