Quantum Degeneracy in Atomic Point Contacts Revealed by Chemical Force and Conductance

Abstract

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 / F 2 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 Sið111Þ-ð7 Â 7Þ surface reconstruction where the Si adatom possesses a strongly localized dangling-bond state at the Fermi level. The invention of scanning probe microscopy (SPM), almost three decades ago, boosted research of matter at the nanoscale. Nowadays, SPM techniques are routinely used not only for imaging with unprecedented atomic resolution [1,2] or single atom manipulation [3] but also for an advanced characterization on an atomic scale [4][5][6][7][8][9]. What is more, SPM provides direct access to the nanoscale where the quantum phenomena tend to emerge. Many of them have been the subject of intensive SPM studies [10,11]. Nevertheless, quantum degeneracy, one of the basic concepts of quantum mechanics, has received little attention so far. The quantum degeneracy is defined as the presence of two or more quantum states localized at the same energy level. Among others, the degeneracy plays an important role in the low temperature charge transport phenomena at the nanoscale, such as the Kondo effect modulated by mechanical action [12], resonant tunneling [13], or Coulomb blockade [14]. Recent progress in scanning probe instrumentation has allowed the combination of atomic force microscopy (AFM) and scanning tunneling microscopy (STM) [15] where both tunneling current and force are collected simultaneously. This approach opens new possibilities not only in the characterization at the atomic scale but also to understand the fundamental relation between the chemical force and the conductance in a well-defined atomic contact [see Fig. 1(a)]. In this Letter, we demonstrate that the quantum degeneracy of frontier electronic states of two interacting bodies forming an atomic point contact can be explored by precise AFM/STM experiments, even at room temperature, through an intimate relation between the chemical force and the conductance.The understanding of the mechanical and transport properties at the atomic scale is of importance not only in fundamental physics but also for practical applications in nanotechnology. An atomic scale junction forms when two objects (e.g., scanning probe and sample) are brought near to mechanical contact with a subnanometer distance control. In a f...

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