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

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

Yoshiaki Sugimoto, Martin Ondráček, Masayuki Abe, Pablo Pou, Seizo Morita, Ruben Perez, Fernando Flores, and Pavel Jelínek

Phys. Rev. Lett. 111, 106803 – Published 5 September 2013

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 $G \propto F$ . However, we show that a square relation $G \propto F^{2}$ 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 $Si (111) − (7 \times 7)$ surface reconstruction where the Si adatom possesses a strongly localized dangling-bond state at the Fermi level.

Received 31 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.106803

Authors & Affiliations

Yoshiaki Sugimoto^1,*, Martin Ondráček², Masayuki Abe³, Pablo Pou⁴, Seizo Morita¹, Ruben Perez⁴, Fernando Flores⁴, and Pavel Jelínek^2,†

¹Graduate School of Engineering, Osaka University, 2-1 Yamada-Oka, 565-0871 Suita, Osaka, Japan
²Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Prague, Czech Republic
³Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
⁴Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain

^*sugimoto@afm.eei.eng.osaka-u.ac.jp
^†jelinekp@fzu.cz

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Issue

Vol. 111, Iss. 10 — 6 September 2013

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Images

Figure 1
AFM/STM sensor interacting with a sample. (a) Schematic view of a simultaneous AFM/STM measurement using an oscillating sensor on the $Si (111) − (7 \times 7)$ surface. Subtraction of $Δ f (z)$ curves acquired over the adatom (red or light gray curve) and hollow (black curve) positions allows precise estimation of the short-range component (blue or dark gray curve). For more details about the extraction of the short-range force, see Ref. 28. (b),(c) The relation between the short-range force $F$ and the tunneling conductance $G$ in the (b) nondegenerate and (c) degenerate cases. The splitting of the energy levels leading to the presence or absence of degeneracy is sketched below the plots in (b) and (c).Reuse & Permissions
Figure 2
Tunneling conductance and short-range force component. Top: Comparison between calculated (dashed black line with symbols) and measured (thin blue solid line) tunneling conductances $G$ as a function of tip-surface separation $z$ . Bottom: Calculated (dashed black line with symbols) and measured (thin solid red line) $z$ dependences of the short-range force $F$ . Logarithmic plots with estimated decay constants are shown in the insets.Reuse & Permissions
Figure 3
Electron states on the tip and on the surface. Density of states (PDOS) projected on a corner adatom of the $Si (111) − (7 \times 7)$ surface (bottom plot) and on the outermost apex atom of the Si tip (top plot, turned upside-down). Black curves and shaded areas, complete PDOS; red curves, $s$ -orbital contribution to PDOS; green curves, $p$ -orbital contribution to PDOS. Inset: Ball-and-stick model of the SPM tip apex above the surface adatom.Reuse & Permissions
Figure 4
Results of force and conductance measurements. (a) $Δ f_{SR} (z)$ (red or light gray line) and $⟨ I_{t} (z) ⟩$ (blue or dark gray line) curves acquired above the corner adatom of the $Si (111) − (7 \times 7)$ surface. $Δ f_{SR} (z)$ was obtained by subtraction of the long-range force contribution estimated from the curve above the corner hole. (b) $F (z)$ (red or light gray line) and $G (z)$ (blue or dark gray line) curves derived from (a) using the conversion formulas. Here, $G_{0} = 2 e^{2} / h = (12906 Ω)^{- 1}$ . Logarithmic plots are shown in the insets in (a) and (b), respectively. The exponential fitting curves into $F (z)$ and $G (z)$ for $z > 5.25 Å$ are also shown in the inset of (b). The acquisition parameters were $f_{0} = 144.4074 kHz$ , $A = 123 Å$ , $k = 19.8 N / m$ , $Q = 27000$ , and $V_{s} = + 100 mV$ . The imaging set point for dynamic STM was $⟨ I_{t} ⟩ = 20 pA$ . The tip-sample distance, denoted as $z$ , in (a) and (b) is aligned according to the DFT calculations (see Fig. 2). (c) Histogram of the magnitudes of decay parameters $κ_{F}$ and $κ_{G}$ which were acquired using 16 different tips with 8 different cantilevers.Reuse & Permissions

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