Signature of a Chemical Bond in the Conductance between Two Metal Surfaces

Abstract

Conductance in monatomic metal contacts is quantized; it increases in discrete steps of one conductance quantum 2e 2 =h. By contrast, in a vacuum barrier between two metal surfaces we find that conductance increases linearly and continuously with the interaction energy between individual atoms. This behavior shows unambiguously that current flow between single atoms is a measure for their chemical interaction. In the controlled environment of a scanning tunneling microscope it should allow us to study the formation of covalent bonds up to the point where these atoms finally jump into contact. DOI: 10.1103/PhysRevLett.91.036803 PACS numbers: 73.40.Gk, 71.15.Mb, 73.23.Hk Because of their importance for technical applications the conductance properties of metals have been widely researched. In metal break junctions at close to zero temperature the conductance of single atomic contacts has been measured with great accuracy, and it was generally found that conductance increases in discrete steps of one conductance quantum 2e 2 =h [1][2][3][4][5]. The rupture of a bond probes into material properties from the starting point of material stability. Quite the opposite is true for the operation of scanning probe microscopes. There, the interaction between two separate surfaces is generally kept at such a low level that the small changes in the forces between the surfaces or in the number of electrons tunneling through the vacuum barrier can be used as an indication of the surface topographic and electronic properties. The intermediate range between these two methods continues to be problematic. In particular, the role of chemical interactions in scanning probes, even though widely researched [6 -13], is still not well understood. Part of the problem is the theoretical representation of the situation in different frameworks: perturbation methods are generally limited to high distances, they can incorporate chemical interactions only from the outset [13][14][15]. Scattering methods, while electronically accurate, cannot treat atomic interactions and their shift of position at low distances [16]. Nonequilibrium methods are in principle reliable, but they cannot simulate actual probe scans due to their innate restrictions of the symmetry of the combined system [17,18].Here, we propose a new method, which incorporates chemical interactions in a natural way. The method is based on extensive ab initio calculations of coupled systems. These calculations, including chemical interactions from the outset, establish that the suggested perturbation method is in general sufficient to reach the highest level of experimental accuracy.A system, composed of a conducting surface and an equally conducting probe, will be completely decoupled if the distance between the surface atoms and the foremost atom of the probe (apex atom) is substantially greater than 1 nm. Then the electron states of surface and probe are orthogonal: every productwill be zero. If the two systems are brought into closer contact, with a distance of about 0.5-0.6 nm,...

The role of surface elasticity in giant corrugations observed by scanning tunneling microscopes

“…The solution, for gold surfaces, was presented by Hofer et al [19]; it involved calculating the forces and relaxations of coupled systems, and to determine the effect on constant current contours within a firstprinciples approach. It was also shown that tunneling current and interaction energy are in fact proportional to each other [20]. This result, contradicting earlier assumptions by Chen [21], is confirmed by experimental data [22].…”

“…We then introduced interaction forces and the induced relaxations in the following way. Assuming that the interaction energy E is given by E = ÀaG, where G is the tunneling conductance and a a constant, which is determined by first principles simulations [20], then the vertical relaxation of surface atoms z can be determined within the harmonic approximation by E = Àkz 2 . Given that the tunneling current at one point of the surface follows an exponential decay I(z) = I 0 e Àjz , it is possible to relate the modified current I 0 (z), due to relaxations of the surface atoms, to the conductance at this very same point with…”

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

“…The interaction between two nondegenerate and/or delocalized electronic states renders the linear relation G / F [19]. The existence of this regime has been unambiguously confirmed by means of AFM/ STM measurements supported by first principles calculations with nonperturbative treatment of the electron transport in metallic atomic point contacts [21].…”

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

“…39 in [13]) is κ γ = 12 nm −1 at the β-site and κ γ = 16 nm −1 at sites '1'and '2'. The decay constants for κ I and κ γ are equal within the measurement accuracy, thus the theory by Hofer and Fisher [7] appears to hold for the interaction of W with graphite. The damping signal decays with κ ∆Ets = 20 nm −1 at the β-site and κ ∆Ets = 30 nm −1 at sites '1'and '2' as expected from an energy loss proportional to the square of the attractive force.…”

“…Chen [5] has found that the square of the attractive energy between tip and sample should be proportional to I with experimental evidence in [6]. Hofer and Fisher [7] suggested that the interaction energy and I should be directly proportional, experimentally found in [8,9]. In this Letter, we investigate the experimental relationships between tunneling currents and conservative as well as dissipative forces for graphite probed with a W tip by performing local spectroscopy on specific lattice sites.…”