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arXiv:physics/9709030 · Canadian Journal of Physics

Heating-assisted atom transfer inthe scanning tunneling microscope

M. Grigorescu

Published Jan 1, 1998• 2 citations
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Abstract

The effects of a voltage pulse on the localization probability for a Xe atom prepared in a pure state localized on the STM surface at 0 temperature is investigated by numerically integrating the time-dependent Schroedinger equation. In these calculations the environmental interactions are neglected, and voltage pulses of 20 and 7 ns with symmetric triangular and trapezoidal shapes are considered. The atom dynamics at an environmental temperature of 4 K is studied in the frame of a stochastic, non-linear Liouville equation for the density operator. It is shown that the irreversible transfer from surface to tip may be explained by thermal decoherence rather than by the driving force acting during the application of the voltage pulse.

DOI
10.1139/cjp-76-12-911

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The effects of a voltage pulse on the localization probability for a Xe atom prepared in a pure state localized on the STM surface at 0 temperature is investigated by numerically integrating the time-dependent Schroedinger equation. In these calculations the environmental interactions are neglected, and voltage pulses of 20 and 7 ns with symmetric triangular and trapezoidal shapes are considered. The atom dynamics at an environmental temperature of 4 K is studied in the frame of a stochastic, non-linear Liouville equation for the density operator. It is shown that the irreversible transfer from surface to tip may be explained by thermal decoherence rather than by the driving force acting during the application of the voltage pulse.
The quantum dynamics of a Xe atom placed on the STM surfaceis studied considering two important types of nonstationary externalforces. These are the driving forces appearing during the application of avoltage pulse, and the fluctuating forces determined by the coupling to anOhmic environment. The localization probability on the tipduring voltage pulses of 20 and 7 ns with symmetric triangular andtrapezoidal shapes is calculated neglecting the environmental interactions.The results indicate that the atom dynamics in this case is reversible, andafter the pulse the transfer probability is small.The effects of the fluctuating forces produced by the coupling to thesurrounding electrons and surface phonons are studied in a static potential.It is shown that the thermal fluctuations at the environmental temperaturecan lead to irreversible atom tunneling through the potential barrier,described by an exponential decay law.PACS Nos.: 61.16.Di, 73.40.Gk, 05.40.+j
The atom tunneling across the potential barrier separating the surface and the tip of the scanning tunneling microscope is investigated by semiclassical methods, and by integrating numerically the time-dependent Schr\"odinger equation. It is shown that the barrier crossing is explained by the resonance phenomenon of quantum coherence oscillations, rather than by exponential decay. The occurrence of these resonances at the variation of the bias voltage is studied for the first two isomeric states of a Xe atom in a surface-tip potential of double-well shape. The resonant bias voltages for these two states practically coincide, and at the first common resonance the effect of the environmental temperature is discussed. The results provide a useful frame for understanding the mechanism of atom transfer in scanning tunneling microscopy.
Recently Eigler, Lutz, and Rudge [Nature 352, 600 (1991)] have reported a bistable switch that derives its function from the motion of a single Xe atom. It has been shown that this atom can be transferred, in a reversible way, from a scanning-tunneling-microscope tip to a sample by means of a voltage pulse. In this paper we show that the atom transfer process can be understood in terms of a single-atom-tunneling process, while a mechanism similar to the heating-assisted electromigration cannot account for the experimental observations. We find that there is a nonzero probability of atom transfer even at zero applied voltage, i.e., the transfer rate cannot follow a power-law dependence with the applied pulse at small voltages. We present a tunneling model, based on the charge transfer from the metal to the 6s resonance of the Xe atoms, which is consistent with the available experimental data.
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian approach. The estimates concern a Xe atom in a biased double-well junction potential. The exact treatment shows that quantum coherence oscillations of the metastable ground state may occur at particular resonant values of the bias voltage. The effect of decoherence by partial localization is studied within the quasi-classical frame.
We apply the non-equilibrium statistical operator method within the mixed quantum–classical representation to the non-contact atomic force microscopy system in which a macroscopic tip is made to oscillate above a sample surface. In our treatment the tip is treated classically, whereas a microscopic system comprising atoms in the surface and in the nano-tip is considered quantum mechanically. Using a very general non-Markovian approach, we obtain both the Fokker–Planck equation for the tip and, independently, its equation of motion with friction terms and memory effects completely accounted for. In the classical limit (high temperatures) our equations turn exactly into the classical counterparts derived previously.