ar X iv : c on d - m at / 9 31 20 08 v 1 2 D ec 1 99 3 Theory of the Eigler - switch

Abstract

We suggest a simple model to describe the reversible field-induced transfer of a single Xe-atom in a scanning tunneling microscope, — the Eigler-switch. The inelasticly tunneling electrons give rise to fluctuating forces on and damping of the Xe-atom resulting in an effective current dependent temperature. The rate of transfer is controlled by the well-known Arrhenius law with this effective temperature. The directionality of atom transfer is discussed, and the importance of use of non-equlibrium-formalism for the electronic environment is emphasized. The theory constitutes a formal derivation and generalization of the so-called Desorption Induced by Multiple Electron Transitions (DIMET) point of view. 68.45.Da, 61.16.Ch, 05.40.+j Typeset using REVTEX 1 Eigler and Schweizer [1] have been able to manipulate Xe atoms and place them with atomic precision on a Ni surface using an ultra high vacuum scanning tunneling microscope (STM) operated at 4 Kelvin. Experiments by Eigler, Lutz and Rudge show [2], that a single Xe atom physisorbed to a particular kink site on a single crystal Ni-(110) surface, can be transferred reversibly between this surface-site and the W tip in the STM. These experiments are done at 4 Kelvin. Using voltage pulses of ±0.8V for 64msec, they are able to toggle the Xe atom from surface to tip and back to the same position on the surface at will, and find that the direction of transfer is the same as that of the tunneling electrons. For a particular tip-surface configuration with the Xe adatom on the surface, the transfer rate, τ, goes as I, I being the tunneling current. The voltage range in these measurements is from 18mV to 180mV with V/I = 906kΩ± 2%. These phenomena has been investigated theoretically by Walkup, Newns and Avouris [3] and Gao, Persson and Lundquist [4]. These authors suggest that the main mechanism behind the transfer is that the current excite the Xe atom vibrationally in the double-well potential, sustained by the van der Waal attraction to surface and tip. On the other hand the Xe atom dissipates energy to the surface phonons, so they calculate the rate of transfer using rate-equations (Pauli master equations) including the competition between dissipation to surface-phonons and “heating” by inelasticly tunneling electrons. In Ref. [3] the possible mehanisms behind the directionality of transfer is discussed, and they conclude that the adsorbtion-induced dipole is the dominant effect. In this paper we concentrate on showing that the key-features of the experiments can be explained from a less phenomenological point of view, based on a simple model. The main idea in our calculation is the following. We view the Xe atom as a quantum Brownian particle interacting with the environment of electrons in the tip and surface via the adsorbate-resonance, through which the electrons tunnel. Besides this environment the Xe atom also interact with an environment of surface-phonons. The influence of these environments on the atom is described in a path-integral framework using the influencefunctional introduced by Feynman and Vernon [5,6], giving an effective action describing the motion of the atom. For two independent environments, the influence-functional will simply 2 be the product of the individual influence-funtionals [6]. The influence-functional for a harmonic oscillator with a linear coupling to a continuous distribution of harmonic oscillators in thermal equilibrium has been calculated by Caldeira and Legget [7]. This influencefunctional contains the fluctuating force and dissipation caused by the environment which in the classical limit are the ingredients in the Langevin equation describing the classical motion [8]. Our contribution is the calculation of the influence-functional corresponding to the nonequilibrium electronic environment. In general, when a Brownian particle is in equilibrium with a heat-bath, the fluctuating force acting on the particle and the corresponding friction force are “connected” by the fluctuation-dissipation theorem (FDT). This is the situation when no chemical-potential difference between tip and surface drives a current through the adsorbate-resonanse, and the Xe atom is in equilibrium, the surface-phonons and the electrons acting as heat baths. When an external field in some way is transferring energy to the Brownian particle the relation between the fluctuating force and the dissipation, found in the equilibrium case, no longer holds. There will in general occur a extra current-dependent fluctuating force not “compensated” by friction. We show this general feature in our model, where the interaction with the inelasticly tunneling electrons give rise to the uncompensated fluctuating force. At sufficiently low temperature compared with the oscillation frequency in the adsorbtion well, as in the actual experiment, this force will be the dominant. The temperature independent dissipation is due to exitation of surface-phonons and electron-hole-pairs in the surface and tip by the vibrating Xe atom. The time scale of desorbtion is much longer than than the relaxation time of the dissipative system, thus we have a quasi-stationary situation a relaxation time after the current is turned on. In this quasi-stationary situation we can consider the Xe-atom as a damped harmonic oscillator with a wavepacket width given by the usual FDT-result plus a contribution due to the non-equilibrium fluctuating force. From this width we define our effective temperature. The desorbtion rate is then given by the well-known results for escape of a Brownian particle from a potential well in equilibrium with a heat-bath where the new effective temperature depends on the voltage. This leads to the experimentally 3 found result if we assume that the adsorbtion well contains about five bound states, as was done in Refs. [3] and [4] . The dependence of the direction of transfer on the polarity of field follows in our model from the mean occupation of the Xe atom. We stress that it is crucial to use a non-equilibrium formalism to calculate the occupation. Let us now introduce the model and sketch the derivation of our results. The reason why a rare-gas atom like Xe actually can be imaged by STM is explained by Eigler et al. [9]. Thus we will only consider this adsorbate state. Denoting the operator and energy associated with the Xe 6s-orbital d and ǫa, and the operators asociated with surface, respectively tip, ck, cl, we write the Hamiltonian for the electronic part, Hel = Hsurf +Htip + ǫad d+ ∑ k,l d(Tkck + Tlcl) + h.c. (1) We define the weighted density of states for surface and tip,

Cite this paper

@inproceedings{Brandbyge1993arXI, title={ar X iv : c on d - m at / 9 31 20 08 v 1 2 D ec 1 99 3 Theory of the Eigler - switch}, author={Mads Brandbyge}, year={1993} }