Electron Transport in Stretched Monoatomic Gold Wires A. Grigoriev, 1 N.V. Skorodumova, 1 S. I. Simak, 2 G. Wendin, 3 B. Johansson, 1,4 and R. Ahuja 1,4 1 Condensed Matter Theory Group, Department of Physics, Box 530, Uppsala University, S-75121 Uppsala, Sweden 2 Department of Physics, Chemistry and Biology, Linko ¨ping University, SE-581 83 Linko ¨ping, Sweden 3 Department of Microtechnology and Nanoscience–MC2, Chalmers University of Technology, S-41296 Go ¨teborg, Sweden 4 Applied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), S-10044 Stockholm, Sweden (Received 11 April 2006; published 8 December 2006) The conductance of monoatomic gold wires containing 3–7 gold atoms has been obtained from ab initio calculations. The transmission is found to vary significantly depending on the wire stretching and the number of incorporated atoms. Such oscillations are determined by the electronic structure of the one- dimensional (1D) part of the wire between the contacts. Our results indicate that the conductivity of 1D wires can be suppressed without breaking the contact. DOI: 10.1103/PhysRevLett.97.236807 PACS numbers: 73.63.b, 03.65.Yz, 31.15.Ne, 85.65.+h Unique structural and conduction properties of monoa- tomic gold wires have attracted considerable attention both experimentally [1– 5] and theoretically [1,6 –10]. Atomic chains can be fabricated in mechanically controllable break-junction experiments using tunneling microscope or transmission electron microscope techniques [1]. Structures formed in these experiments can be seen as 1D gold molecules or clusters suspended between two surfaces. Although the basic properties of 1D systems can be understood using relatively simple models [1,2], a detailed description of the chain conduction properties requires elaborated quantum-mechanical treatments. The conductance of a monoatomic chain suspended between two gold tips has been measured and shown to be close to the quantum unit G 0  2e 2 =h [1]. Further analysis, how- ever, has revealed the presence of conductance oscillations: Smit et al. [3] have discovered rather small deviations from the value G 0 (  0:1–0:2G 0 ) in Au wires, whereas Costa- Kra ¨mer et al. [4] have reported on strikingly large oscil- lations between 0 and 1G 0 (even 2G 0 ). Moreover, Kizuka et al. [5] have observed the formation of a monoatomic gold wire accompanied by a sudden drop of conductance from the value 2G 0 down to zero. Theoretical studies have shown that conductance can exhibit oscillations depending on the parity of the number of atoms (N) constituting a 1D linear gold wire [9,10]. It has been reported, however, that the equilibrium configu- rations of the wires are not linear but zigzag structures, whose electronic properties essentially differ from those of linear chains [1,8,9]. The analysis of the electronic struc- ture of fully relaxed infinite gold chains has shown that there is a systematic difference between wires with odd and even N. The band structure of the former wires exhibits an s-state conduction channel, whereas for the latter ones the appearance of a small band gap at the Fermi level is observed [8]. Calculations performed by Lee et al. [9] also suggested that the conductance of a 1D wire can change at stretching. Here we present calculated zero-bias transmission spec- tra of monoatomic gold chains suspended between two gold (111) surfaces. We show that the conductance through the system is determined by the properties of the chain. The conductivity can vary significantly depending on both the degree of stretching and the parity of the number of atoms in the 1D wire. The structural and transport properties of suspended 1D gold chains with N  3–7 have been studied using density- functional-theory-based nonequilibrium Green’s function (NEGF) transport theory as implemented in the TRANSSIESTA [11] simulation package. The electron trans- mission obtained from NEGF theory TE tr R G C  L G  C  (1) describes electron transport in the system in terms of scattering in the central (C) region and coupling to the electrodes (L and R) via self-energy terms. Here G C and  LR denote the corresponding Green’s functions and imaginary parts of the self-energies, respectively. The cor- responding density of states nEdE  e 2 X i2L;R G C  i G  C dE (2) sets the limit to transmission in the sense that electron propagation from one electrode to the other is limited by the density on the chain and can be further reduced by reflection at the interface with the second electrode. In our calculations, chain configurations were first opti- mized for infinite wires [12], and then relaxed 1D struc- tures were inserted between two Au(111) electrodes. Subsequently, the distance between the gold surface and the first or last atom of the 1D wire was optimized. We notice that the changes in the transmission spectrum due to this additional relaxation or due to rotation of the wire around the z axis were negligible. We have additionally tested our model of the chain structure by fully relaxing PRL 97, 236807 (2006) PHYSICAL REVIEW LETTERS week ending 8 DECEMBER 2006 0031-9007= 06=97(23)=236807(4) 236807-1  2006 The American Physical Society