Ab initio study of charge transport through single oxygen molecules in atomic aluminum contacts

We present ab initio calculations of transport properties of atomic-sized aluminum contacts in the presence of oxygen. The experimental situation is modeled by considering a single oxygen atom (O) or one of the ${\mathrm{O}}_2$ and ${\mathrm{O}}_3$ molecules bridging the gap between electrodes forming ideal, atomically sharp pyramids. The transport characteristics are computed for these geometries with increasing distances between the leads, simulating the opening of a break junction. To facilitate comparison with experiments further, the vibrational modes of the oxygen connected to the electrodes are studied. It is found that in the contact regime, the change of transport properties due to the presence of oxygen is strong and should be detectable in experiments. All three types of oxygen exhibit a comparable behavior in their vibrational frequencies and conductances, which are well below the conductance of pure aluminum atomic contacts. The conductance decreases for an increasing number of oxygen atoms. In the tunneling regime, the conductance decays exponentially with distance and the decay length depends on whether or not oxygen is present in the junction. This fact may provide a way to identify the presence of a gas molecule in metallic atomic contacts.

Figure 1

(Color online) ${\mathrm{Al}}_{17}\text{−}{\mathrm{O}}_x\text{−}{\mathrm{Al}}_{17}$: Optimized contact geometries and their tip-to-tip distances as obtained by stretching an aluminum (blue) atomic contact in the presence of oxygen (red) molecules. The Al pyramids consist of seven, six, three, and one atoms in the layers from the outside to the inside. (a) $\mathrm{Al}\text{−}\mathrm{O}\text{−}\mathrm{Al}$, (b) $\mathrm{Al}\text{−}{\mathrm{O}}_2\text{−}\mathrm{Al}$, (c) $\mathrm{Al}\text{−}{\mathrm{O}}_3\text{−}\mathrm{Al}$.

Figure 2

$\mathrm{Al}\text{−}{\mathrm{O}}_x\text{−}\mathrm{Al}$: Energy of the vibrational modes of the oxygen molecule connected to Al pyramids as a function of the distance $d$ between the Al tip atoms. The arrows and plus and minus signs denote the directions of relative displacements of the atoms in a given mode: → and ← denote motion along the axis of the contact while +,− and ↑,↓ denote motion in the two directions perpendicular to the axis. (a) $\mathrm{Al}\text{−}\mathrm{O}\text{−}\mathrm{Al}$, (b) $\mathrm{Al}\text{−}{\mathrm{O}}_2\text{−}\mathrm{Al}$, (c) $\mathrm{Al}\text{−}{\mathrm{O}}_3\text{−}\mathrm{Al}$.

Figure 3

(Color online) Al-Al: Transmission as a function of energy. Both the total transmission $\left(T\right)$ and its channel contributions $\left(T_n\right)$ are shown. The vertical dashed line indicates the Fermi energy of bulk Al. The corresponding contact geometry with a distance of $3.4\mathrm{\AA }$ between the Al tip atoms is depicted on the right.

Figure 4

(Color online) $\mathrm{Al}\text{−}{\mathrm{O}}_x\text{−}\mathrm{Al}$: Transmission as a function of energy for the structures shown in Fig. 1. The tip-to-tip distance increases from the top to the bottom and is given in the panels. The vertical dashed lines indicate the Fermi energy.

Figure 5

(Color online) $\mathrm{Al}\text{−}{\mathrm{O}}_x\text{−}\mathrm{Al}$: LDOS corresponding to the second row in Fig. 4. The solid (black) curve is for the region including the Al tip atoms and the O atoms, the dash-dotted (red) one is for one of the oxygen atoms, and the dashed (blue) curve is for one of the Al tip atoms. The vertical dashed (orange) line indicates the Fermi energy.

Figure 6

(Color online) ${\mathrm{Al}}_{17}\text{−}{\mathrm{O}}_x\text{−}{\mathrm{Al}}_{17}$: Orbitals of the contact geometries of Fig. 1. Orbitals 1–3 belong to ${\mathrm{Al}}_{17}\text{−}\mathrm{O}\text{−}{\mathrm{Al}}_{17}$ with a tip-to-tip distance of $d=3.7\mathrm{\AA }$, orbitals 4–6 to ${\mathrm{Al}}_{17}\text{−}{\mathrm{O}}_2\text{−}{\mathrm{Al}}_{17}$ with $d=4.5\mathrm{\AA }$, and orbitals 7–9 to ${\mathrm{Al}}_{17}\text{−}{\mathrm{O}}_3\text{−}{\mathrm{Al}}_{17}$ with $d=5.6\mathrm{\AA }$. The energies of the orbitals are $-10.537\mathrm{eV}$ (1), $-7.238\mathrm{eV}$ (2), $-7.176\mathrm{eV}$ (3), $-6.274\mathrm{eV}$ (4), $-5.606\mathrm{eV}$ (5), $-2.133\mathrm{eV}$ (6), $-5.197\mathrm{eV}$ (7), $-2.175\mathrm{eV}$ (8), and $+0.153\mathrm{eV}$ (9), where the number of the orbital is given in parentheses.

Figure 7

$\mathrm{Al}\text{−}{\mathrm{O}}_x\text{−}\mathrm{Al}$: Conductance as a function of the distance between the Al tip atoms.

Figure 8

(Color online) Robustness of the transmission for an $\mathrm{Al}\text{−}{\mathrm{O}}_2\text{−}\mathrm{Al}$ contact at a tip-to-tip distance of $4.5\mathrm{\AA }$ [Fig. 1b]. Shown are $T\left(E\right)$ curves for an increased number of Al atoms in the pyramids, as well as for different partitionings of the contact into $L$, $C$, and $R$ regions. The solid black line is the transmission of $7\text{−}6\text{−}\mid 3\text{−}1\text{−}{\mathrm{O}}_2\text{−}1\text{−}3\mid \text{−}6\text{−}7$ (Fig. 4). The numbers stand for the Al atoms in each layer of the pyramid and “∣” indicates how the system is divided into the three different regions. The dash-dot-dotted line corresponds to the system $6\text{−}12\text{−}\mid 10\text{−}6\text{−}3\text{−}1\text{−}{\mathrm{O}}_2\text{−}1\text{−}3\text{−}6\text{−}10\mid \text{−}12\text{−}6$, the dashed line to $6\text{−}12\text{−}10\text{−}\mid 6\text{−}3\text{−}1\text{−}{\mathrm{O}}_2\text{−}1\text{−}3\text{−}6\mid \text{−}10\text{−}12\text{−}6$, and the dash-dotted line to $6\text{−}12\text{−}10\text{−}6\text{−}\mid 3\text{−}1\text{−}{\mathrm{O}}_2\text{−}1\text{−}3\mid \text{−}6\text{−}10\text{−}12\text{−}6$. The vertical dashed line indicates the Fermi energy.

Figure 9

(Color online) $\mathrm{Al}\text{−}{\mathrm{O}}_2\text{−}\mathrm{Al}$: Example of a possible geometrical configuration when the Al tip atoms are included in the relaxation process in addition to the molecule, and the corresponding transmission as a function of energy. The vertical dashed line indicates the Fermi energy.