### Atomic- and Molecular-Scale Junctions

It is now possible to examine the electronic, magnetic, and optical properties of materials down to the atomic scale in certain circumstances. These systems are of fundamental scientific interest and are likely to be relevant to next-generation technologies.

This research has been supported in part by the Robert A. Welch Foundation, The Research Corporation, the Packard Foundation, the National Science Foundation, the W. M. Keck Program in Quantum Materials at Rice.

One overarching topic of interest in truly nanoscale devices is dissipation. If you connect a wire from one terminal of a battery to the other, current flows and the wire gets warm. The organized chemical energy of the battery ends up dissipated in the disorganized vibrations of the atoms that constitute the wire. We understand this process well when we consider macroscopic wires, but if your conductor of interest consists of only a small number of atoms, the flow of energy and the nature of dissipation are much more challenging to assess experimentally.

In some ways the simplest kind of nanoscale device is an atomic-scale junction between two pieces of metal. Imagine breaking a metal wire into two pieces. At the last instant before the wire breaks, the two sides are linked by an atomic-scale connection. The electronic conduction of such a junction are dominated by quantum effects even at room temperature. For metals with mostly s-type conduction electrons (e.g., Au) the conductance of an atomic point contact is given by $$2e^{2}/h$$, where $$e$$ is the electronic charge and $$h$$ is Planck's constant.

We have developed methods to measure high frequency, broadband (200-500 MHz) noise in atomic-scale structures. Current noise (mean square fluctuations about the average current) can reveal much about correlations between the motions of electrons. If electrons transit a system (without inelastic scattering) with some characteristic rate but are otherwise uncorrelated (Poisson statistics), the current noise is white (frequency independent out to some cutoff) and given by $$2eI$$, where $$I$$ is the average current. Adding in correlations changes this result. For example, perfectly coordinated electron equally spaced in time would suppress the current noise all the way to zero. Conversely, electrons travelling in bunches rather than independently would enhance the noise. Noise in quantum nanostructures is known to show suppression under particular circumstances (see here for example). We can see this inherently quantum mechanical suppression of shot noise even at room temperature, as reported here. We have been looking at the evolution of this noise as a function of the bias across the junctions, both in ensembles of junctions (as reported here) and in individual junctions (as reported here). Of particular interest is an apparent increase in noise at relatively large currents and voltages above simple expectations, and whether this is due to electron-electron and electron-vibrational inelastic processes. See here and here for recent examinations of this.

We are one of a relatively small number of research groups in the world who have successfully made single-molecule transistors (SMTs). A readable article for nonexperts is here (pdf). SMTs are three-terminal devices, with source and drain electrodes to pass current into and out of a molecule, and also a gate electrode to shift molecular level energies up or down relative to the source and drain. In SMTs, the small molecular size implies that both the Coulomb charging energy and the single-particle level spacing can be hundreds of meV, vastly higher than in conventional metal or semiconductor single-electron devices. As a result, physical chemistry issues such as molecular vibrational modes and conformational changes can become relevant. Depending on the strength of the molecule/electrode coupling, higher order tunneling processes can strongly affect conduction as well. In molecules with unpaired spins, magnetic effects can result in the development of strongly correlated electronic states (e.g.the Kondo resonance) that span the device. The details of the contact also determine the relative alignment of the electrode and molecular levels, with major implications for transport. The interplay between all of these issues means that conduction through SMTs can exhibit a rich variety of phenomena.

We have used these devices to study some interesting physics problems:

• We fabricated SMTs incorporating individual C60 molecules. We were the first group to observe Kondo physics in C60, as well as strong interplay between the Kondo resonance and vibrational levels.
• In SMTs with transition metal complexes provided by our chemist colleagues, we have examined Kondo physics in detail. These devices exhibit very strong Kondo physics, with a characteristic Kondo temperature on the order of 70 K. Furthermore, the gate dependence of the Kondo temperature is (anomalously) very weak, demonstrating that these systems exhibit many-body physics different from that in standard semiconductor devices. This work has been reported here. Most recently, we have looked in detail at the voltage and temperature scaling of Kondo physics in molecular devices. We have found (here) that Kondo resonances in our molecular devices do scale with the same functional form seen in Kondo measurements on semiconductor quantum dots (even though our Kondo temperatures differ from those in GaAs dots by a factor of 100), though there are systematic differences in the numerical details that remain unexplained. Put simply, for a given temperature dependence, the Kondo resonances in the molecular case are considerably broader in voltage than the semiconductor case. We have written a review article summarizing the state of the art in Kondo physics in molecular transistors.
• We have looked in detail at the nonequilibrium scaling of conduction in Kondo junctions, as a function of temperature and bias, as reported here and here.
• We continue to have a strong interest in Kondo physics, particular in the ultimate limit of small size, and in systems driven out of equilibrium.