The Natelson Group is interested in nanoscale condensed matter physics, in particular the electronic, magnetic, and optical properties of systems with characteristic dimensions approaching the atomic scale. A variety of unusual phenomena arise in this size regime, and an understanding of the properties of matter on these scales will likely be essential for future technologies.
Imagine taking some nanoscale structure and somehow hooking it up to a battery via a couple of wires. As the voltage across the nanosystem is increased, many things can happen. An electric field develops across the structure, and charge rearranges itself in response to that field. When there is conduction, electrons are driven from one side of the nanosystem to the other, pushing the distribution of electrons (as a function of both position and energy) out of equilbrium. Those electrons interact with each other, and energy can pass between them; the electrons can also deposit energy into the vibrational motion of the atoms, driving those degrees of freedom out of equilibrium. The electrons can interfere quantum mechanically, though their coherence (and therefore the importance of quantum interference) degrades as they interact with their environment. The spins of the electrons can become entangled with each other. All of this takes place on very short time and distance scales, and somehow leads to the macroscopic world we see all around us. Sometimes electron-electron interactions play only a minor role in determining material properties (as in aluminum or silicon); in other material systems, however, the electron-electron repulsion can be critically important. Our group tries to understand the physics in both driven and "correlated" systems, through experiments and their analysis. We are particularly interested in trying to get information at the nanoscale in nanoscale structures driven out of equilibrium, and in materials where strong electron-electron interactions determine material properties.
Techniques now exist for controllably fabricating structures with characteristic lengths below 10 nm, through both "top-down" methods (combining electron beam lithography, directional etching, and metal deposition) and "bottom-up" approaches (chemical fabrication, self-assembly). We can now examine "traditional" solid state systems at previously unexplored scales by making samples in this newly accessible regime. Further, we can develop tools for studying novel materials such as organic semiconductors and other molecular and molecular-scale objects.
In addition to learning a lot of neat physics, people in this research group develop skills in micro- and nanofabrication, sensitive electrical measurements, various microscopy techniques, semiconductor physics, low temperature physics, and vacuum systems. Graduate students or interested undergraduates are encouraged to send email (firstname.lastname@example.org).
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.
Atomic-scale metal junctions
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 2e2/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.
In collaboration with the Untiedt group at Alicante, we have found evidence for Kondo physics in atomic-scale junctions between ferromagnetic metals. This is rather surprising, since Kondo physics involves antiferromagnetic process that couple a local electronic spin to the spins of conduction electrons. It appears that the undercoordination of the atom(s) at the contact region modifies the local electronic structure, making this physics possible. This system is an attractive target for noise measurements, as predictions exist regarding noise in the Kondo regime.
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. These structures generally act like single-electron devices, shown schematically at right. In the limit shown, electronic conduction through SMTs is strongly affected by the single-particle level spacing (the energy required to promote an electron from the highest occupied level to the lowest unoccupied level) and the Coulomb charging energy (the energy needed to add an additional electron to the molecule).
In SMTs, the small molecular size implies that both of these energy scales 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.
Prof. Natelson has written an extensive review article about single-molecule transistors. Please contact Prof. Natelson if you would like a copy. Similar matters are discussed in these two papers (1, 2).
We have used these devices to study several interesting physics and physical chemistry 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 using transition metal complexes provided by our chemist colleagues, we implemented gate-modulated inelastic electron tunneling spectroscopy at the single molecule level. We saw nontrivial changes in vibrational levels when the vibrational energy and the energetic cost to make an electronic transition became comparable. This gate modulation of vibrational energies is a nonperturbative effect that we are studying further.
- In SMTs with the same complexes, 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 examined the relationship between semiconductor mobility and contact resistance in devices based on P3HT and Au electrodes, showing that, for the diffusion-limited injection regime, contact resistance is inversely proportional to the mobility over four decades in mobility.
- We developed a method for extracting the current-voltage characteristics of just the metal-organic contact.
- We showed that surface chemistry may be used to manipulate those metal/organic interfacial energetics. With self-assembly of the appropriate work function-raising molecule, Au electrodes may be modified so that their injection properties act like those of Pt. This is one route to optimizing contacts in organic FETs.
- We pointed out that transport in these materials crosses over from thermal activation to a field emission regime at low temperatures and very large electric fields.
- Finally, we found good evidence that interfacial charge transfer at the Pt/P3HT interface effectively dopes the P3HT with mobile holes very locally, and that similar physics is at work in graphene devices.
Surface-enhanced Raman spectroscopy and Nano-optics
Raman spectroscopy is a common chemical characterization technique in which incident light interacts inelastically with a system, either losing energy toa vibrational or electronic mode of the system ("Stokes scattering"), or gaining energy from the system ("anti-Stokes scattering"). Raman cross-sections for single molecules tend to be small (~ 10-29 cm2). However, nanostructured metal surfaces can act like little optical antennas due to electronic excitations called plasmons. The local electric field in the presence of plasmons can be enhanced by a factor g over that of the incident light. This translates into an enhancement of Raman emission by roughly g4 for molecules in the region of this near-field effect. The result is surface-enhanced Raman scattering (SERS), which can have single-molecule sensitivity.
In 2007 we demonstrated that the nanoscale electrodes used for the SMT experiments are outstanding plasmonic antennas and therefore wonderful substrates for SERS. This work was picked up by Nature Photonics.
(Here and here), we successfully performed simultaneous electronic transport and SERS measurements on single molecules. This confirms that transport is through the molecule of interest (via the unique Raman spectroscopic signature) and demonstrates that we can make single-molecule sensitivity Raman "hotspots" in predefined locations. This opens up many exciting experimental possibilities!
When light shines on a metal nanojunction and excites the local plasmon modes responsible for the enhancement, the plasmons lead to a voltage across the nanojunction, oscillating at optical frequencies (exceeding 1014 Hz). Combining optical and electronic transport measurements in junctions without molecules, we have used optical rectification to determine this voltage experimentally. Using the simultaneously measured tunneling conductance, we can then infer quantitatively the enhanced electric field in the junction. Consistent with our Raman results, we find that field enhancements can exceed 1000x. Recently we have gained new insights into the interesting plasmon modes responsible for this enhancement.
We have used Raman scattering to examine the pumping of vibrational and electronic populations as current flows through a molecule-containing junction. This work demonstrates that it is possible to access experimentally the energetic distributions of electrons and vibrational modes in driven junctions, in situ, at the single molecule scale. While there has been much theoretical discussion of these distributions, attaining experimental information about the situation is very difficult. We have reviewed such experiments by our group and others here. More recently, we found that a voltage bias may actually be used to tune molecular vibrational frequencies in some circumstances. Current efforts are looking at controlling electron-vibrational inelastic processes at the molecular scale, discerning between electronic and lattice heating processes, and leveraging our understanding of plasmonic modes for other surface-enhanced spectroscopies.
Strongly correlated nanostructures
Most experiments examining the electronic properties of nanostructured materials have focused on simple metals and semiconductors. We are very interested in applying nanoscale transport techniques to strongly correlated materials, systems in which the simple single-electron approach of conventional band theory fails. Such nanostructure-based experiments, while challenging, can (1) apply large electric fields without the need for large voltages, discriminating between different physical processes; (2) probe inhomogeneous systems on a scale smaller than their inhomogeneity; and (3) enable sensitive studies of noise and contact effects not readily performed in macroscopic structures. We published a review article about this exciting topic here, as well as an overview of Rice University research on strongly correlated materials.
One example of a strongly correlated material is VO2. This material has a high temperture metallic state with a rutile (tetragonal) crystal structure, and a low temperature insulating state with a monoclinic crystal structure, separated by a first-order "metal-insulator" phase transition at around 65oC. This transition is very dramatic, with a 10000x change in the electronic conductivity. For decades the roles of electron-electron interactions (particularly from the half-filled d band of the V ions) and the electron-phonon interactions (as seen in the structural change at the transition) have been debated. Current understanding is that both strong e-e and e-ph interactions are important.
Recently, working with single-crystal nanobeams of VO2, we have found that this material can be reversibly doped by intercalation of atomic hydrogen. (It turns out that it has been known for over forty years that atomic hydrogen is readily taken up by the structurally related semiconductor, TiO2.) This doping process suppresses the insulating state (!), both by changing the effective V d occupancy and by expanding the lattice slightly. One of our ongoing efforts is the detailed understanding of the resulting low temperature conducting state. We now have a greater understanding of the resulting structures and the nature of the hydrogen diffusion process.
In prior studies of electronic conduction in magnetite nanostructures, we found that at temperatures below the Verwey transition it is possible to kick the material out of the insulating state and back into a more conducting state via electric fields. The result is dramatic switching in the electronic conduction, and we are continuing to investigate this newly found nonequilibrium phase transition. We have found that while the switching from low- to high-conductance is driven by electric field, the hysteresis shown in the figure is a signature of local heating, and may be eliminated by performing pulsed measurements. In more recent work, we have looked at the response of another correlated low-T insulator, NdNiO3, at high electric fields.
Current investigations are focused on "bad" or "strange" metals where the conventional quasiparticle picture of low energy electronic excitations may fail. We are interested in examining charge transport on mesoscopic scales. If the long-lived, low energy excitations in these systems do not look like conventional electrons, how should one think about them and their quantum corrections to classical conduction? Similarly, what information can shot noise reveal about the nature of charge transport in such systems - are these weird materials just masking essentially ordinary Fermi liquids, or is the situation more complex?
This work is supported by the Material Sciences and Engineering Division of the Department of Energy's Office of Basic Energy Sciences.
Older projects: Resistive switching
There are a number of systems that have electronic conduction properties that may be switched, through voltage or current cycling, between two states, a high-conductance "on" state, and a low-conductance "off" state. As you might imagine from the terminology, there is much industrial interest in employing such systems as switches or nonvolatile memories. Hewlett Packard has coined the term "memristor" to describe such a device, though the phenomenon itself is not surprising. The physics challenge is distinguishing between the multiple mechanisms that can lead to similar observed properties. Collaborating with Prof. James Tour and Prof. Lin Zhong, we have found that silicon oxide, a material often treated cavalierly as an inert insulator, can show this kind of switching, as described here. Here is a recent review of this and other phenomena related to ion motion in nanostructures.
Older projects: organic semiconductors
Organic semiconducting materials are widely recognized as having tremendous potential for certain electronics applications. The charge transport properties of such materials are determined by both the microstructural arrangement of molecules (as in inorganic semiconductors) and by the chemical structure of the molecules themselves.
In previous years, the Natelson group pursued a research effort aimed at understanding transport mechanisms and contact phenomena in organic semiconductors, based largely on bottom-contacted organic field-effect transistors (OFETs). Material systems that we examined included polythiophene and solution-processable derivatives of pentacene. Our accomplishments included:
This project had been supported by the NSF.
Older projects: Quantum coherence
Electrons are quantum mechanical objects, yet in daily experience one does not worry about quantum interference effects when, for example, turning on the lights. The reason for this is decoherence. As electrons interact inelastically with their environment (including other electrons), their quantum mechanical phase relationships become scrambled on a time scale called the coherence time (and a corresponding distance scale, the coherence length). At room temperature, this length scale is ~ 1 nm. At low temperatures, however, it can reach easily accessible scales and produce significant quantum corrections to the electrical properties of conducting systems.
Information about decoherence processes must be inferred from measurements of those corrections. An important outstanding question is, Do different quantum corrections probe the same decoherence physics? In the past we have concentrated on measuring universal conductance fluctuations and weak localization.
We have used these measurements to probe the nature of quantum-enhanced noise in normal metal nanowires, including the surprising effects of surface chemistry on the source and distribution of that noise. These measurements also revealed interesting magnetic properties of partially oxidized titanium.
We have also performed similar measurements in ferromagnetic metal nanowires as well as InMnAs dilute magnetic semiconductor nanowires. Quantum coherence effects in ferromagnetic systems remain relatively unexplored experimentally, and ferromagnetism leads to new collective modes (e.g., spin waves) that may profoundly affect electronic coherence. While we are not currently pursuing this project actively, the general topic of coherence remains of much interest to us. It is interesting to ask, what coherence effects are seen and how may they be understood in materials where the conventional quasiparticle picture of electronic excitations is inadequate?