Focus of Research in the Ashoori Group

Ray Ashoori

The principal focus of research in our laboratory lies in the study of interacting electronic systems in low dimensional semiconductor structures. Systems in which electrons exist purely in two or one dimensions and even small boxes (quantum dots) containing as few as one electron can now be produced with relative ease. While simple quantum mechanical calculations determine the motion of a single electron in such a confining structures, it is far from simple to understand the behavior of many trapped electrons. Not only do the electrons repel one another, they are indistinguishable. This fact, along with the principle that only one electron can exist in any quantum mechanical orbit, produces unusual and sometimes counterintuitive correlations in the motions of electrons.

Here, I describe how we have used methods of extremely sensitive methods to detect minuscule amounts of electrical charge inside materials. This capability has permitted us to perform some rather unique and fundamental measurements on low dimensional electronic systems, and I believe that exceptional possibilities exist for future measurements.

We invented a method known as single electron capacitance spectroscopy (SECS) which permits measurement of the electronic energy levels of a single quantum dot or artificial atom. It allows us to vary controllably the number of electrons in artificial atoms (starting from the first electron) and to measure precisely the energy required to add successive electrons. Our artificial atoms are much larger than real atoms, and this has the consequence of greatly accentuating the effects of electron-electron interactions and resulting in quite different physics. While some features appear in the spectra that could be predicted from a simple noninteracting model of the artificial atom, the spectra clearly display features attributable to electron-electron interactions. For instance, we observe effects of ferromagnetism of the electron gas: for particular values of an applied magnetic fields, electronic spins flip and all line up in the same direction. At higher or lower fields, the spins depolarize. At high magnetic fields, the electron density in the artificial atom even undergoes a bifurcation into discrete inner and outer shells with low electron density between the shells.

While many of the spectroscopic features that we have observed can now be understood theoretically, we have uncovered a profound puzzle. In larger artificial atoms that contain few electrons, a physical process exists which appears to exactly cancel the interaction between electrons! In SECS spectra of small artificial atoms, we always observe that there is an increased energy cost for adding successive electrons to the system. This is simple to understand: electrons already in the artificial atom repel additional electrons from being added to the system. However, in larger artificial atoms, sometimes two or even more electrons can be added to the system with no additional energy cost for successive electrons. Even more strikingly, for intermediate size artificial atoms, every fourth and fifth electron addition to the system appears as a pair. The periodicity of the bunching suggests that it is associated with electron additions into spatially distinct regions within the artificial atoms. Recently we have performed experiments on artificial atoms with adjustable shape, allowing us to separately adjust energies of electrons in different positions within the artificial atoms. After the shape is varied beyond a threshold, the pairs suddenly split, and with more shape variation new pairs form. This behavior is consistent with the model that paired electrons enter distinct positions within the atom. However, the long range mechanism that binds the two distant electrons into pairs is still entirely a mystery.

Our work comprises study of other low-dimensional electronic systems. One of the most intriguing among these is the two-dimensional electronic system (2DES). In an applied magnetic field, this system gives rise to the quantum Hall effects. As quantum dots simply often consist of confined regions of 2DES, study of quantum dots is often closely related to study of the physics of the quantum Hall effects. Moreover, the potential landscape within a two dimensional system inevitably contains local potential minima and maxima. For this reason, it may be sometimes appropriate to think of the system as consisting of many quantum dots (potential valleys) and antidots (potential maxima).

Of course, actual images of the distribution of electronic charges inside confined structures may be even more valuable than inferences drawn from spectroscopic measurements. Such imaging is useful not only for quantum dot systems, but for a variety of low dimensional systems. A major challenge arises in producing such images because the electronic systems exist deep beneath the surfaces of semiconductors. We have overcome this difficulty in developing a cryogenic scanned probe technique called subsurface charge accumulation (SCA) imaging. It permits very high resolution examination of electronic systems inside materials. We have used our SCA microscope to image directly the nanoscale structures that exist in the 2DES. Amazingly, we can now actually see some of the processes that give rise to features in SECS spectra. We have learned how to produce samples with tailored local density minima or maxima. Compressible (high thermodynamic density of states) and incompressible (very low density of states) regions associated with regions of different Landau level filling factor can be clearly identified. Finally, images of regions of local shallow potential minima directly depict the bifurcation of the electron density into inner and outer shells as discussed above for structures similar to artificial atoms.

Our work on SCA imaging is still in its infancy, but we can already make some key remarks about the behavior of a 2DES that does not contain intentionally produced density minima or maxima. First, the 2DES appears uniformly compressible for fields away from the integer Landau level filling factors (i.e., away from quantum Hall plateaus). Second, spatial compressibility structure appears only near integer Landau level filling factors, and this structure evolves with enormous sensitivity to magnetic field. Imaging the compressibility at fields differing by only 0.5% yields images which appear to have no correlation of spatial features. Both of these results are fundamentally surprising; several theoretical notions exist, and some predicted structure between the plateaus, but none seem to have predicted the rapid evolution of the observed structure.

Our ability to sense very small amounts of electrical charge has permitted us to make some basic queries about interacting electronic systems. So far I have describe two basic questions that the experiments can answer: how much energy does it take to add an electron to a quantum dot and where does charge flow in an electron system as a result of a change in the chemical potential of the system? The simplicity of the charge sensing measurement can often result in fundamental information about low dimensional electronic systems not available with other measurement techniques.

There are many other basic questions that can be answered with these techniques. Among them is the following: how likely is it that an electron with a given energy will be able to tunnel into a two-dimensional or any other electronic system? Such measurements have often been unrealizable because it may be practically impossible to produce separate electrical to an isolated low-dimensional electronic system and a neighboring metallic electron injector. We have overcome this difficulty by developing a contactless capacitance method for making such measurements. We call this method time domain capacitance spectroscopy (TDCS). We have used TDCS to understand in detail the characteristics of tunneling of electrons into a 2DES in magnetic field. We discovered a universal shape of the tunneling density of states (growing linearly with excitation) that has arisen in each of the 6 samples (including high mobility samples) that we measured.

As I see it, interest in the low temperature electronic properties of low dimensional structures has been driven largely by two factors. Firstly, the systems display astonishing properties in very particular regions of the experimental parameter space. For instance, in the case of the integer and fractional quantum Hall effects, the Hall conductance of the two-dimensional electronic system is quantized to a few parts in a billion precision. Secondly, it is possible to make the theoretical determinations of exact or nearly exact solutions for the ground state of systems at particular narrow regions of parameter space. In some cases, approximate solutions around these regions can be well understood through the language of pseudoparticles such as Laughlin quasi-particles, skyrmions, and composite fermions. However, a large parameter space still exists in which it is not presently possible to produce reasonable approximate solutions, and traditional transport measurements produce results which cannot presently be understood by theory. I feel strongly that new techniques such as the capability of actually looking at electronic structure with a scanning probe will be required to produce any detailed understanding of these regimes.

Our laboratory is presently unique in the world for our ability to make extremely sensitive charge measurements on a variety of semiconductor structures. Each of the techniques described above grew from this capability. Moreover, the methods can be used in combination. For instance, we are working to study the injection of single electrons into quantum dots using a combination of SECS and TDCS. We continue to improve the sensitivity and the versatility of these measurements to probe more deeply into the problems of interacting electrons in low-dimensional or small structures. Our scanned probes offer the possibility of observing electronic structure together with in-situ transport measurements, thus helping to develop a more fundamental understanding of how currents flow within materials. Among the many problems available for study are the low density regime of a 2D system where many groups now claim to observe a metal-insulator transition, the fractional quantum Hall effect, edge states, and states of localized traps and impurities. Finally, we intend to use our microscope to study a number of artificially patterned structures. Physical chemists have learned to make chemically derived small clusters (size scale around 100 Angstroms or perhaps larger) with remarkable uniformity. By producing arrays of such clusters on top of GaAs samples and using them as templates for ion bombardment, we will be able to produce arrays of very closely spaced potential minima within a sample. As the coupling between minima can be adjusted, many different types of 2D materials, from tight binding lattices to nearly free electron metals, can be approximated by this type of lateral superlattice. We can thereby produce artificial materials whose atoms lie on a size scale that the SCA microscope can see and thus directly image the basic physics that gives rise to the electronic properties of solids.