We have developed methods of wide bandwidth, high fidelity, and very sensitive charge sensing to perform some unique and fundamental measurements on these low dimensional electronic systems. These capabilities have permitted us to make some basic queries about interacting electronic systems.
Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the "single-particle" density of states spectrum of a system. This density of states is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy, and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proved difficult to probe spectroscopically. This quantity, known as the "single particle density of states" is among the most fundamental and calculable quantities in interacting electron systems. 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, over the past 15 years, a contactless capacitance method for making such measurements. We call this method time domain capacitance spectroscopy (TDCS).
Our early experiments using capacitance methods to study tunneling lead us to discover a "Coulomb Gap" that manifests itself as a diminished probability for electrons to tunnel into a 2DES in he presence of magnetic field. It arises because an electron tunneling into a 2DES must push away electrons already in the 2DES. In the absence of magnetic field, the electrons in the 2DES readily make way. However, when a magnetic field is applied perpendicular to the plane of the 2DES, the existing electrons cannot readily move away - they are effectively pinned down by the magnetic field. Our experiments in the 1990's with TDCS allowed us to discover 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.
Over the last few years we have greatly advanced our measurement techniques so that we can now produced tunneling spectra with energy resolution limited only by temperature at dilution refrigerator temperatures (<100mK). Our recent embodiment of the TDCS method eliminates all of the major problems associated with 2D tunneling spectroscopy by abandoning steady-state measurement. By using a repetitive pulsed measurement with a very short duty cycle, electrons always tunnel into a pristinely cold electronic system, effectively eliminating the blurring effects of electron heating on the spectra. TDCS also allows tunneling into systems of arbitrarily low conductivity. This is ideal for studying quantum Hall states or an empty quantum well. TDCS also allows us to tune the electron density in our samples over a wide range (starting from zero) and also precisely calibrate the energy axis in the spectra. Finally, TDCS has demonstrated 10,000 times higher energy resolution than photoemission methods. Unlike photoemsssion, spectroscopy, it can measure spectra above and below the Fermi surface, and it can study electronic systems underneath the sample surface. I believe that it will revolutionize single particle spectroscopy.
Using TDCS, we recently have produced a major discovery. We have discovered a new and unexpected quasiparticle. This quasiparticle appears to consist of a electron with one magnetic flux quantum attached. Amazingly, the spectra display a fan of levels (a Landau fan) that makes the quasiparticles appear as long lived and non-interacting particles albeit with a different mass than for electrons and with a different apparent value of applied magnetic field. While theorists have predicted objects known as composite fermions where one electron attaches two flux quanta, the appearance in our spectra is a complete surprise. Our observance of a Landau fan for this particle suggests that it is weakly interacting, and such a result is not readily apparent from theory. Finally, the mathematics of a one flux quantum quasiparticle forms the foundation of one of several theories for important and mysterious "5/2 quantum Hall state". It may turn out that our observation of this new quasiparticle will constrain such theories. As we move to yet lower temperatures and higher magnetic fields (with a new magnet and a more powerful dilution refrigerator), it is reasonable to believe that we will make more discoveries in this system that has consistently proven so rich with new physics.
Given the extraordinary resolution and flexibility of the TDCS method, we have started work to apply it to other systems. Chief among these are the high-temperature superconductors. Because TDCS permits spectroscopy of insulators, we can use it to probe tunneling into the insulating antiferromagnetic state and in the regime of low dopings inaccessible to photoemission or STM measurements. Such measurements may allow us to measure the formation of a Fermi surface and any small Fermi pockets (of electrons rather than holes) that have been suggested by recent experiments.
So far I have described how our charge sensing techniques can answer the basic question of 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? There are other questions that these techniques allow us to answer such as: how much energy does it take to add an electron to a system, be it a quantum dot or a large two-dimensional system, and how does disorder on very small length scales effect charge flow in an electron system.
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. 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, but the mechanism that appears to bind the two distant electrons into pairs is still a mystery. Finally, our group was the first to perform charge sensing on GaAs samples single electron transistors made from metal (aluminum). Unlike the line shapes in optical spectra of atoms, we found that the line shape of quantum dot levels originates essentially in a many-body interaction between electrons in the dot and in the reservoir.
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 high spatial resolution examination of electronic systems inside materials. We have used our SCA microscope to image directly the nanoscale structures that exist in the 2DES in the quantum Hall regime. Applying a dc bias voltage to the metal scanning tip induces a ring-shaped "incompressible strip" in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the incompressible strip. These islands enable resonant tunneling across the IS, enhancing its conductance by more than 4 orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across incompressible strips. Our measurements suggest that, at the lowest temperatures, resonant tunneling may be the fundamental mechanism for charge transport in the quantum Hall system
Each of the charge sensing methods described above may be applied to a range of systems. As mentioned above, we are working to use our TDCS method on high temperature superconductors. We are also using charging methods to study chemical potential shifts in novel electronic systems formed at the interface between two polar oxides, and we are applying the SCA imaging to study graphene. The methods each probe physical quantities that are inaccessible to more conventional methods. As a result, we have achieved a long record of discovery of unexpected phenomena that I believe will continue as we advance our experimental methods and apply them to new material systems.