Fluctuation phenomena in low dimensional conductors

Central topic of this thesis are fluctuation phenomena in the electrical current of high-mobility semiconductors. Such time dependent fluctuations of the current around its mean value occur due to the discrete nature of the electron charge and are called shot noise. They are present even at zero temperature. In contrast to classical music, where noise is most often a disturbance, the noise in the electrical current contains additional information on how the electrons move in a conductor. This information is not available from common conductance measurements.
For example, the statistics or the charge of the particles involved in transport can be probed by shot noise. Furthermore, electrical noise has become an alternative and very accurate method to determine the temperature of electrons in a solid. Thus, measuring the noise in the electrical current is a very powerful tool in mesoscopic physics. It will certainly play an important role in the future, too, for example within the field of quantum computing in order to probe the correlations caused by entanglement.
This thesis starts with an introduction into some basic concepts of electrical transport and noise in mesoscopic systems and a very brief review of the properties of twodimensional electron gases. In the follwoing chapters the processing of heterostructure devices (chap. 3) as well as the technique to detect low-frequency noise (chap. 4) are described. The main results on fluctuation phenomena in low dimensional conductors of this thesis are presented in the last chapters (5-8):
Chapter 5: In the fifty’s of the last century a new field, nowadays called quantum statistics, was invoked by a fundamental experiment of Hanbury Brown and Twiss (HBT). The statistics of inherent indistinguishable quantum particles is different from that of classical particles which always can be distinguished by their unique classical trajectories. As is well known, there are two different kinds of quantum particles, Bosons and Fermions, which differ in the symmetry of the wave function upon interchange of two particles. HBT explored the statistics of a thermal photon field which is made out of Bosons performing an intensity correlation experiment. In this chapter we present an analogous experiment carried out with electrons which are Fermions.
Chapter 6: The amount of shot noise in mesoscopic conductors is not arbitrary but equals various so called universal values for different systems. Here, ‘universal’ means that the noise level is insensitive to microscopic properties of the device. Cavities of micrometer dimensions in which electrons scatter randomly are one example of a system where the shot noise is believed to be universal. Here, we present the first experimental confirmation of this theoretical prediction for the shot noise in so called open chaotic cavities.
Chapter 7: Shot noise was first discovered in classical systems, namely in vacuum tubes by W. Schottky in 1918. The detailed investigation of shot noise in nano-conductores started only during the last ten years ago and since than has provided a tremendous amount of new information about charge transport. Surprisingly, the mathematical expressions for shot noise in classical systems like vacuum tubes and in coherent (mesoscopic) conductors are very similar which leads to the question about differences and similarities in the origin of shot noise in classical and quantum mechanical systems. In this chapter I discuss an experiment which clearly shows that the shot noise present in mesoscopic devices is a purely quantum mechanical effect, which disappears in the case that electronic motion is governed by laws of classical mechanics alone.
Chapter 8: In this final chapter I investigate the crossover of shot noise from a single scatterer to the limit of a large number of scatterers in series. Experimentally, each single scatterer can be modeled as a quantum point contact. Whereas for one scatterer shot noise is highly sensitive to the probability for transmission through the contact it reaches the same universal value for an infinite number of scatters independently of the transmission probability. Theoretically, this problem has been considered before for a series of planar tunnel junctions. In our case however, the system does not consist of a one-dimensional array of barriers, but cavities are formed in between the contacts. We therefore present a theoretical model which includes the additional cavity noise contribution to the partition noise of the contacts, and compare it to our experimental results.