Correlation and interference experiments with edge states

In this thesis experiments are presented which belong to the field of mesoscopic physics which is situated at the border between the macroscopic world with the laws of classical physics and the microscopic world where quantum mechanics rules. In quantum mechanics the properties of a physical system are described by a complex wave function. The length scale on which its phase is defined is called the coherence length Lφ which is a good measure in order to define the border mentioned above. Even though this description would also fit to optical measurement configurations with very large Lφ ’s, the notion mesoscopic physics is in general used for a sub-field of solid state physics dealing with small devices in the micron and nanometer range. Mesoscopic physics is strongly related to the technological development of processing techniques which allows the controlled design of structures smaller than or in the range of the coherence length. This gives an additional possibility to study quantum mechanics by having a wider control over the parameters of the system. For instance the separation of the energy levels of a quantum dot can be controlled by varying its size. The base material used in this thesis are two-dimensional electron gases (2DEG) which are conducting planes that establish on the sharp interface between two semiconductors with different band gap. Applying a perpendicular magnetic field, the electron transport is governed by one-dimensional channels along the edge of the border. This 1D-channels can be considered as electron beams in a solid state environment. A description of sample preparation techniques is given in chapter 3. Electronic transport measurements are an often used tool for the characterization of mesoscopic devices. Applying a voltage V and measuring the mean current I gives the mean transmission through the device and a first information about its electronic structure. The fluctuations of the current around its mean value ∆I(t) = I(t) − I provide further information
as the quantization of the charge. They are characterized by the variance ∆I 2 = I 2 − I 2 , which is called noise. In addition, in multi-terminal devices, the sign of the cross correlation of fluctuations between different terminals, ∆I1 ∆I2 , can provide additional information as for instance the particle statistics. The basics of electron transport in mesoscopic systems are described in chapter 2. In phase coherent systems, interference pattern develop. Single particle or amplitude interference arises from a superposition of single-particle processes and can be seen in the mean current I which is a function of the phase difference between the individual processes. It is also possible to probe the interference capability by two-particle or intensity interference. This is a consequence of a superposition of indistinguishable two-particle processes and appears in the cross correlation ∆I1 ∆I2 of the currents between two detectors and is as well a function of the phase difference between the two-particle processes. Textbook experiments concerning interference are mostly provided by the field of optics. An example for amplitude interference is a double slit experiment where the light passing the two slits is superposed and gives rise to an interference pattern on the screen behind. The first intensity interference experiments have been carried out by Hanbury Brown and Twiss in 1956 [1, 2] where they examined thermal light sources. In addition to an interference pattern they measured positive correlations, which is often labeled as photon bunching and was the starting point of the field of quantum optics [3–5]. It is interesting to compare such experiments with similar ones carried out with electrons. Because electrons interact much more with their surrounding environment, they loose their phase coherence much faster and therefore the length scales of such experiments are much smaller. However, the technical progress allows the production of such small structures, leading to realizations of electronic equivalents [6–9] with negative sign of the cross correlation (electron antibunching). A detailed discussion is given in chapter 4. In chapter 5 the experiments of Henny et al. [6] and Oberholzer et al. [8],which used edge states as electron beams, are extended. Inspired by a proposal of Texier and Büttiker [10], which itself follows from a discussion of Refs. [6, 8], the impact of equilibration of current and current fluctuations between such edge states due to inelastic scattering is investigated. A beam 3 splitter experiment is presented where for the first time positive correlations have been measured in a normal-conducting Fermionic environment [11]. In the mentioned electron anti-bunching experiments [6–9] negative cross correlation have been shown but no interference pattern because the phase difference could not be changed in these experiments. In 2004, Samuelsson et al. [12] proposed a realization of a two-electron interferometer using again edge states as electron beams. This proposal was inspired by the electronic Mach-Zehnder interferometer reported by Ji et al. a year before [13]. While for an electronic Mach-Zehnder interferometer interference effects are seen in the conductance, for the two-electron interferometer they only show up in intensity correlations. Compared to conductance measurements, correlation measurements are much more complex. The signal is much smaller which leads to time consuming averaging processes. In order to produce such a two-source electron interferometer the same technical challenges have to be overcome as for a single-particle Mach-Zehnder interferometer. These are e. g. the small working Ohmic contacts in the middle of the sample or the free-standing bridges. Hence, in chapter 6 of this thesis a Mach-Zehnder interferometer has been produced and characterized in a first step in order to realize a two-source electron interferometer in a second step. Compared to other implementations of electronic Mach-Zehnder interferometers [13– 16] the visibility has been investigated for a broad range of transmission values revealing an unexpected DC bias dependence. Electronic Mach-Zehnder interferometer are very sensitive to a change of the phase difference between the two interferometer arms. Hence, as soon as they are understood good enough, they could be nice phase sensor devices to probe decoherence effects.