Quantum shot noise in mesoscopic superconductor-semiconductor heterostructures

Shot noise in a mesoscopic electrical conductor have become one of the most attentiondrawing subject over the last decade. This is because the shot-noise measurements provide a powerful tool to study charge transport in mesoscopic systems [1]. While conventional resistance measurements yield information on the average probability for the transmission of electrons from source to drain, shot-noise provides additional information on the electron transfer process, which can not be obtained from resistance measurements. For example, one can determine the charge ‘q’ of the current carrying quasi-particles in different systems from the Poisson shot noise SI = 2q�I� [2] where �I� is the mean current of the system. For instance, the quasi-particle charge is a fraction of the electron charge ‘e’ in the fractional quantum Hall regime [3, 4, 5]. The multiple charge quanta were observed in an atomic point contact between two superconducting electrodes [6]. Shot-noise also provides information on the statistics of the electron transfer. Shot noise in general is suppressed from its classical value SI = 2e�I�, due to the correlations. In mesoscopic conductors, due to the Pauli principle in fermion statistics, electrons are highly correlated. As a results, the noise is fully suppressed in the limit of a perfect open channel T = 1. For the opposite limit of low transmission T � 1, transmission of electron follows a Poisson process and recovers the Schottky result SI = 2e�I� [2]. For many channel systems, shot-noise is suppressed to 1/2 × 2e�I� for a symmetric double barrier junction [7, 8], to 1/3 in a disordered wire [9, 10, 11, 12, 13, 14] and to 1/4 in an open chaotic cavity [15, 16, 17]. When a superconductor is involved, the shot-noise can be enhanced by virtue of the Andreev reflection process taking place at the interface between a normal metal and a superconductor. In some limiting cases, e.g. in the tunneling and disordered limit, the shot-noise can be doubled with respect to its normal state value [18, 19, 20, 21]. One of the main results of this thesis is an extensive comparison of our experimental data on conductance and shot noise measurements in a S-N junction with various theoretical models. In addition to measure shot-noise in a two-terminal geometry, one can also perform the fluctuation measurements on multi-terminal conductors. Whereas shotnoise corresponds to the autocorrelation of fluctuations from the same leads, crosscorrelation measurements of fluctuations between different leads provide a wealth of new experiments. For example, the exchange-correlations can be measured directly from these geometry [22]. Experimental attempt in mesoscopic electronic device was the correlation measurements [14, 23] on electron beam-splitter geometry [24] which is the analogue to the Hanbury-Brown Twiss (HBT) experiment in optics. In their experiment, Hanbury-Brown and Twiss demonstrated the intensity-intensity correlations of the light of a star in order to determine its diameter [25]. They measured a positive correlations between two different output photon beams as predicted to the particles obeying Bose-Einstein statistics. This behavior is often called ‘bunching’. On the other hand, a stream of the particles obeying Fermi-Dirac statistics is expected to show a anti-bunching behavior, resulting in a negative correlation of the intensity fluctuations. Latter one was confirmed by a Fermionic version of HBT experiments in single-mode, high-mobility semiconductor 2DEG systems [14, 23]. Whereas in a single electron picture, correlations between Fermions are always negative1 (anti-bunching), the correlation signal is expected to become positive if two electrons are injected simultaneously to two arms and leave the device through different leads for the coincident detection in both outputs2. One simple example is the splitting of the cooper pair in a Y-junction geometry in front of the superconductor. Fig.1.1 shows the possible experimental scheme of the correlation measurement as described here and the sample realized in an high-mobility semiconductor heterostructures. Since all three experiments were done3, only one left unfolded, ‘The positive correlations from the Fermionic system’. The main motivation of this thesis work was to find a positive correlations in the device shown in Fig.1.1. In a well defined single channel collision experiment on an electron beam splitter, it has theoretically been shown that the measured correlations are sensitive to the spin entanglement [29, 30]. This is another even more exciting issue and we would like to mention that the experimental quest for positive correlations is important for the new field of quantum computation and communication in the solid state, [31, 32] in which entangled electrons play a crucial role. A natural source of entanglement is found in superconductors in which electrons are paired in a spin-singlet state. A source of entangled electrons may therefore be based on a superconducting injector.[33, 34, 27, 35, 36, 37, 38, 38, 39, 40, 41] Even more so, an electronic beamsplitter is capable of distinguishing entangled electrons from single electrons.[29, 42] However, the positive correlations have not been observed in solid-state mesoscopic devices until today. This thesis is organized as follows. Chapter 2 is devoted to the theoretical background of the electrical transport and the current fluctuations. We introduce the basic concept of electrical transport and the shot noise in normal state and superconductor-normal metal (S-N) junction. We also briefly review the theoretical proposals and arguments about the current-current cross-correlations in threeterminal systems. In Chapter 3, we describe the sample fabrication techniques which have been done in our laboratory such as e-beam lithography, metallization and etching. We present also the characterization of our particular system, niobium (Nb) / InAs-based 2DEG junction. Chapter 4 describes the reliable low-temperature measurement technique for detecting the noise. We characterize our measurement setup using a simple RC-circuit model. In Chapter 5, our main results about the shot noise of S-N junction are presented in detail