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.