<p>Experiments shows that the conductance of a quantum point contact is quantized in steps of  2e²/h, where e is the charge of the electron and h is Planck’s constant, and thereby Ohm’s law is not valid for nanostructures. By using the approximation method finite difference, the transmission for one-dimensional contacts and one- and two-dimensional potentials are investigated. In the case of two-dimensional contacts and a two-dimensional potential the Green’s function method is used. It turns out that if electrons are treated as waves, the transmission and the conductance just differ by the constant 2e²/h, which in this thesis is interpreted numerically in Matlab by using the Green’s function method.</p>

Experiments shows that the conductance of a quantum point contact is quantized in steps of  2e²/h, where e is the charge of the electron and h is Planck’s constant, and thereby Ohm’s law is not valid for nanostructures. By using the approximation method finite difference, the transmission for one-dimensional contacts and one- and two-dimensional potentials are investigated. In the case of two-dimensional contacts and a two-dimensional potential the Green’s function method is used. It turns out that if electrons are treated as waves, the transmission and the conductance just differ by the constant 2e²/h, which in this thesis is interpreted numerically in Matlab by using the Green’s function method.

<p>In this thesis we report on calculations for open quantum mechanical and certain microwave systems. The models refer to a quantum point contact and an electron cavity. We model this open system with an imaginary potential as source and drain, and use the finite difference method to make our calculations. We report on general features of the model we have found, and compare our calculations with measurements made on microwave cavities.</p>

In this thesis we report on calculations for open quantum mechanical and certain microwave systems. The models refer to a quantum point contact and an electron cavity. We model this open system with an imaginary potential as source and drain, and use the finite difference method to make our calculations. We report on general features of the model we have found, and compare our calculations with measurements made on microwave cavities.

<p>The 1D Wigner crystal is a long sought after strongly correlated quantum state. Here we present electronic transport data of asymmetric quantum point contacts (QPC) tuned to the spin-incoherent regime, which provides evidence for achieving the 1D Wigner state. Our result can be distinguished in several particularly noticeable ways. First, we utilize an asymmetric point contact geometry that is simple to fabricate and has not been studied previously. We are able to tune to the conductance anomalies simply by asymmetrically applying voltages to the gates. Second, we observe clear suppression of the first plateau and direct jumps to the second in these asymmetric QPCs at liquid helium temperatures (4.2 K). Such conductance behavior is indicative of Wigner crystal row formation.</p> <p>This thesis suggests that the novel geometry and gating scheme allows for a novel way to search for strongly correlated electronic behavior in quasi-1D quantum wires. A key finding is the importance of asymmetric QPCs for observation of anomalous transport characteristics. We have observed a strongly developed e<super>2</super>/h feature under asymmetric voltage gating and zero applied magnetic field. Such a feature is attributed to enhanced spin energies in the system. We believe the asymmetric design allows for a relaxing of the 1D confinement so that a quasi-1D electron conformation develops, which in turn allows for various possible magnetic states. In addition, by optimally tuning the confinement potential, we observe an unexpected suppression of the 2e<super>2</super>/h plateau. This provides further evidence for unusual electron arrangements in the asymmetric quantum point contact.</p> <p>I also discuss transport studies on the new FeSe superconductor. Our collaboration discovered the superconducting &beta;-FeSe compound with a Tc approximately 8 K. The crystal lattice structure of &beta;-FeSe is by far the simplest of the Fe superconductors. One of the most interesting observations regarding FeSe is that the crystal structure undergoes a structural transition at approximately 105 K from tetragonal to orthorhombic (or triclinic) symmetry. We believe this structural transition to be closely related to the origin of superconductivity in this class of materials.</p> <p>Transport studies also seem to support this claim. From Hall effect measurements of bulk FeSe, we find that FeSe is likely a two band (electron and hole) superconductor, which suggests it is quite different from the cuprates, and that very unconventional superconducting mechanisms are at play. The temperature dependence of the Hall coefficient is measured, and found to rapidly increase below 105 K. This suggests the scattering time related to hole bands dominate the transport at low temperature. As there is no magnetic ordering observed at low temperature, we do not expect the scattering from random Fe magnetic impurities to play a significant role in the enhanced hole scattering times. Thus, we speculate that this change is related to the structural transition observed.</p> / Dissertation

Thin-film niobium mechanically controlled break junctions and resistively shunted niobium mechanically-controlled break junctions were developed and successfully microfabricated. Using these devices, high-stability atomic size contacts were routinely produced and investigated both in the normal and superconducting states. Investigations of the two-level conductance fluctuations in the smallest contacts allowed the calculation of their specific atomic structure. Embedding resistive shunts close to the superconducting atomic-sized junctions affected the coherence of the electronic transport. Finally, point contact spectroscopy measurements provide evidence of the interaction of conduction electrons with the mechanical degrees of freedom of the atomic-size niobium contacts.

The integer and fractional quantum Hall effects arise in two-dimensional electron systems subject to low temperature and high perpendicular magnetic field. The phenomenology of these two effects is rich and provides interesting insight into quantum physics. We present two experimental studies of phenomena in the fractional quantum Hall regime. The first examines the tunneling conductance of quasiparticles at filling factor 5/2. This state is of significant interest because it lies outside the traditional Jain hierarchy of fractional quantum Hall states and because it may be the first physical system found to exhibit non-abelian particle statistics. A quantum point contact is used to bring edge states on opposite sides of the system in proximity to each other, allowing quasiparticles to tunnel between the edge states. By annealing the gates forming the quantum point contact at different voltages we control the tunneling strength for fixed temperature and bias. We demonstrate a transition from strong to weak tunneling controlled in this manner. In the weak tunneling regime, the DC bias and temperature dependence of the tunneling conductance is fit to a theoretical form, resulting in values for the quasiparticle charge \(e*\) and the interaction parameter \(g\). The values of these parameters are used to help distinguish between proposed candidate states for the 5/2 wave function. Quantitative and qualitative results are most consistent with the abelian 331 state. Our second main focus is the breakdown of the fractional quantum Hall states at filling factors 4/3 and 5/3. Breakdown of integer and fractional quantum Hall states is known to occur when the Hall and longitudinal resistances deviate from their ideal values at nonzero critical currents. Although multiple studies of breakdown in the integer quantum Hall regime have been reported, corresponding results for the fractional regime are scarce. We observe breakdown over a range of integer states that is consistent with previous results. However, breakdown in the fractional regime is found to exhibit markedly different behavior. In particular, the magnitude of the critical current decreases with increased sample width. This behavior is opposite that observed for integer filling factors and does not seem to be explicable based on current theories of breakdown. / Physics

<p>A quantum point contact (QPC) is a quasi-one dimensional electron system, for which the conductance is quantized in unit of $2e^2/h$. This conductance quantization can be explained in a simple single particle picture, where the electron density of states cancels the electron velocity to a constant. However, two significant features in QPCs were discovered in the past two decades, which have drawn much attention: the 0.7 effect in the linear conductance and zero-bias-anomaly (ZBA) in the differential conductance. Neither of them can be explained by single particle pictures.</p><p>In this thesis, I will present several electron correlation effects discovered in asymmetric QPCs, as shown below:</p><p>The linear conductance of our asymmetric QPCs shows conductance resonances. The number of these resonances increases as the QPC channel length increases. The quantized conductance plateau is also modulated by tuning the gate voltage of the QPCs. These two features, observed in the linear conductance, are ascribed to the formation of quasi-bound states in the QPCs, which is further ascribed to the electron-correlation-induced barriers. </p><p>The differential conductance for long channel QPCs shows the zero-bias-anomaly for every other linear conductance resonance valley, suggesting a near even-odd behavior. This even-odd law can be interpreted within the electron-correlation-induced barrier picture, where the quasi-localized non-zero spin in the quasi-bound state (Kondo-like) couples to the Fermi sea in the lead. For a specific case, triple-peak structure is observed in the differential conductance curves, while the electron filling number is still even, suggesting a spin triplet formation at zero magnetic field.</p><p>Small differential conductance oscillations as a function of bias voltage were discovered and systematically studied in an asymmetric QPC sample. These oscillations are significantly suppressed in a low in-plane magnetic field, which is completely unexpected. The oscillations are washed out when the temperature is increased to 0.8K. Numerical simulation, based on the thermal smearing of the Fermi distribution, was performed to simulate the oscillation behavior at high temperatures, using the low temperature data as an input. This simulation agrees with the oscillations off zero-bias region, but does not agree with the temperature evolution of the structure near zero-bias. Based on the above oscillation characteristics, all simple single particle pictures were carefully considered, and then ruled out. After exhausting all these pictures, we think these small oscillations are related to novel electronic and spin correlations.</p> / Dissertation

The quantum point contact (QPC) is a one-dimensional constriction with the differential conductance quantised in units of $G_Q=2e^2/h$. However, the transport behaviour below the first plateau is still not fully understood, including the 0.7 anomaly and the 0.25 anomaly in the linear and non-linear transport regimes respectively. In this work, we utilise a multiplexing technique and statistically investigate the 0.7 anomaly observed on the first three plateaus respectively in 571 QPCs, fitting well the van-Hove model. The 0.7 anomaly shows the transconductance suppression due to the effective electron interactions which are modified by the local density of states (LDOS). At the maximum of LDOS, the interaction strength becomes strongest, resulting in the strongest transconductance suppression. The strongest interaction strength is determined by the ratio of transverse confinement curvature and longitudinal barrier curvature. Moreover, we realise measurements of the effective g factor ($g^*$) and high-field offset ($\Delta E^{hfo}$) in numerous devices in a single cooldown at T=40 mK. The statistical results show both the $g^*$ and $\Delta E^{hfo}$ increase with the potential confinement, which supports the predictions about the role of interaction strength on $g^*$ and $\Delta E^{hfo}$ in a 1D tight-binding model. We explore the origin of $\Delta E^{hfo}$ and find that it is only considerable for the first plateau. Using a short and narrow QPC could result in a stronger potential confinement and thus a higher $g^*$, which could be beneficial for its use in spintronic applications. Last, we investigate the formation and development of the DC-bias-induced 0.75 and 0.25 anomalies for 402 QPCs. We find the anomalies evolve similarly in a magnetic field. To explain the anomaly behaviours, we propose a phenomenological DC-bias-induced spin-splitting model. In the model, with the increasing DC bias (V_DC), the 0.75 anomaly occurs first at a differential conductance of 0.75 $G_Q$, while the 0.25 anomaly is formed at a differential conductance of 0.5 $G_Q$ and moves to 0.375 $G_Q$. The spin gap of the first subband opens to be e|V_DC|, which enables an all-electric manipulation of spin polarisation simply by applying a DC bias.

L'effet Kondo observé dans des objets individuels constitue un système modèle pour l’étude de corrélations électroniques. Ces dernières jouent un rôle moteur dans le domaine émergent de l'électronique de spin (ou spintronique) où l’utilisation d’atomes issus des terres rares et des métaux de transition est incontournable. Dans ce contexte, l’étude de l'interaction d’une impureté Kondo avec des électrodes ferromagnétiques ou avec d’autres impuretés magnétiques peut donc s’avérer fondamental pour la spintronique. L’effet Kondo est sensible à son environnement magnétique car en présence d’interactions magnétiques la résonance ASK se dédouble. Dans une certaine mesure, la résonance ASK agit comme un niveau atomique discret doublement dégénérée qui subit un dédoublement Zeeman en présence d'un champ magnétique ou plus généralement d’un champ magnétique effectif. Inversement, la détection d'un dédoublement Zeeman indique l'existence d'un champ magnétique. Dans une boîte quantique, le couplage de la boîte avec les deux électrodes est faible en général et la largeur de la résonance ASK est donc de l'ordre de quelques meV. Beaucoup d’études de l’effet Kondo en présence d’interactions magnétiques ont été menées sur les boîtes quantiques, grâce notamment au contrôle qui peut être exercé sur la résonance ASK, mais aussi grâce au faible élargissement de la résonance qui peut alors être dédoublée avec un champ magnétique de l’ordre de 10 Tesla ou moins. A ces études, s’ajoutent de nombreux travaux similaires menés avec des dispositifs tels des jonctions cassées comprenant une molécule individuelle jouant le rôle de l’impureté magnétique. En revanche, peu d’études de ce type ont été consacrées aux atomes individuels. Cela est dû à l’hybridation plus marquée entre l'impureté atomique et la surface comparée aux boîtes quantiques, qui entraine une largeur typique de 10 meV ou plus pour la résonance ASK. Un champ magnétique d'environ 100 T ou plus est alors nécessaire afin de dédoubler la résonance et donc en pratique difficile à mettre en oeuvre. Cette thèse est consacrée précisément à l’étude de l'interaction entre une impureté Kondo individuel et son environnement magnétique à l’aide d’un STM. Une nouvelle stratégie est adoptée ici par rapport aux études antérieures de ce genre. Tout d'abord, nous éliminons la barrière tunnel en établissons un contact pointe-atome. Nous formons ainsi un point de contact quantique comprenant une seule impureté Kondo. Deuxièmement, nous utilisons des pointes ferromagnétiques. Le contact pointe-atome permet de sonder l'influence du ferromagnétisme sur l'impureté Kondo vial’observation de la résonance ASK. La géométrie de contact permet tout particulièrement de produire une densité de courant polarisé en spin suffisamment élevée pour qu’elle entraîne un dédoublement de la résonance ASK. Ce dédoublement constitue la première observation à l’échelle atomique d’un phénomène connu sous le nom d’accumulation de spin, laquelle se trouve être une propriété fondamentale de la spintronique. / The Kondo effect of these single objects represents a model system to study electron correlations, which are nowadays of importance in relation to the emerging field of spin electronics, also known as spintronics, where chemical elements with partially filled d or f shells play a central role. Also of particular interest to spintronics is the interaction of single Kondo impurities with ferromagnetic leads or with other magnetic impurities. A Kondo impurity is in fact sensitive to its magnetic environment as the ASK resonance is usually split into two resonances in the presence of magnetic interactions. To some extent, the ASK resonance acts as a two-fold degenerate energy level of an atom which undergoes a Zeeman splitting in the presence of an effective magnetic field. Conversely, the detection of a Zeeman splitting indicates the existence of a magnetic field. In a QD, the coupling of the QD to the two leads is very weak in general, and the Kondo resonance is in the range of a few meV. Many studies focusing on magnetic interaction have been carried out on QDs, due to the high control that can be extended to the ASK resonance and its low energy range, allowing to split the resonance with a magnetic field of 10 T. Similar work has also been carried out in single-molecule or lithographically-defined devices. Although STM is an ideal tool to study the Kondo effect of single atoms, there is still a strong lack of experimental studies concerning atoms in the presence of magnetic interactions. This is partly due to the stronger impurity-metal hybridization compared to QDs, which places the ASK width in the range of 10 meV. An effective magnetic field of 100 T would be needed to split the resonance. The present Thesis is devoted precisely at studying the interaction between a single Kondo impurity with its magnetic environment through STM. A new strategy is adopted herecompared to former studies of this kind. Firstly, we contact a single-magnetic atom on a surface with a STM tip thereby eliminating the vacuum barrier. Secondly, we use ferromagnetic tips. The contact with a single atom allows probing the influence of ferromagnetism on the Kondo impurity i. e. its ASK resonance. But most importantly, the contact geometry produces sufficiently high current densities compared to the tunneling regime, so that the ASK resonance becomes sensitive to the presence of a spin-polarized current. This constitutes the first atomic scale detection of a spin-polarized current with a single Kondo impurity.