The quantum mechanical nature of electrons at very low temperatures has posed interesting results in the resistivity of metals over the last century. When the temperature nears absolute zero, the resistivity due to electron-electron interactions and electron-phonon interactions become very small and the dominant source of resistance is the scattering of electrons due to small concentrations of impurity atoms in bulk metal. When the impurity atoms are not magnetic, such that there is no net electron spin, the zero temperature resistivity due to impurity scattering is proportional to the impurity concentration. When the impurity is magnetic, typically spin-1/2, the resistivity rises logarithmically as the temperature is lowered below a characteristic temperature. This is known as the Kondo effect and the characteristic temperature is called the Kondo temperature. This temperature is expected to be the only energy scale that is involved in a Kondo system. This report investigates the universality of the Kondo energy scale. Interactions between impurity atoms and itinerant electrons can be reproduced in a single-electron transistor (SET). By isolating a small region of bound electrons, called a quantum dot, and coupling these to reservoirs of electrons, the biased tunneling current is a direct measurement of the interactions between the bound electrons and the reservoir electrons. SETs provide a unique measurement system with great variability to measure the nature of the Kondo effect.
Five experiments have been performed in this report. The first two experiments, performed in a regime where the quantum dot is weakly coupled to the reservoirs, demonstrate measurements of the properties of a quantum dot, such as the tunneling rate and coupling symmetry. The co-tunneling regime introduces spin dependent transport through a quantum dot without strong spin correlations related to the Kondo effect. As the tunneling rate is increased, spin correlations form and the Kondo effect emerges as a peak in the conductance at zero bias. These delicate correlations are broken when external energies are added to the system and a characteristic energy scale arises, known as the Kondo temperature. Measurements of this energy scale are made by increasing the electron temperature and applying a magnetic field. Universality of both temperature and the magnetic field are demonstrated with respect to the Kondo temperature.
The main focus of this work is the relationship between the Kondo temperature and the time spin correlations take to form. I show a distinct regime transition when the Kondo temperature is held constant and the frequency of bias oscillations are increased past a characteristic frequency related to the Kondo energy. The transition also is seen when the Kondo temperature is increased. Lastly, a unique conductance signature is observed when an "fast" oscillation is applied and the magnetic field is increased. At small magnetic fields, well below the Kondo temperature, the Kondo conductance peak is enhanced. I find that the magnetic field value at which the peak occurs is linearly proportional to the frequency applied and only occurs at frequencies above the Kondo temperature.