Conductance in quantum point contacts

During the last decades, technology has made it possible to produce devices at smaller and smaller length scales. Central in these devices are their conducting properties, as they can be made very clean, making it easy for electrons to flow through them. One particular device, known as a quantum point contact, exhibits such good conducting properties that the electrons can pass form one side to the other without colliding with impurities or defects. Due to quantum confinement in the direction perpendicular to the flow of electrons, the conductance shows quantized steps at integer values of 2e^2/h. This reflects the wave nature of the electrons and is thus a remarkable demonstration of quantum mechanics. Although the quantum point contact has been studied for more than two decades it exhibits a feature which is not yet fully understood, the 0.7 anomaly. It appears as a 'shoulder', or extra step, below the lowest conductance plateau, and is a deviation from the non-interacting picture leading to the conductance steps. In this thesis, conductance in quantum point contacts will be treated in the non-interacting case, but we keep in mind the rich nature of phenomena that are present in QPCs