Microscopic Origin of the 0.7-Anomaly in Quantum Point Contacts
A Quantum point contact (QPC) is a one dimensional constriction, separating two extended electron\nsystems allowing transport between them only though a short and narrow channel.\nThe linear conductance of QPCs is quantized in units of the conductance quantum\nG_Q=2e^2/h, where e is the electron charge and h is Planck's constant. Thus the \nconductance shows a staircase when plotted as a function of gate-voltage which\ndefines the width of the channel. In addition measured curves show a shoulder-like\nstep around 0.7G_Q. In this regime QPCs show anomalous behaviour in quantities\nlike electrical or thermal conductance, noise, and thermopower, as a function of\nexternal parameters such as temperature, magnetic field, or applied voltage. These\nphenomena, collectively known as the 0.7-anomaly in QPCs are subject of controversial\ndiscussion.\n\nThis thesis offers a detailed description of QPCs in the parameter regime of the \n0.7-anomaly. A model is presented which reproduces the phenomenology of the \n0.7-anomaly. We give an intuitive picture and a detailed description of the \nmicroscopic mechanism leading to the anomalous behavior. Further, we offer detailed\npredictions for the behavior of the 0.7-anomaly in the presence of spin-orbit\ninteractions. \n\nOur best theoretical results were achieved using an approximation scheme within the \nfunctional renormalization group (fRG) which we developed to treat inhomogeneous\ninteracting fermi systems. This scheme, called the coupled ladder approximation\n(CLA), allows the flow of the two-particle vertex to be incorporated even if the \nnumber of interacting sites N, is large, by reducing the number of independent\nvariables which represent the two-particle vertex from O(N^4) to\nO (N^2).