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Bauer, Florian (2014): Microscopic Origin of the 0.7-Anomaly in Quantum Point Contacts. Dissertation, LMU München: Faculty of Physics



A Quantum point contact (QPC) is a one dimensional constriction, separating two extended electron systems allowing transport between them only though a short and narrow channel. The linear conductance of QPCs is quantized in units of the conductance quantum G_Q=2e^2/h, where e is the electron charge and h is Planck's constant. Thus the conductance shows a staircase when plotted as a function of gate-voltage which defines the width of the channel. In addition measured curves show a shoulder-like step around 0.7G_Q. In this regime QPCs show anomalous behaviour in quantities like electrical or thermal conductance, noise, and thermopower, as a function of external parameters such as temperature, magnetic field, or applied voltage. These phenomena, collectively known as the 0.7-anomaly in QPCs are subject of controversial discussion. This thesis offers a detailed description of QPCs in the parameter regime of the 0.7-anomaly. A model is presented which reproduces the phenomenology of the 0.7-anomaly. We give an intuitive picture and a detailed description of the microscopic mechanism leading to the anomalous behavior. Further, we offer detailed predictions for the behavior of the 0.7-anomaly in the presence of spin-orbit interactions. Our best theoretical results were achieved using an approximation scheme within the functional renormalization group (fRG) which we developed to treat inhomogeneous interacting fermi systems. This scheme, called the coupled ladder approximation (CLA), allows the flow of the two-particle vertex to be incorporated even if the number of interacting sites N, is large, by reducing the number of independent variables which represent the two-particle vertex from O(N^4) to O (N^2).