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Heyder, Jan (2014): The 0.7 anomaly in quantum point contacts: a microscopic model for the first conductance step. Dissertation, LMU München: Faculty of Physics



This thesis aims at shedding light on the microscopic origin of a phenomenon in the field of semiconductor nanostructures, which occurs in transport through a short and narrow quasi one-dimensional constriction, the quantum point contact (QPC). Unlike the stepwise increase of linear conductance of a QPC as function of its width in units of the quantum GQ, which is well understood and was predicted already in the 1950s, an additional shoulder-like step at 0.7xG_Q raises questions since its discovery in 1996 : the 0.7 anomaly. Subsequent experimental investigations revealed a plethora of accompanying features of this fascinating structure. Most famously these include a strong reduction of conductance in the sub-open regime of a QPC as function of external parameters such as magnetic field, temperature or bias voltage. While it is agreed upon that the 0,7 anomaly arises from electron-electron interactions, the high number of theoretical attempts at an explanation indicates that the detailed microscopic origin of the peculiar shoulder is still subject to controversal discussions. In particular no theory seems to describe the whole variety of signatures of the 0.7 anomaly sufficiently. Here, we present a microscopic model that qualifies to meet this requirement. We model the effective barrier of the lowest transport mode of a QPC by a one-dimensional parabolic potential with short-ranged Coulomb interactions. By systematic analysis of experimental data we show that a parabolic barrier approximates the actual barrier shape of the QPC adequately well. In order to understand the physics of a QPC in detail, we put emphasis on the noninteracting properties of our model; we find a pronounced maximum in the local density of states in the vicinity of the barrier center at energies just above the potential. Importantly, this "van Hove ridge", which can be associated with slow electrons above the barrier coincides with the chemical potential if the QPC is tuned to be sub-open. Here, it causes an enhancement of backscattering at finite interactions and a subsequent anomalous reduction of conductance. In case of a magnetic field the underlying mechanism for this reduction is an interaction-enhanced local depopulation of the disfavoured spin species' subband; at finite excitation energies the reduction is a consequence of an interaction-enhanced inelastic backstattering probability. Hence, the interplay of van Hove ridge and electron-electron interactions provides a natural explanation for the appearance of the 0.7 anomaly and its various features. We calculate properties of our interacting one-dimensional QPC model using two methods: A specially developed approximation scheme within the functional renormalization group (fRG) provides reliable results for the magnetic field dependence of the 0.7 anomaly at zero temperature. At finite temperature and finite bias voltage we rely on second order perturbation theory in the interaction (SOPT). Since SOPT's validity is restricted to weaker interaction strength, where calculations clearly show the right trend but not yet the full manifestation of the 0.7 anomaly, we are currently setting up an extension of our fRG approach within the Keldysh formalism, which will allow us to also explore finite excitation energies.