Magnetotransport theory in quantum dots: 3D-0D and 2D-0D tunneling and angular momentum selection rules

A study of magnetotransport through quantum dots is presented. The model allows one to analyze tunneling both from bulk-like contacts and from 2D accumulation layers. The fine features in the $I-V$ characteristics due to the quantum dot states are known to be shifted to different voltages depending upon the value of the magnetic field. While this effect is also well reproduced by our calculations, in this work we concentrate on the amplitude of each current resonance as a function of the magnetic field. Such amplitudes show oscillations reflecting the variation of the density of states at the Fermi energy in the emitter. Furthermore the amplitude increases as a function of the magnetic field for certain features while it decreases for others. In particular, we demonstrate that the behavior of the amplitude of the current resonances is linked to the value of the angular momentum of each dot level through which tunneling occurs. We show that a selection rule on the angular momentum must be satisfied. As a consequence, tunneling through specific dot states is strongly suppressed and sometimes prohibited altogether by the presence of the magnetic field. This will allow to extract from the experimental curves detailed information on the nature of the quantum-dot wave functions involved in the electronic transport. Furthermore, when tunneling occurs from a two-dimensional accumulation layer to the quantum dot, the presence of a magnetic field hugely increases the strength of some resonant features. This effect is predicted by our model and, to the best of our knowledge, has never been observed.