Kondo-model for quantum-dots with spin-orbit coupling – Niels Bohr Institute - University of Copenhagen

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Kondo-model for quantum-dots with spin-orbit coupling

 

Master Thesis Defense by Andreas Andersen

Experiments have demonstrated the presence of Kondo-effect in quantum dot devices based on materials with substantial spin-orbit coupling.
One might wonder why the Kondo-effect is observed in such materials where spin is no longer a good quantum number.

If an external magnetic field is applied, the Kondo peak is Zeeman split into two peaks. Experiments have showed an asymmetry in these peaks. This asymmetry can not be explained by the Kondo model for a quantum dot where SO interactions are not present.

Starting from the Anderson model for a quantum dot, with Rashba type spin-orbit interactions, coupled to two metallic electrodes, we derive an effective low-energy Hamiltonian describing the dynamical spin-fluctuations, i.e. the cotunneling processes, which remain in the Coulomb blockade regime. This projection to the low-energy states of the Hilbert space is performed by means of two consequtive unitary transformations. First we eliminate the spin-orbit coupling to second order in the SO-coupling, which results in an Anderson model with different spin-quantization axis on the dot and in the metallic electrodes. Subsequently, we eliminate all but second order charge-fluctuations, leaving the quantum dot with a single electron, i.e. a single spin-1/2, which can be flipped by the cotunneling conduction electrons traversing the dot. Due to the spin-dependent tunneling amplitude deriving from the SO-coupling, we end up with an effective Kondo-model having a very low spin rotational symmetry in a finite magnetic field. We show that this can give rise to a nonlinear conductance which is asymmetric under reversal of the applied bias-voltage.

Supervisor: Jens Paaske, NBI
Censor: Antti-Pekka Jauho, DTU