# Atomic Physics Workshop

Rashid Nazmitdinov, Universitat de les Illes Baleares

Interplay between Zeeman interaction and spin-orbit coupling in a two-dimensional semiconductor system

Manuel Valin-Rodriguez1 and Rashid G. Nazmitdinov1,2
1Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
2Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

The effects produced by different spin-dependent interactions in semiconductor structures under magnetic field are currently in the forefront of experimental and theoretical efforts in mesoscopic physics. The explosive activity is motivated by the desire for a deep understanding of quantum coherence phenomena. The other driving force is the hope that the spintronics research would provide novel, low-dissipative microelectronic devices.

In two-dimensional (2D) semiconductors, the bulk inversion asymmetry of the crystalline structure gives rise to the spin-orbit interaction between electrons, described by the Dresselhaus term, ${\cal H}_D={\beta}\left(p_x\sigma_x-p_y\sigma_y\right)/{\hbar}$. Here, the $\sigma$'s are the Pauli matrices, and $\beta$ is the intensity of this interaction. The other spin-orbit interaction is due to the inversion-asymmetry of the confining potential. It is called the Rashba interaction which has the form ${\cal H}_R={\alpha}\left(p_y\sigma_x-p_x\sigma_y\right)/{\hbar}$, where $\alpha$ is the corresponding strength. In numerous papers, only the interplay between the Zeeman and one of the spin-orbit terms (Rashba or Dresselhaus), or between the Rashba and the Dresselhaus term are considered.

In this contribution we analyse the interplay between Dresselhaus, Rashba, and Zeeman interactions in a 2D semiconductor under the action of a magnetic field. When a vertical magnetic field is considered, we predict that the interplay results in an effective cyclotron frequency that depends on a spin-dependent contribution. For in-plane magnetic fields, we found that the interplay induces an anisotropic effective gyromagnetic factor that depends on the orientation of the applied field as well as on the orientation of the electron momentum.