Asymmetric g Tensor in Low-Symmetry Two-Dimensional Hole Systems

Abstract

The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin-3/2hole systems compared to common spin-1/2electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman interaction. We have investigated this anisotropy inGaAs/AlAsquantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a nondiagonal tensorgthat manifests itself in unusual precessional motion, as well as distinct dependencies of hole-spin dynamics on the direction of the magnetic fieldB. We quantify the individual components of the tensorgfor [113]-, [111]-, and [110]-grown samples. We complement the experiments by a comprehensive theoretical study of Zeeman coupling in in-plane and out-of-plane fieldsB. To this end, we develop a detailed multiband theory for the tensorg. Using perturbation theory, we derive transparent analytical expressions for the components of the tensorgthat we complement with accurate numerical calculations based on our theoretical framework. We obtain very good agreement between experiment and theory. Our study demonstrates that the tensorgis neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude. The tensorgencodes not only the Zeeman energy splitting but also the direction of the axis about which the spins precess in the external fieldB. In general, this axis is not aligned withB. Hence our study extends the general concept of optical orientation to the regime of nontrivial Zeeman coupling.

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Plain Language Summary

Traditional computers and electronic devices work by moving electric charges from one place to another. Quantum spins could play a similar role in the growing field of spintronics. Research in this field has focused mainly on manipulating the spins of freely moving electrons (i.e., electrons in the conduction band) in semiconductors. However, holes in the valence band (vacancies in normally occupied electron energy states) offer much richer spin physics, making them attractive candidates for quantum information schemes. Researchers have not yet fully investigated many basic properties of valence band holes. Here, we are able to fully characterize, for the first time, a fundamental quantity of valence holes known as thegtensor, which impacts various spin behaviors in the presence of an external magnetic field.

Specifically, thegtensor determines Zeeman splitting (the separation of energy levels) and precession of hole spins in a magnetic field. Using optical spectroscopy, we measure spin precession of holes in a series of quantum wells exposed to strong magnetic fields at low temperature (1.2 K). Depending on the orientation of the applied field, we observe highly unusual hole-spin precession; for example, a magnetic field applied along a particular in-plane direction mostly acts like an out-of-plane field. We combine the experimental data with comprehensive theoretical calculations to determine the holegtensor, and we find good agreement between experiment and theory.

Our study paves the way for making use of thegfactor to employ hole spins in quantum information processing schemes.