Abstract
The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin- hole systems compared to common spin- electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman interaction. We have investigated this anisotropy in quantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a nondiagonal tensor that manifests itself in unusual precessional motion, as well as distinct dependencies of hole-spin dynamics on the direction of the magnetic field . We quantify the individual components of the tensor for [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 fields . To this end, we develop a detailed multiband theory for the tensor . Using perturbation theory, we derive transparent analytical expressions for the components of the tensor that 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 tensor is neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude. The tensor encodes not only the Zeeman energy splitting but also the direction of the axis about which the spins precess in the external field . In general, this axis is not aligned with . Hence our study extends the general concept of optical orientation to the regime of nontrivial Zeeman coupling.
- Received 21 September 2017
- Revised 7 March 2018
DOI:https://doi.org/10.1103/PhysRevX.8.021068
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular 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 the tensor, which impacts various spin behaviors in the presence of an external magnetic field.
Specifically, the tensor 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 hole tensor, and we find good agreement between experiment and theory.
Our study paves the way for making use of the factor to employ hole spins in quantum information processing schemes.
