Author details

5. Conclusion

Functional Materials

In this chapter, firstly, we consider two distinct regimes of the control of the SO interaction in conventional semiconductor quantum wells. Specifically, we have performed a detailed self-consistent calculation on realistic GaAs wells with gatealtered electron occupations from two subbands to one subband, thus determining how the SO coupling (both the magnitude and sign) changes as a function of the gate voltage Vg. We have considered a set of wells of the width w in a wide range and found two distinct regimes. In the first regime, the behavior of the SO interaction is usual, e.g., a linear gate control of the Rashba terms. In contrast, in the second regime, there are emerging new features that one has to pay attention to when controlling SO couplings, e.g., the relative signs (same or opposite) of α<sup>1</sup> and α<sup>2</sup> can be controlled by the gate, α<sup>2</sup> can attain zero in certain asymmetric configurations, and α<sup>2</sup> remains essentially constant within a particular gate voltage range. In addition, we have determined the persistent-spin-helix symmetry points of the two subbands and found that the condition α<sup>2</sup> ¼ �β2, <sup>e</sup>ff always holds over a broad range of Vgs, thus possibly facilitating the locking of the symmetry point for the second subband in practice. Some of these features in the second regime can in principle be observed in proper double-well structures [24], as wide wells behave like "effective" double wells owing to the electron Hartree potential-induced central barrier. Moreover, the "symmetric configuration" mentioned throughout this work only refers to regions near the well (i.e., not far into the barriers). We cannot make our wells universally/fully symmetric by only tuning the gate voltage, due to the one-side doping in our system. This partial symmetric configuration is enough to render the intrasubband Rashba couplings to zero, since the envelope wave functions decay very quickly into the barriers. Our results should be timely and important for experiments controlling/tailoring the SO coupling universally, particularly

for the unusual electrical control of the SO coupling in the second regime.

interaction in semiconductor nanostructures.

(Grant No. 11874236), FAPESP, and Capes.

Acknowledgements

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Secondly, we have investigated the full scenario of the electrical control of the SO interaction in a realistic GaAs/Al0:3Ga0:7As well with one or two additional AlxGa1�<sup>x</sup>As barriers embedded, in the course of the transition of our system from single to double and triple wells. We constantly consider the two-subband electron occupancy for all values of gate voltage Vg studied here. As the Al content of the embedded barrier(s) x varies, we find distinct scenarios of the electrical control of SO terms, e.g., linear or nonmonotonic dependence of α<sup>2</sup> on Vg, same or opposite signs between α<sup>1</sup> and α2, and inert or abrupt change of η with Vg near the symmetric configuration. In addition, we find that the gate dependence of SO terms is more smooth and βν is more stronger in our triple well, compared to the double well case. Moreover, we observe that the basic scenario of the electrical control of the SO interaction in our triple and double wells is similar, in the parameter range studied here. These results are expected to be important for a broad control of the SO

As a final remark, in the case of three-subband electron occupancy which is not considered here, the electrical control of SO couplings is possibly distinct between double and triple wells because of a higher third subband occupation. More work is

This work was supported by the National Natural Science Foundation of China

needed to investigate this interesting possibility (higher electron density).

Jiyong Fu<sup>1</sup> \*, Wei Wang<sup>2</sup> and Minghua Zhang<sup>2</sup>

1 Department of Physics, Qufu Normal University, Qufu, Shandong, China

2 Department of Physics, Jining University, Qufu, Shandong, China

\*Address all correspondence to: jiyongfu78@gmail.com

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
