# Spin Interference Effects in a Ring with Rashba Spin-Orbit Interaction Subject to Strong Light–Matter Coupling in Magnetic Field

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## Abstract

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## 1. Introduction

## 2. Model

#### 2.1. The Hamiltonian

#### 2.2. The Eigenvalue Problem

## 3. Transport Properties

#### 3.1. Conductance

#### 3.2. Spin-Filtering Effect

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

## Appendix A. Transmission Probabilities

## References

- Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev.
**1955**, 100, 580. [Google Scholar] [CrossRef] - Bychkov, Y.A.; Rashba, E.I. Properties of a 2D electron gas with lifted spectral degeneracy. JETP Lett.
**1984**, 39, 78. [Google Scholar] - Bercioux, D.; Lucignano, P. Quantum transport in Rashba spin-orbit materials: A review. Rep. Prog. Phys.
**2015**, 78, 106001. [Google Scholar] [CrossRef] [PubMed] - Pichugin, K.; Puente, A.; Nazmitdinov, R. Kramers degeneracy and spin inversion in a lateral quantum dot. Symmetry
**2020**, 12, 2043. [Google Scholar] [CrossRef] - Sheremet, A.S.; Kibis, O.V.; Kavokin, A.V.; Shelykh, I.A. Datta-and-Das spin transistor controlled by a high-frequency electromagnetic field. Phys. Rev. B
**2016**, 93, 165307. [Google Scholar] [CrossRef] [Green Version] - Goldman, N.; Dalibard, J. Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields. Phys. Rev. X
**2014**, 4, 031027. [Google Scholar] [CrossRef] [Green Version] - Holthaus, M. Floquet engineering with quasienergy bands of periodically driven optical lattices. J. Phys. B
**2016**, 49, 013001. [Google Scholar] [CrossRef] - Meinert, F.; Mark, M.J.; Lauber, K.; Daley, A.J.; Nägerl, H.-C. Floquet Engineering of Correlated Tunneling in the Bose-Hubbard Model with Ultracold Atoms. Phys. Rev. Lett.
**2016**, 116, 205301. [Google Scholar] [CrossRef] - Cohen-Tannoudji, C.; Dupont-Roc, J.; Grynberg, G. Atom-Photon Interactions: Basic Processes and Applications; Wiley–VCH: Hoboken, NJ, USA, 2004. [Google Scholar]
- Teich, M.; Wagner, M.; Schneider, H.; Helm, M. Semiconductor quantum well excitons in strong, narrowband terahertz fields. New J. Phys.
**2013**, 15, 065007. [Google Scholar] [CrossRef] - Joibari, F.K.; Blanter, Y.M.; Bauer, G.E.W. Light-induced spin polarizations in quantum rings. Phys. Rev. B
**2014**, 90, 155301. [Google Scholar] [CrossRef] [Green Version] - Koshelev, K.L.; Kachorovskii, V.Y.; Titov, M. Resonant inverse Faraday effect in nanorings. Phys. Rev. B
**2015**, 92, 235426. [Google Scholar] [CrossRef] [Green Version] - Foa Torres, L.E.F.; Perez-Piskunow, P.M.; Balseiro, C.A.; Usaj, G. Multiterminal Conductance of a Floquet Topological Insulator. Phys. Rev. Lett.
**2014**, 113, 266801. [Google Scholar] [CrossRef] [PubMed] - Mikami, T.; Kitamura, S.; Yasuda, K.; Tsuji, N.; Oka, T.; Aoki, H. Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators. Phys. Rev. B
**2016**, 93, 144307. [Google Scholar] [CrossRef] [Green Version] - Nagasawa, F.; Frustaglia, D.; Saarikoski, H.; Richter, K.; Nitta, J. Control of the spin geometric phase in semiconductor quantum rings. Nat. Commun.
**2013**, 4, 2526. [Google Scholar] [CrossRef] - Molnár, B.; Peeters, F.M.; Vasilopoulos, P. Spin-dependent magnetotransport through a ring due to spin-orbit interaction. Phys. Rev. B
**2004**, 69, 155335. [Google Scholar] [CrossRef] [Green Version] - Frustaglia, D.; Richter, K. Spin interference effects in ring conductors subject to Rashba coupling. Phys. Rev. B
**2004**, 69, 235310. [Google Scholar] [CrossRef] [Green Version] - Citro, R.; Romeo, F.; Marinaro, M. Zero-conductance resonances and spin filtering effects in ring conductors subject to Rashba coupling. Phys. Rev. B
**2006**, 74, 115329. [Google Scholar] [CrossRef] [Green Version] - Kozin, V.K.; Iorsh, I.V.; Kibis, O.V.; Shelykh, I.A. Quantum ring with the Rashba spin-orbit interaction in the regime of strong light-matter coupling. Phys. Rev. B
**2018**, 97, 155434. [Google Scholar] [CrossRef] [Green Version] - Frustaglia, D.; Nitta, J. Geometric spin phases in Aharonov-Casher interference. Sol. State Comm.
**2020**, 311, 113864. [Google Scholar] [CrossRef] - Meijer, F.E.; Morpurgo, A.F.; Klapwijk, T.M. One-dimensional ring in the presence of Rashba spin-orbit interaction: Derivation of the correct Hamiltonian. Phys. Rev. B
**2002**, 66, 033107. [Google Scholar] [CrossRef] [Green Version] - Eckardt, A.; Anisimovas, E. High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective. New J. Phys.
**2015**, 17, 093039. [Google Scholar] [CrossRef] - Heiss, W.D.; Nazmitdinov, R.G. Orbital magnetism in small quantum dots with closed shells. JETP Lett.
**1998**, 68, 915. [Google Scholar] [CrossRef] [Green Version] - Ihn, T. Semiconductor Nanostructures; Oxford University Press: New York, NY, USA, 2010. [Google Scholar]

**Figure 1.**Conductance versus irradiation intensity I. Electron effective mass $m=0.045{m}_{e}$, the Rashba coupling constant $\alpha =5\times {10}^{4}$ ms

^{−1}, and the ring radius is $R=200$ nm. The dressing field has the frequency $\omega =1.6\times {10}^{12}$ s

^{−1}, the magnetic flux $\mathsf{\Phi}=0$.

**Figure 2.**Conductance versus irradiation intensity I for different Rashba coupling constant $\alpha $. Electron effective mass $m=0.045{m}_{e}$ and the ring radius is $R=200$ nm. The dressing field has the frequency $\omega =1.6\times {10}^{12}$ s${}^{-1}$, the magnetic flux $\mathsf{\Phi}=0.5{\mathsf{\Phi}}_{0}$.

**Figure 3.**Spin polarization P versus the irradiation intensity I. The calculations are performed at the magnetic flux $\mathsf{\Phi}=0.25{\mathsf{\Phi}}_{0}$; the dressing field frequency is $\omega =0.8\times {10}^{12}$ s${}^{-1}$. The solid (blue) line corresponds to the strength $\alpha =2\times {10}^{4}$ m/s, while the dashed (red) line corresponds to $\alpha ={10}^{4}$ m/s.

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**MDPI and ACS Style**

Pudlak, M.; Nazmitdinov, R.
Spin Interference Effects in a Ring with Rashba Spin-Orbit Interaction Subject to Strong Light–Matter Coupling in Magnetic Field. *Symmetry* **2022**, *14*, 1194.
https://doi.org/10.3390/sym14061194

**AMA Style**

Pudlak M, Nazmitdinov R.
Spin Interference Effects in a Ring with Rashba Spin-Orbit Interaction Subject to Strong Light–Matter Coupling in Magnetic Field. *Symmetry*. 2022; 14(6):1194.
https://doi.org/10.3390/sym14061194

**Chicago/Turabian Style**

Pudlak, Michal, and R. Nazmitdinov.
2022. "Spin Interference Effects in a Ring with Rashba Spin-Orbit Interaction Subject to Strong Light–Matter Coupling in Magnetic Field" *Symmetry* 14, no. 6: 1194.
https://doi.org/10.3390/sym14061194