Chin. Phys. Lett.  2021, Vol. 38 Issue (7): 077304    DOI: 10.1088/0256-307X/38/7/077304
Generalized Rashba Coupling Approximation to a Resonant Spin Hall Effect of the Spin–Orbit Coupling System in a Magnetic Field
Rui Zhang1, Yuan-Chuan Biao1, Wen-Long You2, Xiao-Guang Wang3, Yu-Yu Zhang1*, and Zi-Xiang Hu1
1Department of Physics, Chongqing University, Chongqing 400044, China
2College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
3Department of Physics, Zhejiang University, Hangzhou 310027, China
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Rui Zhang, Yuan-Chuan Biao, Wen-Long You et al  2021 Chin. Phys. Lett. 38 077304
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Abstract We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field. A solvable Hamiltonian is obtained by performing a simple change of basis, which has the same form as that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state. Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting, exhibiting the validity of the analytical approximation. By using the eigenstates, spin polarization correctly displays a jump at the energy-level crossing point, where the corresponding spin conductance exhibits a pronounced resonant peak. As the component of the Dresselhaus coupling increases, the resonant point shifts to a smaller value of the magnetic field. In contrast to pure Rashba couplings, we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.
Received: 19 April 2021      Published: 18 June 2021
PACS:  72.20.My (Galvanomagnetic and other magnetotransport effects)  
  71.10.Ca (Electron gas, Fermi gas)  
  75.47.-m (Magnetotransport phenomena; materials for magnetotransport)  
  42.50.-p (Quantum optics)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 12075040, 11875231, 11974064, and 12047564), and the Chongqing Research Program of Basic Research and Frontier Technology (Grant No. cstc2020jcyj-msxmX0890).
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Rui Zhang
Yuan-Chuan Biao
Wen-Long You
Xiao-Guang Wang
Yu-Yu Zhang
and Zi-Xiang Hu
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