The Analytical Approximate Solution And Spin Hall Effect Of The Spin-orbit Coupled System In A Magnetic Field

From theoretical predictions to experimental discoveries,the spin Hall effect has proved that the Hall effect can be achieved in non-magnetic materials even without an external magnetic field.The use of the spin Hall effect can generate spin current in the lateral response to an external electric field,which is used as a standard spin generator and detector in semiconductor devices,and plays a great role in spintronics.The successive proposals of Rashba and Dresselhaus spin-orbit coupling have made the spin Hall effect in two-dimensional electron gas a research hotspot,while the external magnetic field of the system exhibits an interesting resonant spin Hall effect.Considering that the spin Hall effect is realized in one of the Rashba and Dresselhaus coupling systems,it can be rigorously solved in both the zero magnetic field and the magnetic field,and the research results under the zero magnetic field are abundant,and the spin Hall conductance is a universal Constant,and spin Hall conductance resonance with an external magnetic field.At the same time,there are not many research results considering the analytical solution of the Rashba and Dresselhaus coupling system.The biggest difficulty is that the exact solution cannot be found in a closed space.Only when the Rashba coupling and the Dresselhaus coupling strength are equal,the specific situation of zero magnetic field can be solved by transformation.Analytical approximate solution,but when the Zeeman splitting cannot be ignored in the system,there are few research results on effective methods to solve the analytical eigenproblems under the external electric field.In this article,when the Rashba and Dresselhaus spin-orbit coupling are considered in the system,it is found that the single-electron Hamiltonian with a magnetic field perpendicular to the two-dimensional plane is equivalent to the anisotropic Rabi model in quantum optics.Rashba spin-orbit coupling approximation(Generalized Rashba Coupling Approximation(GRCA))is performed through translational unitary transformation to reform the effective Hamiltonian of the system to obtain a solvable Hamiltonian.By retaining the Rashba coupling term and gradually increasing the Dresselhaus coupling term,the Landau energy levels cross each other,and each Landau state becomes a new displacement-Fock state with displacement,instead of the original harmonic oscillation Fock state,resulting in a closed state.The analytical eigenstates of,even in the strong Zeeman splitting,the comparative analytical energy and value are consistent within the effective coupling strength of 0?0.4?.Using the analytical eigenstate under the action of an external electric field,the spin current and the firstorder modified spin Hall conductance are obtained.The results show that the spin current shows a jumping behavior under the 1/B change and the modified spin Hall The electrical conductance diverges at the intersection of the energy levels,and a series of stable states of the quantified charge conductance are observed.The comparative analysis and the numerical results are very consistent.As the proportion of Dresselhaus coupling in the system increases,it is found that Rashba coupling and Zeeman splitting compete with each other,while Dresselhaus coupling enhances the effect of Zeeman splitting.At the same time,the spin Hall conductance resonance divergence point will also appear at 1/B larger.local.In short,in a system that simultaneously considers the three mechanisms(Rashba,Dresselhaus,and Zeeman split)that lead to energy level splitting,this article provides an easy-to-implement analytical approximation method for studying the spin Hall effect in 2DEG,which will help It is helpful to study the intrinsic spin Hall effect,and at the same time provide another possibility for the quantum spin Hall effect and the fractional quantum Hall effect in future research.