Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms
- Departamento de Física do polo universitário de Volta Redonda, Instituto de Ciências Exatas—Universidade Federal Fluminense, R. Des. Ellis Hermydio Figueira, 783, Volta Redonda, RJ CEP 27215-350 (Brazil)
We consider a particle with spin 1/2 with position-dependent mass moving in a plane. Considering separately Rashba and Dresselhaus spin-orbit interactions, we write down the Hamiltonian for this problem and solve it for Dirichlet boundary conditions. Our radial wavefunctions have two contributions: homogeneous ones which are written as Bessel functions of non-integer orders—that depend on angular momentum m—and particular solutions which are obtained after decoupling the non-homogeneous system. In this process, we find non-homogeneous Bessel equation, Laguerre, as well as biconfluent Heun equation. We also present the probability densities for m = 0, 1, 2 in an annular quantum well. Our results indicate that the background as well as the spin-orbit interaction naturally splits the spinor components.
- OSTI ID:
- 22403083
- Journal Information:
- Journal of Mathematical Physics, Vol. 56, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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