One-dimensional ring in the presence of Rashba spin-orbit interaction: Derivation of the correct Hamiltonian

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 3, 2002, Pages 1-3

  Meijer, F E ^a   Morpurgo, A F ^a   Klapwijk, T M ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

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EID: 84863980269     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.033107     Document Type: Article

References (13)

1. E. I. Rashba, Sov. Phys. Solid State 2, 1109 (1960).
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3. Y. S. Yi, T. Z. Qian, and Z. B. Su, Phys. Rev. B 55, 10 631 (1997).
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6. S. L. Zhu, Y. C. Zhou, and H. Z. Li, Phys. Rev. B 52, 7814 (1995).
7. T. Z. Qian, Y. S. Yi, and Z. B. Su, Phys. Rev. B 55, 4065 (1997).
8. We note that the Hamiltonian used by Aronov and Lyanda-Geller becomes Hermitean in the limit of large angular momentum (formula presented) In this limit, the eigenfunctions of the Hamiltonian calculated by these authors are correct.
9. Y. C. Zhou, H. Z. Li, and X. Xue, Phys. Rev. B 49, 14 010 (1994).
10. T. Choi, S. Y. Cho, C. M. Ryu, and C. K. Kim, Phys. Rev. B 56, 4825 (1997).
11. D. Loss, P. Goldbart, and A. V. Balatsky, Phys. Rev. Lett. 65, 1655 (1990);
12. Phys. Rev. Lett.A. Stern, 68, 1022 (1992).
13. Using the resulting approximate radial wave function, Eq. (9), we obtain (formula presented) This is a small quantity when the radius of the ring is much larger than the width of the arms that goes to zero for a truly 1D ring (formula presented) Therefore (formula presented) can be neglected in the 1D limit.