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2
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0003917411
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edited by T. Ando, Y. Arakawa, K. Furuya, S. Komiyama, and H. Nakashima (Springer, Berlin)
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Mesoscopic Physics and Electronics, edited by T. Ando, Y. Arakawa, K. Furuya, S. Komiyama, and H. Nakashima (Springer, Berlin, 1998).
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Mesoscopic Physics and Electronics
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3
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0032573499
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G. A. Prinz, Science 282, 1660 (1998).
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Prinz, G.A.1
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4
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0035900398
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S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
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Science
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Wolf, S.A.1
Awschalom, D.D.2
Buhrman, R.A.3
Daughton, J.M.4
Von Molnár, S.5
Roukes, M.L.6
Chtchelkanova, A.Y.7
Treger, D.M.8
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8
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0000696553
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E. I. Rashba, Fiz. Tverd. Tela (Lertingrad) 2, 1224 (1960) [Sov. Phys. Solid State 2, 1109 (1960)].
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Sov. Phys. Solid State
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10
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J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, Phys. Rev. Lett. 78, 1335 (1997).
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Nitta, J.1
Akazaki, T.2
Takayanagi, H.3
Enoki, T.4
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12
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33646662616
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note
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Several theoretical proposals (Refs. 14, 20, and 22-26) as well as experimental realizations (Refs. 27 and 28) exist.
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22
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37649028022
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M. Hentschel, H. Schomerus, D. Frustaglia, and K. Richter, Phys. Rev. B 69, 155326 (2004).
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(2004)
Phys. Rev. B
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, pp. 155326
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Hentschel, M.1
Schomerus, H.2
Frustaglia, D.3
Richter, K.4
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28
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0032472661
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A. F. Morpurgo, J. P. Heida, T. M. Klapwijk, B. J. van Wees, and G. Borghs, Phys. Rev. Lett. 80, 1050 (1998).
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(1998)
Phys. Rev. Lett.
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, pp. 1050
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Morpurgo, A.F.1
Heida, J.P.2
Klapwijk, T.M.3
Van Wees, B.J.4
Borghs, G.5
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30
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33646665997
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note
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We neglect the Dresselhaus spin-orbit coupling (Ref. 30) having in mind, e.g., InAs or InSb semiconductors where the Rashba interaction dominates (Ref. 31).
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34
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0010211392
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T. Choi, S. Y. Cho, C.-M. Ryu, and C. K. Kim, Phys. Rev. B 56, 4825 (1997).
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(1997)
Phys. Rev. B
, vol.56
, pp. 4825
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Choi, T.1
Cho, S.Y.2
Ryu, C.-M.3
Kim, C.K.4
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35
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33646653106
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note
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0〉 ≫ 1).
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36
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33646643771
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note
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See, e.g., that for large angular momentum the effective Rashba field BR is determined by the second line of Eq. (2), corresponding to an effective radial field (i.e. (anti)parallel to r̂ = cos ψx̂ +sin ψŷ).
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38
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42749103922
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The Dirac notation refers only to the spin states. Here we assume that the particles escape from the ring after half a winding which holds true for strongly coupled leads. Below we will see that this actually provides a fairly good description of the conductance when comparing with complete 2D numerical quantum calculations. Moreover, our results agree with a related model for 1D rings based on a transfer matrix approach (including arbitrary winding numbers) which has been developed in parallel by B. Molnar, F. M. Peeters, and P. Vasilopoulos, Phys. Rev. B 69, 155335 (2004).
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(2004)
Phys. Rev. B
, vol.69
, pp. 155335
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Molnar, B.1
Peeters, F.M.2
Vasilopoulos, P.3
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39
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33646656649
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note
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This makes sense since we see from Sec. II B that such pairs of spins are actually parallel.
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41
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33646644948
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note
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0 (Refs. 5 and 41).
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45
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33646654881
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note
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This is based on the standard recursive method (Ref. 45) which uses a tight-binding model arising from the real-space discretization of the corresponding Schrödinger equation in a 2D geometry (Fig. 3). Here, the technique is generalized for including spin (Refs. 20, 22, and 46). This requires to replace the tight-binding on-site and hopping energies by 2 × 2 spin matrices and projecting the obtained Green function (matrix) onto transverse mode spinors (of incoming and outgoing states) in the leads for the calculation of the spin-dependent quantum transmission.
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47
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33646653864
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Ph.D. thesis, TU Dresden
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D. Frustaglia, Ph.D. thesis, TU Dresden, 2001.
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(2001)
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Frustaglia, D.1
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48
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33646650114
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note
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The number of incoming and outgoing open channels is kept constant within such energy window. Physically, the energy average can be associated either with an ensemble average on rings of slightly different size or, alternatively, with a finite temperature (sufficiently low for neglecting decoherence effects).
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49
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33646642610
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note
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Note that here the term adiabatic is used in a sense different from the one introduced previously in the context of adiabatic spin transport.
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50
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33646661668
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note
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The adiabatic switching of the Rashba coupling is introduced in order to avoid an abrupt transition between the region of interest subject to finite coupling (the ring) and the leads connected to reservoirs free of spin-orbit coupling. For a given energy, some differences can arise in the computed conductance when using or not the adiabatic switching in the case of strong Rashba coupling. However, no significant differences survive when performing an energy average in the way discribed above.
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54
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33646644341
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note
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Assuming (efficient) spin injection into semiconductors.
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55
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33646655733
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note
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Note the difference with respect to the Datta-Das proposal (Ref. 5), where incoming spin-polarized states point along the z or x axis to get spin oscillations.
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