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Volumn 79, Issue 12, 2009, Pages

Multiterminal spin-dependent transport in ballistic carbon nanotubes

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EID: 65249122511     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.125422     Document Type: Article
Times cited : (4)

References (53)
  • 7
    • 20044372065 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.71.125401
    • M. Zaffalon and B. J. van Wees, Phys. Rev. B 71, 125401 (2005). 10.1103/PhysRevB.71.125401
    • (2005) Phys. Rev. B , vol.71 , pp. 125401
    • Zaffalon, M.1    Van Wees, B.J.2
  • 23
  • 28
    • 33845473883 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.74.235316
    • A. Cottet and M.-S. Choi, Phys. Rev. B 74, 235316 (2006). 10.1103/PhysRevB.74.235316
    • (2006) Phys. Rev. B , vol.74 , pp. 235316
    • Cottet, A.1    Choi, M.-S.2
  • 30
    • 0000675193 scopus 로고
    • 10.1103/PhysRevB.48.7099
    • T. Valet and A. Fert, Phys. Rev. B 48, 7099 (1993). 10.1103/PhysRevB.48. 7099
    • (1993) Phys. Rev. B , vol.48 , pp. 7099
    • Valet, T.1    Fert, A.2
  • 32
    • 33749406012 scopus 로고
    • 10.1103/PhysRevLett.57.1761
    • M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986). 10.1103/PhysRevLett. 57.1761
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 1761
    • Büttiker, M.1
  • 36
    • 0012632893 scopus 로고
    • 10.1103/PhysRevB.42.11479
    • H. U. Baranger, Phys. Rev. B 42, 11479 (1990). 10.1103/PhysRevB.42.11479
    • (1990) Phys. Rev. B , vol.42 , pp. 11479
    • Baranger, H.U.1
  • 37
    • 65249107307 scopus 로고    scopus 로고
    • Spin conservation allows mapping of the scattering description of each spin component σ, onto a spinless problem. Time-reversal symmetry in each of these spinless problems implies tjm = t jm ′, ujm = u jm ′, and vjm = v jm ′.
    • Spin conservation allows mapping of the scattering description of each spin component σ, onto a spinless problem. Time-reversal symmetry in each of these spinless problems implies tjm = t jm ′, ujm = u jm ′, and vjm = v jm ′.
  • 38
    • 65249150846 scopus 로고    scopus 로고
    • From Eq. 14, the phase of t1m t 1m ′ / r 1m ′ can also affect signals Gc and Vc. However, since the scattering matrix of contact 1 is unitary, one finds t1m t 1m ′ / r 1m ′ =- r1m | t1m / r1m | 2. It is thus sufficient to use arg (r1m) as a parameter.
    • From Eq. 14, the phase of t1m t 1m ′ / r 1m ′ can also affect signals Gc and Vc. However, since the scattering matrix of contact 1 is unitary, one finds t1m t 1m ′ / r 1m ′ =- r1m | t1m / r1m | 2. It is thus sufficient to use arg (r1m) as a parameter.
  • 39
    • 65249109953 scopus 로고    scopus 로고
    • The complete parametrization of the scattering matrices of contacts j { 2,3 } requires extra parameters φ j,p U, and Δ φ j,p U such that arg (uj (p,σ)) = φ j,p U +σΔ φ j,p U /2 and r jm ″ =- (1-2 | ujm | 2) 1/2 eiarg [(ujm) 2 / (Ajm + Bjm)]. However, one can check that, with the assumptions made in Sec. 4, signals Gc and Vc are independent of φ j,p U and Δ φ j,p U for both setups (a) and (b).
    • The complete parametrization of the scattering matrices of contacts j { 2,3 } requires extra parameters φ j,p U, and Δ φ j,p U such that arg (uj (p,σ)) = φ j,p U +σΔ φ j,p U /2 and r jm ″ =- (1-2 | ujm | 2) 1/2 eiarg [(ujm) 2 / (Ajm + Bjm)]. However, one can check that, with the assumptions made in Sec. 4, signals Gc and Vc are independent of φ j,p U and Δ φ j,p U for both setups (a) and (b).
  • 40
    • 65249172114 scopus 로고    scopus 로고
    • For completeness, we point out that the condition on jm can be relaxed if tjm =0.
    • For completeness, we point out that the condition on jm can be relaxed if tjm =0.
  • 41
    • 65249147277 scopus 로고    scopus 로고
    • For j { 2,3 }, one has | ujm | 2 ≤1/2 because we assume that an electron arriving from contact j enters the top and bottom portions of the CNT with the same probabilities.
    • For j { 2,3 }, one has | ujm | 2 ≤1/2 because we assume that an electron arriving from contact j enters the top and bottom portions of the CNT with the same probabilities.
  • 42
    • 0000075522 scopus 로고
    • 10.1103/PhysRevB.37.5312
    • M. Johnson and R. H. Silsbee, Phys. Rev. B 37, 5312 (1988). 10.1103/PhysRevB.37.5312
    • (1988) Phys. Rev. B , vol.37 , pp. 5312
    • Johnson, M.1    Silsbee, R.H.2
  • 43
    • 0037299223 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.67.052409
    • S. Takahashi and S. Maekawa, Phys. Rev. B 67, 052409 (2003). 10.1103/PhysRevB.67.052409
    • (2003) Phys. Rev. B , vol.67 , pp. 052409
    • Takahashi, S.1    Maekawa, S.2
  • 44
    • 65249118386 scopus 로고    scopus 로고
    • We find that the sign changes of VP can already occur in the spin-degenerate case. Accordingly, a change in sign of VP has already been observed for a CNT with four normal-metal leads by sweeping the CNT back-gate voltage (Ref.).
    • We find that the sign changes of VP can already occur in the spin-degenerate case. Accordingly, a change in sign of VP has already been observed for a CNT with four normal-metal leads by sweeping the CNT back-gate voltage (Ref.).
  • 45
    • 65249087469 scopus 로고    scopus 로고
    • We have checked analytically that this property is true even when contacts 2 and 3 are spatially asymmetric, i.e., u (2) 3m v (2) 3m.
    • We have checked analytically that this property is true even when contacts 2 and 3 are spatially asymmetric, i.e., u (2) 3m v (2) 3m.
  • 47
    • 65249147853 scopus 로고    scopus 로고
    • In the IFC case, MV and MG are sensitive to the Δ φ 2 (3), p R [T] parameters through the reflection probabilities of contacts 2 and 3 but not through the scattering phases.
    • In the IFC case, MV and MG are sensitive to the Δ φ 2 (3), p R [T] parameters through the reflection probabilities of contacts 2 and 3 but not through the scattering phases.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.