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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 ′.
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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 ′.
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65249150846
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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.
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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.
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39
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65249109953
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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).
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For completeness, we point out that the condition on jm can be relaxed if tjm =0.
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For completeness, we point out that the condition on jm can be relaxed if tjm =0.
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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.
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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.
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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.).
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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.).
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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.
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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.
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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.
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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.
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