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Spin-orbit interaction induced anisotropic property in interacting quantum wires.

Cheng F, Zhou G, Chang K - Nanoscale Res Lett (2011)

Bottom Line: : We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI).The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW.The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej.

View Article: PubMed Central - HTML - PubMed

Affiliation: SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P, O, Box 912, Beijing 100083, China. kchang@semi.ac.cn.

ABSTRACT
: We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI). The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW. The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej.

No MeSH data available.


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The dc conductivity dependence of the angle θ. The dc conductivity (in units of e2/h) of electron in an infinitely long-interacting QW as a function of the angle θ with a fixed strength of Coulomb interaction g = 0.4 (a) for (001) plane, (c) for (110) plane, where the solid line (red online) is for α = 0.2 and β = 0.4; the dashed line (green online) for α = 0.3 and β = 0.2; and the dotted line (blue online) for α = 0.2 and β = 0.2; (b, d) is the same as (a, c), but with fixed SOI strengths α = 0.2 and β = 0.2 for different strengths of Coulomb interaction. (b) is for (001) plane and (d) for (110) plane, where the dotted line (blue online) corresponds to g = 0.4; the dashed line (green online) to g = 0.6; and the solid line (red online) to g = 0.
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Figure 4: The dc conductivity dependence of the angle θ. The dc conductivity (in units of e2/h) of electron in an infinitely long-interacting QW as a function of the angle θ with a fixed strength of Coulomb interaction g = 0.4 (a) for (001) plane, (c) for (110) plane, where the solid line (red online) is for α = 0.2 and β = 0.4; the dashed line (green online) for α = 0.3 and β = 0.2; and the dotted line (blue online) for α = 0.2 and β = 0.2; (b, d) is the same as (a, c), but with fixed SOI strengths α = 0.2 and β = 0.2 for different strengths of Coulomb interaction. (b) is for (001) plane and (d) for (110) plane, where the dotted line (blue online) corresponds to g = 0.4; the dashed line (green online) to g = 0.6; and the solid line (red online) to g = 0.

Mentions: Next, we turn to study the transport property of electron in an interacting QW. In the dc case, Equation (9) shows that the charge conductivity of an infinitely long interacting QW for the different parameters g and δv. For the noninteracting QW structure, there is only single transverse mode, and thus no anisotropy of the dc conductivity can be found. This result can also be obtained from Equation (9) by taking g = 0, i.e., non-interacting case, ; we easily obtain σρ = 2e2/h. When the Coulomb interaction is included but without the SOIs, i.e., α = β = 0, we can obtain an isotropic conductivity σρ = 2Kρe2/h from Equation (9). The spin and charge excitations propagate independently at the velocities vρ and vσ in this case. In the presence of both the Coulomb interaction and the SOIs, the SOIs mix the spin and charge excitations, leading to anisotropic velocities of the collective excitations u1 and u2 (see Equation 8), or equivalently the anisotropic interaction parameter , consequently resulting in the anisotropic conductivity . Therefore, the dc conductivity of the infinitely long-interacting QW depends sensitively on the crystallographic direction θ of the QW, i.e., the anisotropic transport behavior (see Figure 4). Interestingly, the dc conductivity oscillates with varying the angle θ with a periodicity π. With increasing the strengths of the DSOI and/or RSOI (see Figure 4a) or the strengths of the Coulomb interaction (see Figure 4b), the oscillation of the conductivity for the infinitely long-interacting QW becomes stronger. This is because the anisotropy of the interaction parameter depends on the anisotropic velocities of the mixed spin and charge excitations, which increases when the strengths of the SOIs or the Coulomb interaction increase.


Spin-orbit interaction induced anisotropic property in interacting quantum wires.

Cheng F, Zhou G, Chang K - Nanoscale Res Lett (2011)

The dc conductivity dependence of the angle θ. The dc conductivity (in units of e2/h) of electron in an infinitely long-interacting QW as a function of the angle θ with a fixed strength of Coulomb interaction g = 0.4 (a) for (001) plane, (c) for (110) plane, where the solid line (red online) is for α = 0.2 and β = 0.4; the dashed line (green online) for α = 0.3 and β = 0.2; and the dotted line (blue online) for α = 0.2 and β = 0.2; (b, d) is the same as (a, c), but with fixed SOI strengths α = 0.2 and β = 0.2 for different strengths of Coulomb interaction. (b) is for (001) plane and (d) for (110) plane, where the dotted line (blue online) corresponds to g = 0.4; the dashed line (green online) to g = 0.6; and the solid line (red online) to g = 0.
© Copyright Policy - open-access
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getmorefigures.php?uid=PMC3211270&req=5

Figure 4: The dc conductivity dependence of the angle θ. The dc conductivity (in units of e2/h) of electron in an infinitely long-interacting QW as a function of the angle θ with a fixed strength of Coulomb interaction g = 0.4 (a) for (001) plane, (c) for (110) plane, where the solid line (red online) is for α = 0.2 and β = 0.4; the dashed line (green online) for α = 0.3 and β = 0.2; and the dotted line (blue online) for α = 0.2 and β = 0.2; (b, d) is the same as (a, c), but with fixed SOI strengths α = 0.2 and β = 0.2 for different strengths of Coulomb interaction. (b) is for (001) plane and (d) for (110) plane, where the dotted line (blue online) corresponds to g = 0.4; the dashed line (green online) to g = 0.6; and the solid line (red online) to g = 0.
Mentions: Next, we turn to study the transport property of electron in an interacting QW. In the dc case, Equation (9) shows that the charge conductivity of an infinitely long interacting QW for the different parameters g and δv. For the noninteracting QW structure, there is only single transverse mode, and thus no anisotropy of the dc conductivity can be found. This result can also be obtained from Equation (9) by taking g = 0, i.e., non-interacting case, ; we easily obtain σρ = 2e2/h. When the Coulomb interaction is included but without the SOIs, i.e., α = β = 0, we can obtain an isotropic conductivity σρ = 2Kρe2/h from Equation (9). The spin and charge excitations propagate independently at the velocities vρ and vσ in this case. In the presence of both the Coulomb interaction and the SOIs, the SOIs mix the spin and charge excitations, leading to anisotropic velocities of the collective excitations u1 and u2 (see Equation 8), or equivalently the anisotropic interaction parameter , consequently resulting in the anisotropic conductivity . Therefore, the dc conductivity of the infinitely long-interacting QW depends sensitively on the crystallographic direction θ of the QW, i.e., the anisotropic transport behavior (see Figure 4). Interestingly, the dc conductivity oscillates with varying the angle θ with a periodicity π. With increasing the strengths of the DSOI and/or RSOI (see Figure 4a) or the strengths of the Coulomb interaction (see Figure 4b), the oscillation of the conductivity for the infinitely long-interacting QW becomes stronger. This is because the anisotropy of the interaction parameter depends on the anisotropic velocities of the mixed spin and charge excitations, which increases when the strengths of the SOIs or the Coulomb interaction increase.

Bottom Line: : We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI).The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW.The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej.

View Article: PubMed Central - HTML - PubMed

Affiliation: SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P, O, Box 912, Beijing 100083, China. kchang@semi.ac.cn.

ABSTRACT
: We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI). The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW. The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej.

No MeSH data available.


Related in: MedlinePlus