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HH and LH states are spin-3/2-projection eigenstates with eigenvalues ±3/2 and ±1/2, respectively.
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This approach applies in dilute magnetic hole wires (Ref.) where the bulk-hole g factor is enhanced by a p-d exchange mechanism (Ref.).
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This approach applies in dilute magnetic hole wires (Ref.) where the bulk-hole g factor is enhanced by a p-d exchange mechanism (Ref.).
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Helicity ± distinguishes the two subspaces spanned by J z eigenstates with quantum numbers { ±3/2, 1/2 }, respectively.
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Helicity ± distinguishes the two subspaces spanned by J z eigenstates with quantum numbers { ±3/2, 1/2 }, respectively.
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The cubic-symmetry term that accounts for band-warping effects depends on the wire's direction with respect to crystallographic axes (Ref.). For a wire oriented parallel to the [001] direction, it reads g orb,cub (α) =- (γ2 - γ3) [12 (J z2 - 5 4 14×4) L z α -5 i x + k + J +2 -i x - k - J -2 α - i x + k + J -2 -i x - k - J +2 α] 20.
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The cubic-symmetry term that accounts for band-warping effects depends on the wire's direction with respect to crystallographic axes (Ref.). For a wire oriented parallel to the [001] direction, it reads g orb,cub (α) =- (γ2 - γ3) [12 (J z2 - 5 4 14×4) L z α -5 i x + k + J +2 -i x - k - J -2 α - i x + k + J -2 -i x - k - J +2 α] 20.
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25
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48449106156
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In this work, we neglect inversion-asymmetry-induced spin-orbit coupling, which could shift quasi-1D subband edges to finite kz.
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In this work, we neglect inversion-asymmetry-induced spin-orbit coupling, which could shift quasi-1D subband edges to finite kz.
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26
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48449102805
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Taking the limit Bz →0 circumvents ambiguities in the definition of g factors associated with the, in general, nonlinear magnetic-field dependence of spin splitting. For wires with cylindrical or square cross section, our obtained values for subband-edge g factors are then universal, i.e., independent of wire width.
-
Taking the limit Bz →0 circumvents ambiguities in the definition of g factors associated with the, in general, nonlinear magnetic-field dependence of spin splitting. For wires with cylindrical or square cross section, our obtained values for subband-edge g factors are then universal, i.e., independent of wire width.
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27
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0001496026
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We did not address a possible exchange enhancement of spin splitting, which is known to exist in electron systems [PRLTAO 0031-9007 10.1103/PhysRevLett.77.135
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We did not address a possible exchange enhancement of spin splitting, which is known to exist in electron systems [K. J. Thomas, J. T. Nicholls, M. Y. Simmons, M. Pepper, D. R. Mace, and D. A. Ritchie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.135 77, 135 (1996)]
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In hole systems, exchange enhancement appears to be conditional on a finite spin-3/2 dipole moment [PRBMDO 0163-1829 10.1103/PhysRevB.72.195321
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In hole systems, exchange enhancement appears to be conditional on a finite spin-3/2 dipole moment [R. Winkler, E. Tutuc, S. J. Papadakis, S. Melinte, M. Shayegan, D. Wasserman, and S. A. Lyon, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.195321 72, 195321 (2005)]
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Further investigations of this effect in quasi-1D hole systems are needed; see also PRBMDO 0163-1829 10.1103/PhysRevB.76.201302
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