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Universal spin dynamics in quantum wires

E. A. Fajardo, U. Zülicke, and R. Winkler
Phys. Rev. B 96, 155304 – Published 13 October 2017
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  • INTRODUCTION
  • EFFECTIVE 2D HAMILTONIAN
  • EFFECTIVE HAMILTONIAN FOR QUASI-1D…
  • POSITION AND VELOCITY OPERATORS
  • UNIVERSAL (PSEUDO-) SPIN DYNAMICS IN…
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We discuss the universal spin dynamics in quasi-one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and valley pseudospin characterizing single-layer transition metal dichalcogenides (TMDCs) such as MoS2, WS2, MoS2, and WSe2. All these systems can be described by the same Dirac-like Hamiltonian. Spin-dependent observable effects in one of these systems thus have counterparts in each of the other systems. Effects discussed in more detail include equilibrium spin currents, current-induced spin polarization (Edelstein effect), and spin currents generated via adiabatic spin pumping. Our work also suggests that a long-debated spin-dependent correction to the position operator in single-band models should be absent.

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    • Received 24 July 2017

    DOI:https://doi.org/10.1103/PhysRevB.96.155304

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    SpintronicsValleytronics
    1. Physical Systems
    Quantum wires
    1. Techniques
    k dot p method
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    E. A. Fajardo1,*, U. Zülicke2, and R. Winkler1,3

    • 1Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
    • 2School of Chemical and Physical Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
    • 3Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

    • *On leave from Department of Physics, Mindanao State University-Main Campus, Marawi City, Lanao del Sur, Philippines 9700; eafajardo@niu.edu

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    Vol. 96, Iss. 15 — 15 October 2017

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    Images

    • Figure 1
      Figure 1

      Energy dispersion near the points K and K′ for the lowest conduction and highest valence band in MoS2. Here Δ′ is the fundamental gap in the absence of SO coupling and λc (λv) is the spin splitting in the conduction (valence) band. The bands marked in red and green thus correspond to decoupled replicas of Hamiltonian (1) with gaps Δ±=Δ′±(λv+λc). It was found in Ref. [13] that for WS2 the sign of λc is opposite to the sign in MoS2 so that the ordering of the spin-split conduction bands near K and K′ relative to the ordering of the spin-split valence bands is opposite to the one shown here.

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    • Figure 2
      Figure 2

      (a) Spin-split dispersion and (b) expectation value of the velocity v4×4 for a quantum wire described by the 4×4 Hamiltonian (1) augmented by an inversion-asymmetric mass confinement in the y direction. The numerical results shown here were obtained using the quadrature method described in Ref. [34].

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    • Figure 3
      Figure 3

      Qualitative sketch of the dispersion E(k) of a quantum wire with Rashba-like SO coupling at T=0 (a) in thermal equilibrium with electric field Ex=0, (b) in the presence of a driving electric field Ex>0 along the wire and a dissipative regime with ν=0, and (c) Ex>0 with ν>0. Horizontal colored lines indicate the quasi Fermi levels for left and right movers in the two spin subbands. In (a) and (b) the net spin polarization and the spin current are exactly zero. In (c) the driving electric field results in a steady state with a net spin polarization (Edelstein effect).

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    • Figure 4
      Figure 4

      Schematic diagram for an adiabatic (pseudo-) spin pump [25]. A potential barrier Vbar is present at the left end of the wire. A perpendicular electric field Ey is applied in the blue shaded region of length L in order to tune the coupling coefficient α∝Ey.

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