Spin density wave in spin chain/quantum wire

  • To understand better the interplay of electron correlations and symmetry-lowering spin-orbital interaction (of Rashba type), we have considered the model problem of quantum wire subject to spin-orbital interaction (along Sx axis, for example) and external magnetic field (along Sz axis).

  • The resulting band structure allows for novel, Cooper-type tunneling process (shown in the left figure) when two particles with opposite Fermi-momenta in one subband tunnel into states at the opposite Fermi-points in the other subband. This process is only made possible by spin non-conservation, and is of second order in spin-orbital coupling constant.
    To describe correctly the limit of vanishing magnetic field one needs to consider also asymmetric two-particle processes (center figure).
    Changing the angle between spin-orbital axis and that of the magnetic field from 90o leads to mis-alignment of the centers-of-mass of the two subbands and eventual suppression of the pair-tunneling by the momentum-non-conservation (right figure).
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  • This pair-tunneling process turns out to be always relevant (regime III can not be reached for any ratio of the spin-orbital splitting to the Zeeman energy), in RG sense, and its RG analysis reduces to the BKT flow.
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  • The resulting order is of spin-density wave (SDW) type, with ordering axis along Sx. It is present in both quantum wires, where it leads to unusual suppression of single-particle backscattering off potential impurity, and in spin chains.

    These results are described in Spin-orbit induced spin-density wave in a quantum wire, Jianmin Sun, Suhas Gangadharaiah and Oleg A. Starykh, Phys. Rev. Lett. 98, 126408 (2007), and in Spin-orbital effects in magnetized quantum wires and spin chains, Suhas Gangadharaiah, Jianmin Sun, and Oleg A. Starykh, Phys. Rev. B 78, 054436 (2008). The findings are different from the case of staggered Dzyaloshinskii-Moriya interaction analyzed in an important work of M. Oshikawa and I. Affleck, Phys. Rev. B 65, 134410 (2002).