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
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).
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.
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).