Spin-orbit induced effects in quantum wire and quantum dot

We consider interactions in a quantum wire and a quantum dot in the
presence of a magnetic field and spin-orbit interaction. An interplay
of Zeeman and spin-orbit terms in the quantum wire opens up a new
scattering channel when the magnetic field and the spin-orbit axes are
orthogonal: two electrons with opposite momentum and in the same
spin-subband scatter into a different spin-subband while conserving
momentum. This scattering process is relevant and results in a
spin-density wave (SDW) state. We will discuss the role of this state
for transport in the presence of single impurity.

In the second part of this talk I will consider a double quantum dot
set-up and show that spin-orbit induces a novel spin-spin
coupling. This coupling is of the van der Waals type and, unlike the
standard exchange coupling, is present even in the absence of wave
function overlap between the two electrons in quantum dots.