  We consider the symmetry breaking of a matter-wave soliton formed by spinor
Bose-Einstein condensates (BECs) illuminated by a two-spot laser beam. This
laser beam introduces spin-orbit (SO) coupling in the BECs such that the SO
coupling produces an effect similar to a linear doublewell potential (DWP). It
is well known that symmetry breaking in a DWP is an important effect and has
been discussed in many kinds of systems. However, it has not yet been discussed
in a DWP formed by SO coupling. The objective of this work is to study the
symmetry breaking of spinor BECs trapped by a DWP formed by SO coupling. We
find that two kinds of symmetry breaking, displacement symmetry breaking and
bimodal symmetry breaking, can be obtained in this model. The influence of the
symmetry transition is systematically discussed by controlling the interaction
strength of the BECs and the distance between the center of the two spots.
Moreover, because SO coupling violates Galilean invariance, the influence of
symmetry breaking in the moving system is also addressed in this paper.
