  We extend the well-known theoretical treatment of the spontaneous symmetry
breaking (SSB) in two-component systems, combining linear coupling and
self-attractive nonlinearity, to a system in which the linear coupling competes
with repulsive interactions. First, we address one- and two-dimensional (1D and
2D) ground-state (GS) solutions and 2D vortex states with topological charges
S=1 and 2, maintained by a confining harmonic-oscillator potential. The system
can be implemented in BEC and optics. By means of the Thomas-Fermi
approximation and numerical solution of the underlying coupled Gross-Pitaevskii
equations, we demonstrate that SSB takes place, in the GSs and vortices alike,
when the cross-component repulsion is stronger that the self-repulsion in each
component. The SSB transition is categorized as a supercritical bifurcation,
which gives rise to states featuring broken symmetry in an inner area, and
intact symmetry in a surrounding layer. Unlike stable GSs and vortices with
S=1, the states with S=2 are unstable against splitting. We also address SSB
for 1D gap solitons in the system including a lattice potential. In this case,
SSB takes place under the opposite condition, i.e., the cross-component
repulsion must be weaker than the self-repulsion, and SSB is exhibited by
antisymmetric solitons.

Pattern Formation and Solitons;Quantum Gases;Optics