  We investigate the structure of vortex states in rotating two-component
Bose-Einstein condensates with equal intracomponent but varying intercomponent
coupling constants. A phase diagram in the intercomponent-coupling versus
rotation-frequency plane reveals rich equilibrium structures of vortex states.
As the ratio of intercomponent to intracomponent couplings increases, the
interlocked vortex lattices undergo phase transitions from triangular to
square, to double-core lattices, and eventually develop interwoven "serpentine"
vortex sheets with each component made up of chains of singly quantized
vortices.
