  We investigate vortex states of immiscible two-component Bose-Einstein
condensates under rotation through numerical simulations of the coupled
Gross-Pitaevskii equations. For strong intercomponent repulsion, the two
components undergo phase separation to form several density domains of the same
component. In the presence of the rotation, the nucleated vortices are aligned
between the domains to make up winding chains of singly quantized vortices, a
vortex sheet, instead of periodic vortex lattices. The vortices of one
component are located at the region of the density domains of the other
component, which results in the serpentine domain structure. The sheet
configuration is stable as long as the imbalance of the intracomponent
parameter is small. We employ a planar sheet model to estimate the distance
between neighboring sheets, determined by the competition between the surface
tension of the domain wall and the kinetic energy of the superflow via
quantized vortices. By comparing the several length scales in this system, the
phase diagram of the vortex state is obtained.
