In a rotating two-component Bose-Einstein condensate (BEC), the traditional triangular vortex lattice can be replaced by a rectangular vortex lattice or even a structure characterized in terms of vortex sheets, depending on the interspecies interactions. We study the dynamics of this system by analyzing the Bogoliubov excitation spectrum. Excitations familiar to BEC vortex systems are found such as Tkachenko modes, hydrodynamic modes and surface waves, however, the complex two-component morphology also gives rise to new phenomena including shear flow between vortex sheets.
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