Excited de Sitter brane worlds localized by a kink

We reconsider, in five-dimensional space-time, the issue of thick brane localized in the extra dimension by a kink formed by a scalar field. The localization is achieved by a sine-Gordon potential. Apart from a fundamental brane (where the scalar field is a monotonic function of the extra dimension [R. Koley and S. Kar, Classical Quantum Gravity 22, 753 (2005)]), we show that a series of new solutions exist as well, labeled by the number of zeros of the scalar field. These solutions are regular, localized on the brane, and mirror-symmetric with respect to the extra dimension. They form a tower of "excited branes". The study of some perturbations of the solutions reveals that the new solutions are not stable. Finally, fermions are coupled to the scalar field by means of a Yukawa potential and their localization in the background of the new solutions is examined. It turns out that the excited branes can localize left and right chiral fermions either on the brane and/or in the bulk but close to the brane.