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Scalar kinks propagating along the bulk in warped spacetimes provide a thickbrane realisation of the braneworld. We consider here, a class of such exactsolutions of the full Einstein-scalar system with a sine-Gordon potential and anegative cosmological constant. In the background of the kink and thecorresponding warped geometry, we discuss the issue of localisation of spinhalf fermions (with emphasis on massive ones) on the brane in the presence ofdifferent types of kink-fermion Yukawa couplings. We analyse the possibility ofquasi-bound states for large values of the Yukawa coupling parameter $\gamma_F$(with $\nu$, the warp factor parameter kept fixed) using appropriate, recentlydeveloped, approximation methods. In particular, the spectrum of the low--lyingstates and their lifetimes are obtained, with the latter being exponentiallyenhanced for large $\nu \gamma_F$. Our results indicate quantitatively, withinthis model, that it is possible to tune the nature of warping and the strengthand form of the Yukawa interaction to obtain trapped massive fermion states onthe brane, which, however, do have a finite (but very small) probability ofescaping into the bulk.Comment: 22 pages, 4 figures, RevTex

Scalar kinks and fermion localization in warped spacetimes