Fermions on thick branes in the background of sine-Gordon kinks

A class of thick branes in the background of sine-Gordon kinks with a scalar potential V () =p (1+cos2q) was constructed by R. Koley and S. Kar Classical Quantum Gravity 22, 753 (2005). In this paper, in the background of the warped geometry, we investigate the issue of localization of spin-1/2 fermions on these branes in the presence of two types of scalar-fermion couplings: and sin. By presenting the mass-independent potentials in the corresponding Schr\"odinger equations, we obtain the lowest Kaluza-Klein modes and a continuous gapless spectrum of Kaluza-Klein states with m^2>0 for both types of couplings. For the Yukawa coupling, the effective potential of the right chiral fermions for positive q and is always positive; hence only the effective potential of the left chiral fermions could trap the corresponding zero mode. This is a well-known conclusion which is discussed extensively in the literature. However, for the coupling sin, the effective potential of the right chiral fermions for positive q and is no longer always positive. Although the value of the potential at the location of the brane is still positive, it has a series of wells and barriers on each side, which ensures that the right chiral fermion zero mode could be trapped. Thus we may draw the following remarkable conclusion: for positive and q, the potentials of both the left and right chiral fermions could trap the corresponding zero modes under certain restrictions.