\xi(y)^2 
 + \frac{1}{\sqrt{3}}\kappa\xi'(y)\big(\bar{\tilde{\Psi}}\tilde{\gamma}^5\tilde{\Psi}\big)\bigg]
 \label{3S}
  \end{aligned}$$

where the higher order terms of $\kappa\xi$ are neglected due to the consideration of $\kappa\xi < 1$. It may be noted that the effective mass of the bulk fermion field in ST theory gets suppressed by a factor of $e^{-\frac{\kappa}{2\sqrt{3}}<\Phi>}$ in comparison to that of $F(R)$ theory i.e. $\tilde{m_5} = m_5e^{-\frac{\kappa}{2\sqrt{3}}<\Phi>}$, where $\tilde{m_5}$ symbolizes the bulk mass in ST theory. Moreover the last three terms in the expression of eqn.(\[3S\]) denote the coupling between scalar field ($\xi(y)$, generated from higher curvature degrees of freedom) and fermion field. Clearly such couplings carry the signature of higher curvature effects.\
With the explicit forms of $\tilde{D}_{\mu}$ and $\tilde{D}_5$, $L_{Dirac}$ is finally written as, $$\begin{aligned}
   L_{Dirac}&=&e^{-4A(y)} \bar{\tilde{\Psi}}\bigg[ie^{A(y)}\tilde{\gamma}^{\mu}\partial_{\mu} 
   + \tilde{\gamma}^{5}\bigg(\partial_{y}-2A'(y)+\frac{\kappa}{\sqrt{3}}\xi'(y)\bigg)\nonumber\\ 
   &-&m_5\bigg(e^{-\frac{\kappa}{2\sqrt{3}}<\Phi>} - \frac{\kappa}{2\sqrt{3}}\xi(y) + \frac{\kappa^2}{24}\xi^2(y)\bigg)\bigg]\Psi
   \label{4S}
  \end{aligned}$$

At this stage, the five dimensional spinor $\tilde{\Psi}(x^{\mu},y)$ is decomposed via KK mode expansion as follows, $$\tilde{\Psi}(x^{\mu},y) = \sum[\tilde{\chi}_L^{n}(x^{\mu})\tilde{\zeta}_L^{n}(y) + \tilde{\chi}_R^{n}(x^{\mu})\tilde{\zeta}_R^{n}(y)]
   \label{5S}$$

$n$ denotes the nth KK mode and the subscripts $L,R$ indicate the left, right chiral (or helicity) states respectively. The above KK mode expansion along with the Dirac field lagrangian given in eqn.(\[4S\]) lead the following equation of motion for $\tilde{\zeta}^{(n)}_{L,R}(y)$ : $$\begin{aligned}
   e^{-A(y)}&\bigg[&\pm\bigg(\partial_{y} - 2A'(y) + \frac{\kappa}{\sqrt{3}}\xi'(y)\bigg)\nonumber\\ 
   &+&m_5\bigg(e^{-\frac{\kappa}{2\sqrt{3}}<\Phi>} - \frac{\kappa}{2\sqrt{3}}\xi(y) 