  The spatial Kibble-Zurek mechanism (KZM) is applied to the Kitaev chain with
inhomogeneous pairing interactions that vanish in half of the lattice and
result in a quantum critical point separating the superfluid and normal-gas
phases in real space. The weakly-interacting BCS theory predicts scaling
behavior of the penetration of the pair wavefunction into the normal-gas region
different from conventional power-law results due to the non-analytic
dependence of the BCS order parameter on the interaction. The Bogoliubov-de
Gennes (BdG) equation produces numerical results confirming the scaling
behavior and hints complications in the strong-interaction regime. The limiting
case of the step-function quench shows the dominance of the BCS coherence
length in absence of additional length scale. Furthermore, the energy spectrum
and wavefunctions from the BdG equation show abundant in-gap states from the
normal-gas region in addition to the topological edge states.
