  The entanglement of different parts of a quantum system is expected to be
proportional to the common interface area. Therefore alterations across the
interface will lead to changes on the behavior of entanglement entropy. In this
work, the effects of bond defects at the boundaries of Kitaev ladders are
considered. We find a logarithmic scaling for the ground state entanglement
entropy between the two pieces. The prefactor of the logarithm (effective
central charge) varies continuously with the defect strength. The energy
dispersion is also obtained and sharp features in the von Neumann entanglement
entropy are observed when bands cross. Phase diagrams for homogeneous Kitaev
hamiltonians with nonzero superconducting paring potential are presented. They
show that for chains/legs that are connected to one another through inter-leg
hopping, when certain parameters are fine-tuned, the phase transition lines
correspond to either single or double gapless modes dispersion. Moreover, even
when the defect is turned on, the effective central charge for ladders with two
gapless modes is exactly twice the one for ladders with a single gapless mode.
On the other hand, in the absence of superconductivity, we can tune the
parameters to obtain homogeneous systems whose number of gapless modes is up to
the number of legs of the ladder. Additionally, in this situation, the presence
of the bond defect makes the effective central charge becomes smaller than the
number of gapless modes times the effective central charge of hamiltonians with
one gapless mode. Furthermore, the relationship between the cases with and
without superconductivity is presented.
