  We study the conductivities and entanglement structures of two different
holographic gapped systems at zero density in the presence of boundaries within
AdS/BCFT. The first gapped system is described by the Einstein-scalar gravity
and the second one is the dual of AdS soliton geometry. We show that in both
these two systems the bulk and boundary conductivities along the spatial
direction of the boundary of BCFT are trivial. For the first system, when we
increase the size of the subsystem the renormalized entanglement entropy is
always non-negative and monotonically decreasing with discontinuous, or
continuous, or smooth behavior, depending on the effective tension of the
brane. While for the AdS soliton with a boundary, the renormalized entanglement
entropy only exhibits a discontinuous drop when we increase the size of the
subsystem.
