Properties of gapped systems in AdS/BCFT

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.