  We study single-channel continuum models of one-dimensional insulators
induced by periodic potential modulations which are either terminated by a hard
wall (the boundary model) or feature a single region of dislocations and/or
impurity potentials breaking translational invariance (the interface model). We
investigate the universal properties of excess charges accumulated near the
boundary and the interface, respectively. We find a rigorous analytic proof for
the earlier observed linear dependence of the boundary charge on the phase of
the periodic potential modulation as well as extend these results to the
interface model. The linear dependence on the phase shows a universal value for
the slope, and is intersected by discontinuous jumps by plus or minus one
electron charge at the phase points where localized states enter or leave a
band of extended states. Both contributions add up such that the periodicity of
the excess charge in the phase over a $2\pi$-cycle is maintained. While in the
boundary model this property is usually associated with the bulk-boundary
correspondence, in the interface model a correspondence of scattering state and
localized state contributions to the total interface charge is unveiled on the
basis of the so-called nearsightedness principle.
