  We study the fractional boundary charges (FBCs) occurring in nanowires in the
presence of periodically modulated chemical potentials and connect them to the
FBCs occurring in a two-dimensional electron gas in the presence of a
perpendicular magnetic field in the integer quantum Hall effect (QHE) regime.
First, we show that in nanowires the FBCs take fractional values and change
linearly as a function of phase offset of the modulated chemical potential.
This linear slope takes quantized values determined by the period of the
modulation and depends only on the number of the filled bands. Next, we
establish a mapping from the one-dimensional system to the QHE setup, where we
again focus on the properties of the FBCs. By considering a cylinder topology
with an external flux similar to the Laughlin construction, we find that the
slope of the FBCs as function of flux is linear and assumes universal quantized
values, also in the presence of arbitrary disorder. We establish that the
quantized slopes give rise to the quantization of the Hall conductance.
Importantly, the approach via FBCs is valid for arbitrary flux values and
disorder. The slope of the FBCs plays the role of a topological invariant for
clean and disordered QHE systems. Our predictions for the FBCs can be tested
experimentally in nanowires and in Corbino disk geometries in the integer QHE
regime.
