  Hubbard chains with periodically modulated coupling constants in a magnetic
field exhibit gaps at zero temperature in their magnetic and charge excitations
in a variety of situations. In addition to fully gapped situations (plateau in
the magnetization curve and charge gap), we have shown [cond-mat/9908398] that
plateaux also appear in the presence of massless modes, leading to a plateau
with a magnetization m whose value depends continuously on the filling n. Here
we detail and extend the arguments leading to such doping-dependent
magnetization plateaux. First we analyze the low-lying excitations using
Abelian bosonization. We compute the susceptibility and show that due to the
constraint of fixed n, it vanishes at low temperatures (thus leading to a
magnetization plateau) even in the presence of one massless mode. Next we study
correlation functions and show that one component of the superconducting order
parameter develops quasi-long-range order on a doping-dependent magnetization
plateau. We then use perturbation theory in the on-site repulsion U to compute
the width of these plateaux up to first order in U. Finally, we compute
groundstate phase diagrams and correlation functions by Lanczos diagonalization
of finite clusters, confirming the presence of doping-dependent plateaux and
their special properties.
