  We investigate a ladder system with two inequivalent legs, namely a Hubbard
chain and a one-dimensional electron gas. Analytical approximations, the
density matrix renormalization group method, and continuous-time quantum Monte
Carlo simulations are used to determine ground-state properties, gaps, and
spectral functions of this system at half-filling. Evidence for the existence
of four different phases as a function of the Hubbard interaction and the rung
hopping is presented. First, a Luttinger liquid exists at very weak interchain
hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an
effective rung exchange coupling is found at moderate interchain hopping or
strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator
with incommensurate excitations and pairing of doped charges is observed at
intermediate values of the rung hopping and the interaction. Fourth, the usual
correlated band insulator is recovered for large rung hopping. We show that the
wavenumbers of the lowest single-particle excitations are different in each
insulating phase. In particular, the three gapped phases exhibit markedly
different spectral functions. We discuss the relevance of asymmetric two-leg
ladder systems as models for atomic wires deposited on a substrate.
