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The zero temperature phase diagram of binary boson-fermion mixtures intwo-colour superlattices is investigated. The eigenvalue problem associatedwith the Bose-Fermi-Hubbard Hamiltonian is solved using an exact numericaldiagonalization technique, supplemented by an adaptive basis truncation scheme.The physically motivated basis truncation allows to access larger systems in afully controlled and very flexible framework. Several experimentally relevantobservables, such as the matter-wave interference pattern and thecondensatefraction, are investigated in order to explore the rich phasediagram. At symmetric half filling a phase similar to the Mott-insulating phasein a commensurate purely bosonic system is identified and an analogy to recentexperiments is pointed out. Furthermore a phase of complete localization of thebosonic species generated by the repulsive boson-fermion interaction isidentified. These localized condensates are of a different nature than thegenuine Bose-Einstein condensates in optical lattices.Comment: 18 pages, 9 figure

Bose–Fermi mixtures in 1D optical superlattices using full and truncated single-band bases