  Layered thallium copper chalcogenides can form single, double, or triple
layers of Cu-Ch separated by Tl sheets. Here we report on the preparation and
properties of Tl-based materials of TlCu2Se2, TlCu4S3, TlCu4Se3 and TlCu6S4,
and compare to reports on layered ACu2nChn+1 materials with A = Ba, K, Rb, and
Cs, and Ch = S, Se. Having no long-range magnetism for these materials is quite
surprising considering the possibilities of inter- and intra-layer exchange
interactions through Cu 3d, and we measure by magnetic susceptibility and
confirm by neutron diffraction. First principles density-functional theory
calculations for both the single-layer TlCu2Se2 (isostructural to the 122
iron-based superconductors) and the double-layer TlCu4Se3 suggest a lack of
Fermi-level spectral weight that is needed to drive a magnetic or
superconducting instability. The electronic structure calculations show a much
greater likelihood of magnetism for multiple structural layers with Fe.
