We investigate the quantum phases of mixed-dimensional cold atom mixtures. In
particular, we consider a mixture of a Fermi gas in a two-dimensional lattice,
interacting with a bulk Fermi gas or a Bose-Einstein condensate in a
three-dimensional lattice. The effective interaction of the two-dimensional
system mediated by the bulk system is determined. We perform a functional
renormalization group analysis, and demonstrate that by tuning the properties
of the bulk system, a subtle competition of several superconducting orders can
be controlled among s-wave, p-wave, dx2βy2β-wave, and
gxy(x2βy2)β-wave pairing symmetries. Other instabilities such as a
charge-density wave order are also demonstrated to occur. In particular, we
find that the critical temperature of the d-wave pairing induced by the
next-nearest-neighbor interactions can be an order of magnitude larger than
that of the same pairing induced by doping in the simple Hubbard model. We
expect that by combining the nearest-neighbor interaction with the
next-nearest-neighbor hopping (known to enhance d-wave pairing), an even
higher critical temperature may be achieved.Comment: 10 pages, 10 figure