  We study the interference between the Fano and Kondo effects in a
side-coupled double-quantum- dot system where one of the quantum dots couples
to conduction electron bath while the other dot only side-couples to the first
dot via antiferromagnetic (AF) spin exchange coupling. We apply both the
perturbative renormalization group (RG) and numerical renormalization group
(NRG) approaches to study the effect of AF coupling on the Fano lineshape in
the conduction leads. With particle-hole symmetry, the AF exchange coupling
competes with the Kondo effect and leads to a local spin-singlet ground state
for arbitrary small coupling, so called "two-stage Kondo effect". As a result,
via NRG we find the spectral properties of the Fano lineshape in the tunneling
density of states (TDOS) of conduction electron leads shows double dip-peak
features at the energy scale around the Kondo temperature and the one much
below it, corresponding to the two-stage Kondo effect; it also shows an
universal scaling behavior at very low energies. We find the qualitative
agreement between the NRG and the perturbative RG approach. Relevance of our
work to the experiments is discussed.
