  We study the interplay between the Kondo and superconducting (SC) proximity
effects, taking place in a triangular triple quantum dot (TTQD) connected to
one normal and two SC leads. This system shows various quantum phases. Without
the SC leads, the lowest two states that belong to the different spin sectors,
$S=0$ and $S=1/2$, become energetically very close to each other near half
filling. The singlet one is a Kondo-screened state by conduction electrons from
the normal lead, and the doublet one is a resonating valence bond state with
unpaired free spin which remains unscreened. Furthermore, when one additional
electron enters the TTQD, the ground state becomes a doublet in which the $S=1$
local moment due to the Nagaoka ferromagnetism is partially screened by
conduction electrons.The Cooper pairs penetrating into the TTQD from the SC
leads reconstruct the wavefunctions and vary the phase boundaries between these
quantum states in the parameter space. We calculate ground-state phase diagrams
using the numerical renormalization group, and show that the SC proximity
effect induces a reentrant transition in-between the three- and four-electron
fillings.
