  We consider a ring of three quantum dots mutually coupled by
antiferromagnetic exchange interactions, and tunnel-coupled to two metallic
leads: the simplest device in which the consequences of local frustration
arising from internal degrees of freedom may be studied within a 2-channel
environment. Two-channel Kondo (2CK) physics is found to predominate at
low-energies in the mirror-symmetric systems considered, with a residual spin
1/2 overscreened by coupling to both leads. It is however shown that two
distinct 2CK phases, with different ground state parities, arise on tuning the
interdot exchange couplings. In consequence a frustration-induced quantum phase
transition occurs, the 2CK phases being separated by a quantum critical point
for which an effective low-energy model is derived. Precisely at the
transition, parity mixing of the quasi-degenerate local trimer states acts to
destabilise the 2CK fixed points; and the critical fixed point is shown to
consist of a free pseudospin together with effective 1-channel spin quenching,
itself reflecting underlying channel-anisotropy in the inherently 2-channel
system. Numerical renormalization group techniques and physical arguments are
used to obtain a detailed understanding of the problem, including study of both
thermodynamic and dynamical properties of the system.
