  We theoretically investigate transport signatures of quantum interference in
highly symmetric double quantum dots in a parallel geometry and demonstrate
that extremely weak symmetry-breaking effects can have a dramatic influence on
the current. Our calculations are based on a master equation where quantum
interference enters as non-diagonal elements of the density matrix of the
double quantum dots. We also show that many results have a physically intuitive
meaning when recasting our equations as Bloch-like equations for a pseudo spin
associated with the dot occupation. In the perfectly symmetric configuration
with equal tunnel couplings and orbital energies of both dots, there is no
unique stationary state density matrix. Interestingly, however, adding
arbitrarily small symmetry-breaking terms to the tunnel couplings or orbital
energies stabilizes a stationary state either with or without quantum
interference, depending on the competition between these two perturbations. The
different solutions can correspond to very different current levels. Therefore,
if the orbital energies and/or tunnel couplings are controlled by, e.g.,
electrostatic gating, the double quantum dot can act as an exceptionally
sensitive electric switch.
