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.
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