A Feynman path analysis of the Fano effect in electronic transport through a parallel double quantum dot structure

We carry out a comprehensive analysis of Fano effect in electronic transport process through a parallel double quantum dot (QD) structure. First, we establish an expression of the linear conductance in the standard Fano form. This expression provides a uniform way to explain the presence of the Fano antiresonance (or a lack of thereof) in various double QD structures. Then, by virtue of the language of Feynman path, we find that there are infinite electron transmission paths to contribute to the Fano interference. In the absence of a magnetic field, the high-order paths play a nontrivial role in the formation of the Fano lineshape. Finally, we find that it is possible to eliminate the contributions of all the high-order paths by tuning the magnetic field to some specific values. Thus, just two lowest-order Feynman paths remain. Only in such a case, the Fano effect can be unambiguously understood to arise from a quantum interference between a resonant and a nonresonant paths.