Reprint of : Regular and singular Fermi liquid in triple quantum dots: Coherent transport studies

• A model of three coupled quantum dots in a triangular geometry was studied.
• Varying gate potentials the system exhibits different many-electron ground states.
• The numerical renormalization group was used for analysis of electron transport.
• The Friedel sum rule reproduces the conductance for the whole gate potential range.
• A phase diagram was constructed with the regular and singular Fermi liquid phases.

A system of three coupled quantum dots in a triangular geometry (TQD) with electron–electron interaction and symmetrically coupled to two leads is analyzed with respect to the electron transport by means of the numerical renormalization group. Varying gate potentials this system exhibits extremely rich range of regimes with different many-electron states with various local spin orderings. It is demonstrated how the Luttinger phase changes in a controlled manner which then via the Friedel sum rule formula exactly reproduces the conductance through the TQD system. The analysis of the uncoupled TQD molecule from the leads gives a reliable qualitative understanding of various relevant regimes and an insight into the phase diagram with the regular Fermi liquid and singular-Fermi liquid phases.