*2.1. Model*

The considered system of three quantum dots (QDs) in an triangular arrangemen<sup>t</sup> is presented in Figure 1. This system is described by the Hamiltonian

$$H\_{tot} = H\_{\text{\ $}QD} + H\_{cl} + H\_{\text{\$ }QD-cl\prime} \tag{1}$$

which consists of parts corresponding to the electrons in the triangular QD system, in the electrodes, and in the coupling between the sub-systems, respectively. The first part is given by

$$H\_{\text{3QD}} = \sum\_{i \in \text{3QD}} \varepsilon\_i \, c\_i^\dagger c\_i + \sum\_{i, j \in \text{3QD}} \left( \tilde{l}\_{ij} c\_i^\dagger c\_j + h.c. \right), \tag{2}$$

where the first term describes the single-level energy, *εi*, at the *i*-th QD and the second term corresponds to electron hopping between the QDs. Here, the hopping parameters ˜*t*12 = *<sup>t</sup>*12*e<sup>ı</sup>φ*/3 = ˜*<sup>t</sup>*<sup>∗</sup>21, ˜*t*23 = *<sup>t</sup>*23*e<sup>ı</sup>φ*/3 = ˜*<sup>t</sup>*<sup>∗</sup>32, and ˜*t*31 = *<sup>t</sup>*31*e<sup>ı</sup>φ*/3 = ˜*t*∗13 include the phase shift *φ* = <sup>2</sup>*π*Φ/(*hc*/*e*), due to presence of the magnetic flux Φ; where *hc*/*e* denotes the one-electron flux quantum. The spin of electrons is irrelevant in our studies and so it is omitted. We consider transport in an open system with the left (L) and right (R) electrodes as reservoirs of electrons, each in thermal equilibrium with a given chemical potential *μα* and temperature *T<sup>α</sup>*. The corresponding Hamiltonian is

$$H\_{cl} = \sum\_{k,\alpha \in L, R} \varepsilon\_{k,\alpha} \mathfrak{c}\_{kn}^{\dagger} \mathfrak{c}\_{kn\prime} \tag{3}$$

where *<sup>ε</sup>k*,*<sup>α</sup>* denotes an electron spectrum. The coupling between the 3QD system and the electrodes is given by

$$H\_{\text{3QD}-el} = \sum\_{k} (t\_L \, c\_{kL}^\dagger c\_1 + t\_R \, c\_{kR}^\dagger c\_2 + h.c.),\tag{4}$$

with tunneling from the electrodes given by the hopping parameters *tL* and *tR*, respectively. The model omits Coulomb interactions and, therefore, one can derive all transport characteristics analytically.

**Figure 1.** Model of the triangular system of three quantum dots (3QDs) threaded by the magnetic flux Φ and attached to the left (L) and the right (R) electrodes.
