Quantum coherence in a model of strongly correlated quantum dots

The building up of quantum coherence among coupled mesoscopic objects is studied in the present paper with a model of “ideal” quantum dots. With strong Coulomb repulsion we show that quantum coherence between dots can build up at an energy scale much larger than energy-level spacing if the number of electrons per dot is fractional. The self-consistent ladder approximation (SCLA) is applied to study the quantum coherences in the two-dot and triple-dot systems where we show how quantum coherence manifests itself in the electron spectral function and in the Aharonov-Bohm (AB) effect.

Figure 1

The diagrams included in SCLA to calculate the renormalized Green’s function of $\alpha \text{th}$ charging state. The thin and thick wave lines represent the bare and full Green’s function of the $\alpha \text{th}$ charging states, respectively. The solid lines represent the occupation number of fermions. The dashed lines represent the interaction between fermions and local charging states.

Figure 2

The diagrams used to calculate physical electron Green’s function. The dotted line represents the frequency carried by the green’s function and the dot dashed lines represent the creation and annihilation of a physical electron. The shaded area represent all the ladder diagrams in Fig. 1.

Figure 3

(Color online) The electronic spectral function for the double-dot system with temperature $T=0.01,0.05,0.1,0.2$, from the top to bottom.

Figure 4

(Color online) The zero bias conductance as the function of gate voltage under different magnetic flux.

Figure 5

(Color online) The normalized dc conductance as the function of magnetic flux $\Phi$.