Average electron number in two-island system

We studied the charge fluctuation in a two-metallic island system using a quantum Monte Carlo simulation. The imaginary-time path integral approach was used to express the system's grand canonical partition function. The average excess charge number on the islands was calculated using the distribution of the winding numbers. In the absence of a source-drain voltage, we found that an average electron number exhibited a Coulomb staircase phenomena and the function of the two gate voltages. Furthermore, as the temperature increased, the sharp step of the Coulomb staircase was smeared out. As a result, the system behaved as a single-electron box containing two coupled islands. We also suggest constructing a quantum stability diagram that accounts for the tunneling effect and temperature dependency from the average electron number. The calculation can be used to investigate the effect of the tunneling conductance on a honeycomb shape. •The average electron numbers of the two-island system were calculated by the quantum Monte Carlo method.•A quantum stability diagram calculation accounting for the tunneling effect and temperature dependency was proposed.•The quantum stability diagram is a tool for understanding island systems beyond the classical picture.