Electron number fluctuations and charge stability in a triple-island system via path integral Monte Carlo simulation

We employed a path-integral Monte Carlo (PIMC) approach to calculate the average electron number in a triple-island system (TIS) and to sketch the corresponding charge stability diagram. When the middle gate is set to zero, the central island settles into an unoccupied state, simply because the charging energy makes that the most stable configuration. The resulting stability diagram resembles the familiar two-island honeycomb structure. However, when the middle dimensionless gate voltage is tuned to a half-integer value, the middle island no longer settles on a definite charge; instead, it hovers at a fractional value due to the influences of the tunnelling and Coulomb forces. These quantum fluctuations soften the usual Coulomb-staircase steps and stretch the surrounding stability boundaries, as reflected in the PIMC simulations. Although the method is technical, the main message is that the PIMC framework captures these charge configurations without relying on perturbative assumptions, and it clearly shows when and how the charge begins to delocalize across the islands, a key feature for understanding mesoscopic Coulomb blockade systems.