Extended Data Fig. 6: Ab initio simulations for local energy offsets.

a, Schematic of the methodology used in the ab initio simulations to reproduce the effect of a local energy offset. The amplitude of the potential V of one of the quantum wells is changed by an amount dV. The variation of the single-well potential by positive or negative dV gives unbalanced site energies. Besides, with the change of eigenstate basis, the hybridization and interaction parameters are also affected in the ab initio calculation. b, c, The ground-state energy and spin configuration (b) and the ferromagnetic to low-spin energy gap ΔE as a function of dV (c). When the potential detuning is dV = 0.11 meV or dV = −0.07 meV, the system undergoes a transition to a low-spin ground state. The transitions at these two directions have a different nature, as drawn in the insets. For dV > 0, the particular quantum dot is deeper and tends to trap more electrons. However, a negative dV raises the energy cost on the particular quantum well and leads to a lower probability of occupation in a three-electron system. Without the ‘mobile’ hole in the ‘half-filled’ system, the ground state becomes a low-spin state instead of a Nagaoka ferromagnetic state.