Near one interdot charge transition of the honeycomb, only two charge states matter: (N₁,N₂) and (N₁−1,N₂+1). Their electrostatic energies from the constant-interaction model form two straight "diabatic" lines that cross linearly in the detuning ε (the gate-voltage combination that drives one electron from dot 1 to dot 2):
E_L(ε) = −ε/2 E_R(ε) = +ε/2
Interdot tunnel coupling tc couples these two basis states through the 2×2 Hamiltonian
H = [ −ε/2 t_c ]
[ t_c ε/2 ]
whose eigenvalues E± = ±√((ε/2)² + t_c²) are the adiabatic bonding/antibonding levels plotted as solid curves — this is exactly the avoided crossing that rounds each honeycomb triple point into a smooth hyperbola, with minimum gap 2tc at ε=0. The same tc and thermal broadening Γ set the resonant tunneling current through the classic Lorentzian:
I(ε) = t_c² / (ε² + t_c² + Γ²)
The ground-state eigenvector gives the electron's localization: mixing angle θ = ½·atan2(t_c, ε/2), left/right dot probabilities cos²θ and sin²θ. Far from ε=0 the electron sits entirely in one dot; at ε=0 it is a 50/50 bonding superposition — the same physics Van der Wiel et al. (Rev. Mod. Phys. 75, 1 (2003)) use to extract tc from real transport data, shown here as a sweep through the transition rather than as a 3D honeycomb height map.
- tc — sets the minimum level gap 2tc and the peak tunneling current; at tc=0 the levels cross sharply and the current vanishes.
- ECm — sets how far apart consecutive triple points sit on the honeycomb, widening the swept detuning range shown here.
- EC1 — single-dot charging energy; sets the gate-voltage-to-energy lever arm of the sweep.
- Γ — broadens the Lorentzian current peak independently of tc.