A double quantum dot is biased by two gate voltages Vg1, Vg2, each pulling a continuous "polarization charge" n₁⁰ = Vg1, n₂⁰ = Vg2 onto its dot. In the constant-interaction model the electrostatic energy of holding integer charges (N₁,N₂) is:
E(N1,N2) = ½Ec1(N1−n1⁰)² + ½Ec2(N2−n2⁰)² + Ecm(N1−n1⁰)(N2−n2⁰)
The ground state — the (N₁,N₂) that minimizes E — is plotted as a colored honeycomb cell across the gate-voltage plane; cell boundaries are Coulomb-blockade charge transitions. Along the diagonal boundary between neighboring cells that differ by one electron hopping dot-to-dot (N₁,N₂) ↔ (N₁−1,N₂+1), the two charge states become degenerate and interdot tunnel coupling tc hybridizes them into bonding/antibonding levels split by 2tc. This produces a resonant tunneling current, modeled here as a Lorentzian:
I(ΔE) = t_c² / (ΔE² + t_c² + Γ²)
where ΔE is the energy detuning between the two charge configurations and Γ is thermal/lifetime broadening. Rendered as a height field, this current forms a bright ridge exactly along the interdot transition line, peaking at the honeycomb's "triple points" — the well-known signature (Van der Wiel et al., Rev. Mod. Phys. 75, 1 (2003)) used experimentally to extract tc from real gate-defined double quantum dots.
- tc — raises and broadens the current ridge; at tc=0 tunneling is forbidden and the ridge vanishes (pure Coulomb blockade).
- ECm — interdot Coulomb coupling; larger values push the two triple points of each hexagon further apart, "opening" the honeycomb.
- EC1 — single-dot charging energy; rescales the cell size along the Vg1 axis.
- Γ — thermal/tunnel-rate broadening that smears the ridge independently of tc.