Double Dot Lab

Two quantum dots side by side, each with its own leads, repelling each other through the inter-dot interaction U12. Tune the two gate levels and the charge arranges itself into the plateaus of a stability diagram. Change the interactions and watch its shape change, then apply a bias or heat one lead to map currents, power and efficiency. Everything is computed with a fully analytical equation-of-motion solution, fast enough to redraw as you drag.

· click or drag on the map to pick a point
Gate levels (v1, v2)
Occupations (n1, n2)
Charge current I
Heat current Q (from L)
Power P = −IV
Efficiency η/ηC
Local spectral functions at the chosen point: dot 1 (amber) and dot 2 (blue) · shaded: transport window between μR and μL · the peaks sit at the addition energies vi, vi+Ui, vi+U12, … weighted by the residues

What you are seeing

  • Stability diagram. Each coloured plateau is a region where the charge on the two dots, (n1, n2), is locked to integer values. Lines between plateaus are where adding one electron costs no energy: the dots can exchange charge with the leads and current can flow.
  • Interaction regimes. When the inter-dot repulsion is weak (Regime I: U12 smaller than both Ui) the dots behave almost independently and the (1,1) region is wide. As U12 grows (Regime II) the (1,1) region shrinks, and in Regime III (U12 > (U1+U2)/2) it disappears: the electrons prefer to sit on the same dot.
  • Bias. A finite bias splits every charge-degeneracy line into a stripe of width eV where current flows. Inside the stripes the occupations take fractional values such as 2/3 or 4/3.
  • Heat engine. With the left lead hotter than the right one, a current flows even against a small opposing bias, and the double dot delivers power. The efficiency map shows where that conversion is most effective.
  • Spectral function. Each dot's spectrum is a sum of peaks at its addition and removal energies. Which peaks carry weight depends on the charge state of both dots, which is how the inter-dot interaction shows up in transport.

Model: parallel double quantum dot with intra-dot interactions U1, U2 and inter-dot interaction U12, each dot coupled to its own left and right leads with total coupling γ (wide-band limit), μL,R = ±eV/2. Green functions, occupations, charge and heat currents follow the fully analytical equation-of-motion solution, accurate in the Coulomb-blockade regime (kBT ≳ γ), with non-equilibrium correlators built from the average of the lead distributions. Energies in units of U2; currents in units of γ (e = ħ = 1). References: N. Sobrino, D. Jacob & S. Kurth, Phys. Rev. B 110, 115121 (2024); Phys. Rev. B 111, 115108 (2025); N. Sobrino, Phys. Rev. B 112, 235101 (2025). Reference implementation: github.com/Nahualcsc/EOM_DQD.