Figure 4: Simulations of electron puddles in magnetic fields.

Spatial distribution of electron puddles in an imperfectly compensated Coulomb system at temperature T=0 K, simulated for the g-factor 6, characteristic Coulomb energy E_c=4.9 meV, and the degree of compensation K=0.95. The coloured surfaces represent where the spatially fluctuating Coulomb potential φ(r) becomes equal to (E₀−μ)−E_Z(B), which is the criterion for the puddle formation (E₀ is the energy of the conduction-band bottom in 0 T, μ is the chemical potential, and E_z is the Zeeman energy). As shown for the magnetic field B of (a) 0 T, (b) 7 T, and (c) 14 T, the volume of the enclosed regions increases with B due to the effect of the Zeeman energy. The chemical potential is assumed to be constant due to the pinning by the impurity levels, which work as a reservoir of delocalized carriers. Simulations are shown for a cube with a width of 40 nm corresponding to ∼3 × 10⁴ dopants. We have checked that the qualitative behaviour does not change in larger systems.