Hysteretic funnel structures in vertical quantum dot molecules

We describe basic properties of hysteretic funnel-like structures in the tunneling current through two weakly coupled vertical quantum dots on application of a weak magnetic field applied parallel to the current in two regimes (referred to as I and II). Regime I is inside the two-electron spin blockade region at comparatively low source-drain bias. The hysteresis displayed in this regime is qualitatively similar, although quantitatively different, to that which was previously reported and attributed to the hyperfine coupling effect. Regime II is well away from the two-electron spin blockade region at high source-drain bias and in the opposite bias direction to where the spin blockade region is located. The hysteresis displayed in this regime has not been previously reported. We suggest how the two regimes may be related.