ROUGH DRAFT authorea.com/57964

Coulomb drag: An experimental evidence

Coulomb drag describes the situation where a current flowing in a so-called “drive” conductor, Coulomb interacting with a “drag” conductor, induces a voltage accros the “drag” conductor. There are already some experimental clues that have attempted to measure Coulomb drag in nanowires (Laroche 2011), Luttinger systems Yama(Yamamoto 2012) and recently in quantum dots (Hartmann 2015).

In double quantum dot system Coulomb drag was investigated within the framework of sequential tunneling using the Master equation formalism. In such work, a drag current is obtained when four states of charge are considered and when the tunneling rates depend on energy, i.e., on the charge state. These results were valid when the temperature of the system is much higher than the tunneling rate. A previous experiment by Hartmann(Hartmann 2015) measured the voltage fluctuations in a double quantum dot setup for a base temperature of $$4.2$$ K ($$360\mu eV$$). However, it was not measured the tunneling rates.

In the D. Goldhaber-Gordon experiment, the base temperature is $$T=20 mK$$ and a double quantum dot coupled capacitatively is considered. The measurements are done to obtain the $$dI_{i}/dV_{Si}$$ where $$i=\{1,2\}$$ labels each dot. There are in-plane and out-of-plane magnetic fields applied of magnitudes $$2$$ and $$0.1$$ T, respectively that do not alter the measurements.

Differential conductances $$G_1$$ and $$G_2$$ versus the dot gates $$\epsilon_1$$ and $$\epsilon_2$$ the triple points indicate when the number of electrons changes in both dots.

The peaks observed in $$G_1+ G_2$$ vs. the dot levels $$\epsilon_i$$ indicate the stability diagram for this setup. The tunneling rates are computed from the nonlinear differential conductances. From these measurements it seems that the tunneling rates $$\Gamma_i$$ and $$\gamma_i$$ are quite similar indeed. Measurements of $$G_2$$ were insensitive to situations where the dot level in dot $$1$$ was occupied or not. There are two striking features in the experiment:

• A drag current in dot $$2$$ was detected, with $$I_2\approx 40 pA$$ even thought the two tunneling rates $$\Gamma$$, and $$\gamma$$ were quite similar, in contradiction with the proposed theory.

• Even more striking the fact that for the situation where charge fluctuations in dot $$2$$ were almost suppressed a drag current on dot 2 is observed. The drag current $$I_2\approx 0.5 pA$$ decreases as $$-\epsilon_2$$ grows.