Monitoring the Motion of Charge Carriers in the Integer Quantum Hall Bulk with a Single Electron Transistor

Using an Al/AlO$_{x}$/Al single electron transistor on top of an antidot etched into a GaAs/AlGaAs heterostructure containing a two-dimensional electron gas, we studied the quantum Hall system in the middle of the $\nu$=2 plateau. In this highly insulating regime, oscillations in single electron transistor resistance indicate that the charges in the system adjust slowly ($\sim$ 1 hour) to changes in the back gate voltage or magnetic field. We find that after a small increase in magnetic field an excess of electrons leave the bulk. Moreover, the presence of the etched antidot under the SET creates a small but clear discrepancy between behavior after a change in magnetic field and change in back gate voltage indicating charging of the antidot after a change in magnetic field. When the antidot is accounted for we find the expected ratio of 2 electrons/flux quanta at $\nu$=2. We also present the time dependence of the charge equilibration for 18 mK to 280 mK. Bulk conductivities in the range of 10$^{-18}$-10$^{- 18}$ /$\Omega$ are obtained from this measurement and compared to conductivies obtained from lock-in measurements at high temperatures (1-10 K).