Apparatus and Procedures
Equipment Used
The equipment used was a Lock-in Amplifier (LIA), a Physical Properties Measurement System (PPMS), a power supply, a switch-box, a resistor, and a computer. The LIA and the 100 MΩ resistor were used together to create a current source of 10 nA with a unique frequency for noise reduction. The Power supply was used to control the charge carrier density through the back-gate voltage. The PPMS cooled the system to 2 K by evaporating liquid helium, applied the magnetic field, and connected chip's pins to the LIA for measurement. The computer gave the instructions to the instruments via GPIB wires and recorded the data collected. The Switch-box was the interface between the computer, the LIA, the PPMS, and the power supply.
Diagram of the Quantum Design PPMS [1]
The Quantum Design PPMS, Lock-in Amplifier and Resistor, Power Source, and Switch Box, respectively, used in this experiment
Two-Probe and Four-Probe Measurements
The locations of the contacts made to the sample are shown in the circuit diagram to the left. There are two different measurement techniques used: a two-probe and a four-probe. The two-probe uses only the yellow and green wires, while the four-probe uses all of the wires. A two-probe sample is significantly quicker to bond, but cannot measure the Hall Conductance independent of the Shubnikov-De Haas oscillations. A four-probe measurement is able to directly measure both, but requires more extensive electron beam lithography. Due to time restrains, we used the two-probe measurement for our sample.
Procedures
The data was taken by loading the sample into the PPMS, cooling the system, and then measuring the voltages probed for back-gate voltages ranging from -80V to +80V for each magnetic field strength. For our measurement, the magnetic field ranged from -8 to +8 T with a resolution of 0.5 T. These sweeps yielded a folder of text files, one file per magnetic field strength.
