Four-terminal transport: why use four wires?
Two contacts carry current into and out of a sample. A separate pair measures the voltage between two points along it. This selects the part of the sample of interest and greatly reduces the contribution from the current leads and contacts.
Separate the current path from the voltage measurement
Imagine four contacts numbered 1 to 4 along a narrow strip. Drive current from 1 to 4 and measure the potential of 2 relative to 3. The voltmeter’s high input impedance draws very little current, so the voltage drop along its leads is small. In the ohmic regime, the ratio of the measured voltage to the applied current gives the resistance of the segment between 2 and 3.
Reverse the current and measure again
A small temperature difference between junctions can add a voltage comparable to a microvolt-scale signal. Keep the voltage leads in the same orientation and measure first at +I, then at −I of equal magnitude. The resistive voltage changes sign. A thermal offset that stays constant between readings cancels when the two voltages are subtracted.
For example, suppose the readings are +12 μV at +1 μA and −8 μV at −1 μA. They include a stable +2 μV offset. Half their difference is 10 μV, which gives a resistance of 10 Ω.
From resistance to resistivity
At zero magnetic field, a uniform bar carrying uniform current along its length has resistivity ρ = R₄A/L, where A is its cross-sectional area and L is the spacing of the voltage contacts. A different sample shape or contact layout can require a different geometrical conversion. Repeating a measurement at lower current also helps check whether Joule heating is changing the sample temperature.
Measurement schematic and relation
I is the positive current magnitude in amperes. V is the voltage in volts with a fixed lead orientation. This expression gives R₄ in ohms for a linear response under stable measurement conditions.
Reading Figure 2: the normalized resistance axis
In Figure 2a of the few-layer MoTe₂ study, each sample’s resistance is divided by its own value at 250 K before the cooling curves are compared. Every curve therefore equals 1 at 250 K, making relative changes easy to see. To recover a resistance in ohms, you would need that sample’s resistance at 250 K.
Open the original experiment ↗Papers from the group
- Giant enhancement of superconductivity in few layers MoTe₂Chinese Physics B · 2019