The magnetic field is a signed quantity, so you need to have a pretty strong model and a clear picture of your starting location to successfully use it to navigate. Thermal gradients can be handled with simple gradient ascent; this will almost always lead you to the region of your circuit with the greatest resistance, which is typically an exfoliated heterostructure if that is what you’re studying. You will likely need to have a helium atmosphere inside the microscope to pursue thermal navigation. A pressure of a few mBar is plenty, but be advised that this may require that you operate at elevated temperatures. Helium 4 has plenty of vapor pressure at 1.5 K, but this is not really an option at 300 mK, and many 300 mK systems struggle with stable operation at any temperature between 300 mK and 4 K. Higher frequencies will generally improve the sensitivity of the nanoSQUID, but if the heterostructure has finite resistance the impedance of the device might prevent operation at very high frequency. It’s worth mentioning that the ‘circuit’ you have made has some extremely nonstandard ‘circuit elements’ in it, because it relies on heat conduction and convection from the device through the helium atmosphere to the nanoSQUID. If you don’t know how to compute the frequency-dependent impedance of heat flow through gaseous helium at 1.5K, then that’s fine, because I don’t either!

I only mention it because it’s important to keep in mind that just because your electrical circuit isn’t encountering large phase shifts and high impedance, blueberries in containers doesn’t mean the thermal signal is getting to your nanoSQUID without significant impedance. I recommend operating at a relatively low frequency for these reasons, as long as the noise floor is tolerable. In practice this generally means a few kHz. I’d also like to point out that if you are applying a current to your device at a frequency ω, then generally the dominant component of the thermal signal detected by the nanoSQUID will be at 2 · ω, because dissipation is symmetric in current direction . Next you will perform your first thermal scan, 10-20 µm above the surface near your first touchdown point. If you have performed a thermal characterization, then pick a region with high thermal sensitivity, but generally this is unnecessary- I usually simply attempt to thermally navigate with a point that has good magnetic sensitivity. Bias the SQUID to a region with good sensitivity. Check the transfer function. Set the second oscillator on the Zurich to a frequency that is low noise . Connect the second output of the Zurich to the trigger of one of the transport lock-ins and trigger the transport lock-in off of it. Trigger the second transport lock-in off of the first one. Attach the output of one of the lock-ins to the 1/10 voltage divider, then to a contact of the sample. Attach the current input of one of the lock-ins to another contact as the drain. You can attach the voltage contacts somewhere if you want to, this is not particularly important though. It may be necessary to a apply a voltage to the gates, especially if you are working with semiconducting materials, like the transition metal dichalcogenides. In practice it is often useful to gate graphene devices too, because graphene samples tend to be resistive near charge neutrality, and you are trying to maximize dissipation power, which obeys P = V 2 R . Increase the voltage until you see 1 µA of current.

In my experience, members of the nanoSQUID team tend to be a little too timid about applying large currents to these samples because they are very susceptible to damage through electrostatic discharge, and of course it feels pretty bad to damage a device somebody else made for you. Although it’s true that researchers doing transport measurements almost never use currents as high as 1 µA, I can tell you that we have never damaged a heterostructure with high current at all, and certainly not at 1 µA. It is generally pretty safe to go as high as 100 µA, and we have gone considerably higher than that too. Currents greater than 1 µA will saturate the lock-in input, but you can still increase the voltage if you need to . Alternatively you can use the Ithacos adjustable transimpedance amplifier as the sink. If you do so, be careful not to adjust any of the knobs on this device while it is hooked up to the heterostructure, because adjusting those knobs can produce pulses of current large enough to damage devices. While you’re increasing the voltage, keep an eye on the SQUID signal. Increase the time constant if it helps you see the signal . Once you see a signal on the nanoSQUID channel of the Zurich, set up a scan. Check that the auxiliary outputs from the Zurich are going to the right ADC inputs, the right ADC inputs are correctly labelled in the scan window, the right auxiliary outputs are set up in the Zurich ‘Aux’ window and are sampling the right channels, and the right channels are set up and activated in the Zurich window. You should definitely see a thermal gradient if the signal is 3-5x the noise floor. If you don’t, I’d recommend investing some time into making sure the measurement is set up correctly you don’t want to just keep increasing current through the sample in response to not seeing features on a scan that isn’t set up right! If you get really frustrated and want a sanity check, click “Set Position” to each of the corners of the scan range and watch the signal on the Zurich control panelit should change if everything is working. There are a lot of issues that can affect scanning, and it isn’t really possible to cover all of themin this document, so you will have to rely on accumulated experience. Some problems will become obvious if you just sit and think about them- for example, if the thermal gradient is precisely along the x-axis and coarse positioner navigation is failing to find a strong local maximum it likely means that the y-axis scanner is disconnected or damaged. In Andrea’s lab, the basic circuits on the 1.5K and 300 mK systems as currently set up should be pretty close to working, so if there’s a problem I’d recommend observing the relevant circuits and thinking about the situation for at least a few minutes before making big changes. The scanners as currently installed on the 1.5K system do not constitute a healthy right-handed coordinate system, so to navigate you will need a lookup table translating scanner axes into coarse positioner axes. I think this issue is resolved on the 300 mK system, but this is the kind of thing that can get scrambled by upgrades and repair campaigns. In all of our note taking Power points and EndNotes, we have a little blue matrix that relates the scan axes to the coarse positioner axes. Use this to determine and write down the direction you need to move in the coarse positioner axes in your notes. You now have an initial direction in which you can start travelling. We will next perform long distance thermal navigation, at a height of 150 µm above the surface. Retract 150 µm using axis 3 of the coarse positioners. I’d recommend doing this in one or two big steps, planting blueberries in pots because the coarse positioner can slide in response to small excursions. Verify that you can still see the thermal signal on the SQUID. It is Ok if it’s faint or close to the noise floor; it will increase in size, and you know which directions to start travelling. If the resistive encoders are working , then use them to move in 100 um steps, checking the SQUID signal in between movements.

There is no need to ground the SQUID in between coarse positioner steps, there will be crosstalk but this is not hazardous for the nanoSQUID. If the resistive encoders are not working, click the Step+ button repeatedly until the SQUID signal increases to a maximum. This might take a few minutes or so of clicking. You can work on a software solution instead if you like , but remember that there is always a simple, safe solution available! Once the signal is at a maximum, take another scan to verify that you’re centered above the device. You should see a local maximum in the temperature in the middle of your scan region. Ground the SQUID. Ramp the current through the device down to zero. Zero and ground any gates you have applied voltages to. Ground the sample. Make sure the SQUID is grounded to the breakout box by a BNC . Hook up the second little red turbo pump to the sample chamber through a plastic clamp and o-ring, and turn it on. Slowly, over 10-20 minutes, open the valve to the sample chamber and pump it out. Make sure the sand buckets for vibration isolation are set up and the bellows aren’t touching the ground. If there are vibration issues you can often feel them on the bellows and on the table with your hand. Repeat the setup for approaching to contact, and approach to contact. Definitely watch the first few rounds of this approach! You can even watch the whole thing- it’ll take 30-45 mintues, but if you’ve messed something up then the approach will destroy both the SQUID and the device, because you’ve carefully aligned the SQUID with the device! Once you’ve reached the surface, you will set up the SQUID circuit. Attach the preamplifier to one of the SMA connectors at the top of the insert. Attach its output to the input of the feedback box. This output goes through the ground breaker that is clamped to the table in Andrea’s lab; all of these analog electronic circuits are susceptible to noise and ringing, so I’m sure there will be different idiosyncracies in other laboratories with other electromagnetic environments. Attach the output of the feedback box to the BNC labelled FEEDBACK . This is the BNC that should get a resistor in series if you wanted to increase the transfer function. We generally use resistors between 1 kΩ and 10 kΩ for this. To start with, just using nothing is fine . Plug the preamp and feedback box into fresh batteries . Turn the preamp on. Turn the feedback OFF. Hook up the SQUID bias wires to SQUID A and SQUID B. You can tell which they are because of the chunky low pass filters on the end, but of course they are also labelled. Make sure both sides of the SQUID are grounded while hooking it up- there is a BNC T there for a grounding cap for this purpose. Hook up Output 2 of the Zurich to signal input on the feedback box. Apply 1 V to signal input. There’s a good chance you just used this same output and cable to apply avoltage to the device, so be careful not to skip this step and apply this voltage to the device itself! You should see the SQUID array transfer function on the oscilloscope . Turn the rheostat/potentiometer on the preamp until this pattern has maximum amplitude. Turn the Offset rheostat/potentiometer on the feedback box until this passes through zero . There is a more sophisticated procedure for minimizing noise in the SQUID array; this is covered in great detail by documents Martin Huber has provided to the lab. But if you are a beginner this simple procedure will work fine. Flip the On switch on the feedback box, and watch the interference pattern vanish, replaced by a line near V = 0. Turn off the AC voltage going to signal input. You are now ready to characterize the SQUID, although you’ll need to unground it. That includes removing the BNC grounding caps from the T’s downstream of the SQUID bias filters and also flipping the BNC switch on the top of the rack. Click ‘preliminary sweep’ on the nSOT characterizer window. Sweep from 0 to 0.1. If you see a linear slope, a ton of stuff is working! The SQUID bias circuit, the SQUID array, the feedback electronics, all the cryogenics- that’s a really good sign. If you see no signal, don’t panic. Once again, there’s a lot of stuff involved in this circuit and a ton of mistakes you can make. Go back through the list and check everything, then check to make sure the SQUID bias isn’t grounded somewhere. Increase the sweep range until you see a critical current or you get above 3.3 V, which is where the feedback box will fail. If you don’t see a critical current, you have a SHOVET but not a SQUID. If you see a critical current, close the window, switch to the nSOT characterizer, and characterize the SQUID.