Many magnetometers are sensitive to magnetic flux, not field, so very high magnetic field sensitivities are achievable by simply sampling a large region, but of course that is not a useful option when imaging microscopic magnetic systems. Suffice to say that nanoSQUID sensors, which had been invented in 2010 and integrated into a scanning probe microscope by their inventors by 2012, combine high spatial resolution with very high magnetic field sensitivity. This combination of performance metrics was and remains unique in its ability to probe the minute magnetic fields associated with gate-tunable electronic phenomena at the length scales demanded by the size of the devices. Gate-tunable phenomena in exfoliated heterostructures and nanoSQUID microscopy were uniquely well-matched to each other, and although at the time I started my graduate research only a small handful of gate-tunable magnetic phenomena had so far been discovered in exfoliated two dimensional crystals, nanoSQUID microscopy seemed like the perfect tool for investigating them.So what exactly is nanoSQUID microscopy? We can start by discussing Superconducting Quantum Interference Devices, or SQUIDs. In summary, SQUIDs are electronic devices with properties that strongly depend on the magnetic field to which they are exposed, which makes them useful as magnetometers. I won’t delve into the details of how and why SQUIDs work here, growing lettuce hydroponically but I will explain briefly how SQUIDs are made, since that will be necessary for understanding how nanoSQUID imaging differs from other SQUID-based imaging technologies.
A SQUID is a pair of superconducting wires in parallel, each with a thin barrier in series . The electronic transport properties of this device depend strongly on the magnetic flux through the region between the wires, i.e. inside the hole in the center of the device in Fig. 1.3. To be a little bit more precise, superconductors transport current without dissipation, so long as the current density stays below a sharp threshold. When this threshold is exceeded, the superconductor reverts to dissipative transport, like a normal metal. Above this critical current, in the so-called ‘voltage state,’ electronic transport is dissipative and highly sensitive to B. Any non-superconductor can function as a barrier, including insulators, metals, and superconducting regions thinner than the coherence length.This makes SQUIDs excellent magnetic field sensors, with the caveat that they do not sample the magnetic field at a point, but averaged over a region A. Making a SQUID is as easy as depositing a superconducting material onto a surface in the correct shape, and it can be done using many of the same techniques used to produce other microscopic electronic devices, like photolithography and thermal evaporation. This is sufficient for many applications, but it presents some issues for producing sensors for scanning probe microscopy. Scanning probe microscopy is a technique through which any sensor can be used to generate images; we simply move the sensor to every point in a grid, perform a measurement, and use those measurements to populate the pixels of a two dimensional array . This can of course be done with a SQUID, and many researchers have used SQUIDs fabricatedthis way to great effect. But the spatial resolution of a scanning SQUID magnetometry microscope is set by the size of the SQUID, and there are limits to how small SQUIDs can be fabricated using photolithography.
It is also challenging to fashion these SQUIDs into probes that can be safely brought close to a surface for scanning; photolithography produces SQUIDs on large, flat silicon substrates, and these must subsequently be cut out and ground down into a sharp cantilever with the SQUID on the apex in order to get the SQUID close enough to a surface for microscopy. In summary, the ideal SQUID sensor for microscopy would be one that was smaller than could be achieved using traditional photolithography and located precisely on the apex of a sharp needle to facilitate scanning. As is so often the case when developing new technologies, we have to make the best of the tools other clever people have already developed. In the case of nanoSQUID microscopy, the inventors of the technique took advantage of a lot of legwork done by biologists. Long ago, glass blowers found that hollow glass tubes could be heated close to their melting point and drawn out into long cones without crushing their hollow interiors. Chemists used this fact to make pipettes for manipulating small volumes of liquid, and biologists later used the techniques they developed to fashion microscopic hypodermic needles that could be used to inject chemicals into and monitor the chemical environment inside individual cells in a process called patch-clamping. A rich array of tools exist for producing these structures, called micropipettes, for chemists and biologists. Eli Zeldov noticed that these structures already had the perfect geometry to serve as substrates for tiny SQUIDs. By depositing superconducting materials onto these substrates from a few different directions, one can produce superconducting contacts and a tiny torus of superconductor on the apex of the micropipette. The same group of researchers successfully integrated these sensors into a scanning probe microscope at cryogenic temperatures.
The sizes of these SQUIDs are limited only by how small a micropipette can be made, and since the invention of the technique SQUIDs as small as 30 nm have been realized. We call these sensors nanoSQUIDs, or nanoSQUID-on-tip sensors. A few representative examples of nanoSQUID sensors are shown in Fig. 1.4. A characterization of the electronic transport properties of such a sensor, and in particular the sensor’s response to an applied magnetic field, is shown in Fig. 1.5. NanoSQUID microscopes share many of the core competencies of more traditional, planar scan-ning SQUID microscopes. They dissipate little power, and the measurements they generate are quantitative and can be easily calibrated by measuring the period of the SQUID’s electronic response to an applied magnetic field. Measuring a magnetic field with a SQUID does not require optical access; many other magnetic field measurement techniques do. Together, these facts mean that scanning SQUIDs are often the best tools available for probing extremely low temperature phenomena. NanoSQUID sensors also have many advantages over planar SQUIDs. The most obvious, of course, has already been discussed, and that is their higher spatial resolution. A less obvious advantage- indeed, an advantage that became clear only after the first nanoSQUID sensors were fabricated and tested- is the geometry of the thin superconducting contacts, which under normal circumstances are aligned with the axis of the applied magnetic field. Large magnetic fields tend to destroy superconducting phases, so superconducting devices are all limited by the maximum magnetic fields at which they can operate. This so-called critical field HC is not an intensive property; there is a large-size limit that can be measured and tabulated for different materials, but the critical field of an individual piece of superconductor is a strong function of geometry. A thin superconducting film in the plane of an applied magnetic field can accommodate much higher magnetic field magnitudes than can be accomodated by a large piece of the same superconductor. The bulk limit for lead at low temperature is about 80 mT; we routinely make lead nanoSQUIDs that can survive magnetic fields of 1 T, and we have on occasion made nanoSQUIDs that can survive magnetic fields above 2 T. It turns out that many of the most useful magnetic imaging techniques are limited to low field operation. This thesis will focus primarily on low field phenomena, but there are also many magnetic phenomena that require high magnetic fields to appear, including the quantum Hall effect and a variety of magnetic phase transitions. The nanoSQUID technique is useful for studying these as well.It remains true that superconducting materials with higher bulk critical fields tend to produce nanoSQUIDs with higher critical fields, growing hydroponically so we must choose the material with which we fabricate nanoSQUID sensors carefully for each application. Characterizations of nanoSQUIDs fabricated from both lead and indium are shown in Fig. 1.6. In the bulk limit, indium has a critical field of HC = 0.03 T. A characterization of electronic transport through an indium nanoSQUID is presented in Fig. 1.6A. Periodic oscillations in the critical current are visible; in this regime, thenanoSQUID is useful as a sensor of local magnetic field. Above about 0.2 T, superconductivity begins to rapidly degrade in the nanoSQUID sensor, destroying the sensitivity of the sensor and rendering it useless as a sensor of magnetic field. This limits this particular nanoSQUID to operation in the regime −0.2T < B < 0.2T. This is fairly general to indium nanoSQUIDs; their precise critical fields vary, but are generally considerably below those of lead nanoSQUID sensors. As with any sensor, measurements with nanoSQUIDs are contaminated with noise, and the dependence of that noise on SQUID bias and magnetic field can be characterized.
A characterization of the noise spectrum of the indium nanoSQUID shown in Fig. 1.6A is shown in Fig. 1.6B. In nanoSQUID sensors, local maxima in critical current are often associated with high noise and thus low magnetic field sensitivity . This produces ‘blind spots’ in magnetic field for nanoSQUID sensors. These blind spots often in practice include B = 0, making true zero-field operation challenging for nanoSQUID sensors. Technologies exist for circumventing this issue, but in practice we mostly work around it. The low magnetic field DC response of a lead nanoSQUID is shown in Fig. 1.6C. A higher magnetic field characterization is shown in Fig. 1.6D, illustrating the collapse of superconductivity in this nanoSQUID at a considerably higher magnetic field of about 0.75 T. The inventor of the technique has been active in developing ways to deposit other materials onto micropipettes for use as nanoSQUID sensors, and has succeeded in producing aluminum, niobium, tin, and alloyed molybdenum/rhenium nanoSQUIDs, in addition of course to indium and lead nanoSQUIDs. The MoRe nanoSQUIDs in particular are capable of operating in extremely large ambient magnetic fields, up to about 5T [6]. The magnetic field noise floor of nanoSQUID sensors seems to vary for different materials as well. We do not have a strong model explaining why this is the case, but it is empirically true that indium and lead nanoSQUIDs have particularly low noise floors. Plots illustrating the dependence on magnetic field of the magnetic field sensitivity of a lead nanoSQUID sensor 80 nm in diamater are shown in Fig. 1.7. NanoSQUID sensors have some unique disadvantages as well. Like planar SQUIDs, nanoSQUIDs require superconductivity to function, which limits them to fairly low operating temperatures. In planar SQUIDs it is often possible to keep the SQUID itself cold while scanning over a much hotter sample, but nanoSQUID sensors are extremely poorly thermalized to their scan heads, which meansthat they generally are thermalized either to the surface over which they are scanning or to the black body spectrum of the vessel in which they are contained . This gives nanoSQUID sensors some interesting capabilities, namely that under the right conditions they can function as extremely sensitive scanning probe thermometers, but it also comes with some drawbacks. NanoSQUIDs composed of superconductors with critical temperatures below 4.2 K, the boiling point of helium-4 at atmospheric pressure, must thus have actively cooled thermal radiation shields to operate in very high vacuum, and of course imaging of hot samples is completely out of the question for these sensors. A variety of exciting opportunities exist for the application of sensitive magnetic imaging techniques to biological systems, and this is not a realistic option for nanoSQUID sensors. NanoSQUIDs are quite fragile and can be easily destroyed by vibrations, necessitating vibration isolation systems, and the superconducting film on the apex of the micropipette is quite thin, typically between 15 and 20 nm, so superconducting materials that oxidize in air will be quickly degraded. Thankfully indium and lead do not oxidize rapidly, but they do oxidize at a finite rate, so nanoSQUIDs composed of these materials only last for a few days when left in air. Storage in high vacuum can improve their lifespan, but generally not indefinitely. In summary, scanning probe microscopes fitted with nanoSQUID sensors can function as magnetometry microscopes with 30-250 nm resolution. Their high sensitivities allow them to detect the minute magnetic fields emitted by electronic phases composed entirely of electrons forced into a two dimensional heterostructure with an electrostatic gate. We will discuss some of the properties of two dimensional heterostructures next.