The Chern number is just a property of a band and does not come with an energy scale, so there is no reason to expect to encounter Chern bands only at low temperatures. Indeed, bands with finite Chern numbers have been shown to support quantized Hall effects in graphene quantum Hall devices at room temperature and high magnetic fields, as illustrated in Fig. 8.5A,B. The energy scale in a Chern magnet is set by the band gap produced by magnetic interactions. So if we’d like to know what the maximum temperature at which we can expect to find Chern magnets is, we need to think about the energy scales of known magnets. Magnetism is an interaction-driven electronic phase, and interaction-driven phases almost always melt at sufficiently high temperatures. However, among interaction-driven electronic phases ferromagnetism is particularly stable. Many common transition metals, including iron, cobalt, and nickel, support ferromagnetism into the range 600-1200 K, and all of these have found applications in a variety of electronic technologies as a result. These are of course all three dimensional crystals, vertical farm tower and Chern magnets are two dimensional crystals. So the next question we can ask is: do two dimensional magnets exist with Curie temperatures as high as room temperature?
The answer turns out to be yes, as illustrated in Fig. 8.5C,D. This magnetic system appears not to be a Chern magnet, unfortunately, but the point is that there is nothing in particular stopping a Chern magnet with a Curie temperature above 300 K from existing. The first intrinsic two dimensional ferromagnets were discovered in 2017, so I think it’s safe to say that our field hasn’t yet come particularly close to identifying all possible two dimensional magnets. It’s hard to do an accurate accounting of all of the so-far discovered two dimensional magnets, and it is certainly the case that many of these are are not Chern magnets. But of the two dimensional magnets we have found, a surprisingly large fraction are intrinsic Chern magnets. We know of eight intrinsic Chern magnets stable in the absence of an applied magnetic field in the published literature so far. These are presented, along with a few of their basic properties, in Table 8.1. We have discussed several of these materials in this thesis, but we have also skipped a few,including the only currently known intrinsic Chern magnet in an atomic crystal, i.e., not on a moir´e superlattice: MnBi2Te4. These other materials all also represent areas of active research. Of the Chern magnets we know about, 2/8 have C < 0 with B > 0, so that property might be quite common. Indeed, there’s no particular reason to expect the B > 0 ground state to have one sign of the Chern number over the other as far as I know. It’s worth mentioning that if we ever find one, a room temperature Chern magnet with C < 0 for B > 0 would also have extremely large ∆m, and will therefore likely be switchable, since ∆m increases linearly with EGap.
It is also the case that two of these materials have been observed to be switchable with pulses of electric current, although it is not yet clear if the tBLG/hBN and ABMoTe2/WSe2 Chern magnets share a common current-switching mechanism, or if their respective mechanisms would generalize well to large gap Chern magnets. I think it’s clear that we are in the early days of the study of this class of material systems, and without discovering more Chern magnets there is little we can say with much generality. All of this is to say that I don’t think it’s crazy to expect to discover Chern magnets at much higher energy scales than we have already encountered, and that should we ever find such a system, there are a variety of intriguing technological applications for which this class of material systems could be exploited.Over the course of my PhD, four nanoSQUID microscopes were proposed, and construction began in some form on all of them. By the time I left we had finished three of these microscopes. The first nanoSQUID microscope we completed was inserted into a bath of liquid helium and could operate at 4 K. The CrI3 magnetic imaging campaign was performed in this system. The second nanoSQUID microscope had a pumped He-4 evaporative cooling pot, and could reach temperatures of 1.5 K. The tBLG/hBN Chern magnet transport measurements, the tBLG/hBN Chern magnet imaging measurements, and the AB-MoTe2/WeSe2 Chern magnet imaging measurements were all performed in this system. The third nanoSQUID microscope had a closed cycle He-3 sorption pump cooling system, and could reach 300 mK. The fourth and final microscope remains under construction, and is designed to operate inside of a dilution refrigerator.
Pictures of several of these microscopes are shown in Fig. 8.6. Acoustic isolation chambers and the 300 mK system are not shown. All nanoSQUIDs have liquid He-4 baths for primary stage cooling, and all are mounted on several thousand pound vibration isolation tables floating on air legs to protect the nanoSQUID sensors from mechanical and acoustic shocks close to the surface. The nanoSQUID sensor circuit is fairly simple, with only one important non-standard circuitelement in it, other than the nanoSQUID itself of course. This is the series SQUID array amplifier. Current is forced into the nanoSQUID sensor in parallel with a shunt resistor of comparable resistance to the nanoSQUID sensor in the voltage state, which is generally a few Ohms. Current through the nanoSQUID side of the circuit is inductively coupled to a series of identical SQUIDs. These SQUIDs in series generate a large voltage, which is detected at room temperature. Current is forced through a feedback coil to maintain constant flux through the SQUIDs in series. This allows the circuit to maintain sensitivity over a wide range of currents . This current amplification circuit has good current sensitivity and enormous dynamics range, easily able to accommodate the several hundred µA necessary to reach the critical current of the nanoSQUID sensor. There are a lot of things that make scanning probe microscopy tough relative to other techniques for performing microscopy. One particularly challenging issue is navigation of the sensor to the sample. Those experienced with optical imaging might be spoiled by a contrast mechanism that is sensitive to a ton of different phenomena- the nanoSQUID can only see local gradients in magnetic field and temperature, vertical plant tower and those are rare unless you have intentionally built structures and devices that generate them for use in navigation. In particular, large thermal gradients and variations in local magnetic field aren’t general properties of surfaces, so it’s very easy to blunder a nanoSQUID sensor into a surface without ever seeing it coming! Experiments are thus much safer and more expedient if we can provide the nanoSQUID sensor with topographic feedback- i.e., some way of detecting surfaces without crashing into them and destroying the sensor. We did this using shear force microscopy, which is a form of atomic force microscopy, or AFM. There is nothing particularly atomic about this contrast mechanism in the nanoSQUID microscope- we don’t have nearly that much resolution- but it is incredibly useful for navigation because it allows us to safely and reliably detect surfaces without destroying the SQUID. Researchers and companies building scanning tunneling microscopes will often accomplish this by gluing their sensor, which is a microscopic metallic wire, onto a piezoelectric tuning fork and then exciting the tuning fork at its resonant frequency. This is a good strategy, but it must be modified for use with the nanoSQUID sensor, because the nanoSQUID sensor is considerably more massive than scanning tunneling microscope wires, so it cannot be glued onto the tuning fork without destroying its quality factor. We preserve the tuning fork’s quality factor by instead pressing a piezoelectric tuning fork against the side of the nanoSQUID sensor and performing shear force microscopy instead of tapping mode microscopy.
The glass micropipettes serving as substrates for the nanoSQUID sensors are so thin that they bend easily when pressed agains the tuning fork, and this keeps them in mechanical contact with the fork. An optical microscope image of a nanoSQUID sensor pressed against a tuning fork is shown in Fig. 8.8A, and the resonant frequency of the piezoelectrically driven tuning fork is shown in Fig. 8.8B, with a fit to a Butterworth Van-Dyke model. A phase-locked loop and PID feedback system together allow us to approach the surface with the nanoSQUID sensor, detect it without crashing into it and destroying the tip, and maintain feedback while scanning. Schematics of this assembly are shown in Fig. 8.9. A calibration of the scan range and height of the nanoSQUID AFM is shown in Fig. 8.10, with a comparison to a Bruker Icon AFM displayed as well.By far the most common experimental campaign for the nanoSQUID microscope during my time in Andrea’s lab involved being handed a sample fabricated primarily for transport or capacitance measurements, with little consideration afforded to the viability or ease of a scanning probe microscopy campaign on the sample. I think this is fairly common in scanning probe microscopy, and it often means that we need to get sensors to samples without much in the way of navigation infrastructure. For this reason the vast majority of nanoSQUID microscopy campaigns start with thermal navigation. Before cooling down the nanoSQUID microscope, an attempt is made to align the nanoSQUID sensor with the heterostructure under an optical microscope, but the nanoSQUID sensor often still starts several hundred microns away from the sample. Once the system is cold, we generally proceed by injecting a few mBar of helium gas into the sample chamber. This facilitates thermal transport between the nanoSQUID sensor and the sample. We then run an AC current through the sample, heating it and generating an AC temperature distribution. The nanoSQUID sensors are excellent thermometers as well as magnetometers, so we can use this thermal gradient to navigate to the sample. An image of the resulting distribution of temperature over the device is shown in Fig. 8.13A. Some of the details are described in a later section, but in summary this technique works surprisingly well- we can usually find samples even several millimeters away from the nanoSQUID sensor using this technique. Once the nanoSQUID is reasonably close to the sample, it is usually necessary to pump out the heat exchange gas before attempting magnetic imaging, since thermal contrast can produce large backgrounds. After the heat exchange gas is removed, further navigation must proceed by imaging the magnetic fields produced by applied current through the Biot-Savart effect, as illustrated in Fig. 8.13B. There are a few engineering challenges associated with fabricating nanoSQUID sensors. I will briefly describe a particularly challenging one in this section. Many of the best elemental superconductors are soft, heavy metals with low melting points like lead and indium. As any person who has spent some time in an experimental physics laboratory knows, solder doesn’t wet too many materials well, and it certainly doesn’t wet glass, so these metals tend to form droplets when deposited onto glass substrates. To form a uniform film, the superconducting metal must freeze instantly upon landing on the glass micropipette. To make sure this occurs, we must cryogencially cool the glass micropipettes while evaporating the superconducting metal onto them. This process involves specialized machinery that is covered in great depth in other documents and publications, so I won’t discuss it here. However, I do want to discuss the nature of the failure modes of this process. When liquids don’t wet surfaces well, they dewet into droplets, and these droplets tend to get more spherical and less film-like the worse they wet the surface. If this process is allowed to proceed to its conclusion before deposited metal solidifies, the resulting films won’t be connected at all, and your nanoSQUID circuit will be open. If the substrate is cold enough, the resulting film will at least be continuous, and it is likely that you will get a nanoSQUID. However, the formation of droplets is impossible to completely stop, especially near the edges of films and on the oblique surfaces of the nanoSQUID sensor . These droplets generally won’t short the sensor, but the nanoSQUID sensor is so small that electrons can reach these droplets through tunneling processes. Whenever droplets form between the two superconducting contacts on the nanoSQUID sensor electrons can tunnel between the contacts through the droplet, with the droplet functioning as a quantum dot.