Stacking two-dimensional sheets of atoms with precise control of their arrangement and orientation is impossible with typical materials growth techniques. Recent breakthroughs in assembling graphene-based devices with a particular rotational alignment between the layers has led to a series of revolutionary discoveries in the field of condensed matter physics. In this issue of Nature Materials and in two independent works, Gregory Burg and collaborators1 and Jeong Min Park and collaborators2 push the field even further, reporting on the assembly of some of the most complicated graphene superlattices to date in the search for interesting physics.

In clean monolayer graphene, electrons travel ballistically and at high speed, effectively ignoring each other. For two sheets of graphene stacked with a slight twist, the two lattices will periodically drift in and out of registry, forming a much larger-period moiré superlattice. When calculating the electronic band structure of this twisted bilayer graphene system, we must now account for the additional periodicity imposed by the moiré superlattice. Calculating the band structure as a function of the relative twist angle revealed that there are a series of ‘magic angles’ at which the group velocity of the electrons vanishes, so electron–electron interactions should determine how electrons arrange themselves3. The key caveat here is that the largest predicted magic angle is very specific: 1.1 ± 0.1°, where the ± corresponds to a rough range in which correlations should be strong. This angle corresponds to a 14 nm moiré period. One cannot simply arbitrarily stack two sheets of graphene and hope to obtain anywhere near this kind of angular accuracy. The brilliant solution to controlling the twist angle to a much higher degree of accuracy was to rip a single sheet of graphene in half and stack the two sections on top of each other with a relative twist4,5. This technique allowed for the successful fabrication of a magic-angle twisted bilayer graphene stack (MAT2G), which amazingly superconducted6.

An explosion of work on flat band moiré systems has followed. Recent theoretical work predicted that an n-layer stack of graphene, where the layers are orientated with a fixed alternating twist angle, maps exactly to coexisting twisted bilayer models7. For stacks with an even (odd) number of layers, n, there are n/2 ((n − 1)/2) twisted bilayer models at different twist angles (and an additional Dirac band). Therefore, each n-layer stack exhibits its own series of magic angles. With the correct angle, theory predicts the existence of flat bands where the ground states may also exhibit superconductivity or other correlated phenomena. Explicitly, the largest magic angle of MAT2G, θm, maps to 2cos(𝜋/n + 1)θm for n layers. The trilayer variant (MA3G) was the first alternating twisted stack to be realized and several such devices have exhibited evidence of superconductivity8,9.

Burg and collaborators have fabricated a pair of four-layer (MAT4G) devices (schematically shown in Fig. 1), one with a twist angle larger and one with a twist angle smaller than the expected magic angle. The former exhibits comparatively strong correlated insulating state but no signs of superconductivity. The smaller angle device exhibits evidence of superconductivity. Park and collaborators fabricated three MAT4G devices and two five-layer (MAT5G) devices, all with twist angles near their respective magic angles. All of the devices presented by Park and collaborators exhibit superconductivity. For the devices that do superconduct, they do so over an unexpectedly large range of carrier densities with transition temperatures comparable to the highest seen in MAT2G. Signatures of correlated insulating states are present in some of the MAT4G and MAT5G samples but generally seem weaker, probably due to the presence of the coexisting bands that are not flat in energy.

Fig. 1: Schematic drawing of MAT4G.
figure 1

The red monolayer graphene sheets are twisted relative to the black monolayer graphene sheets by an angle of θ. The interlayer spacing and twist angle between graphene sheets are not to scale.

Full size image

For nominally two-dimensional superconductors, a particularly interesting measurement is the magnetic field dependence of the superconducting state when the field is orientated in the plane of the sample. For truly two-dimensional samples, this measurement should be sensitive only to the electron spin (Zeeman effect) but not orbital motion. For conventional spin-singlet Bardeen–Cooper–Schrieffer superconductors, the Zeeman effect acting on the spin of the Cooper pairs leads to a Pauli limit at which superconductivity is destroyed: BP = (1.86 T K−1) × Tc, where Tc is the critical temperature at which the superconductivity vanishes. However, when applying an in-plane field to their nominally superconducting MAT4G and MAT5G samples, both sets of authors found that their evidence of superconductivity survived well beyond the Pauli limit (exciting the limit by at least a factor of ~2), suggesting that the state is not a spin singlet. Similar results have been consistently found in MAT3G samples but not in MAT2G samples. This difference in behaviour does not necessarily imply that the MAT2G and thicker stacks exhibit different superconducting mechanisms; we must consider the fact that the samples are not actually two-dimensional.

In an in-plane magnetic field, electrons receive a momentum boost when they tunnel between different layers, leading to a distortion of the Fermi surface10. As we add more layers, the momentum kick changes sign as we ascend layers so that the effect of adjacent pairs of layers cancel. Therefore, we expect to potentially observe this orbital effect only in even layer number stacks. Surprisingly, for MAT2G this coupling is comparable to the Zeeman effect and can lead to Cooper pair breaking, perhaps explaining the lack of Pauli limit violation. For MAT4G, despite its even number of layers, this orbital coupling is calculated by Park and collaborators to be substantially weaker, potentially explaining why a Pauli limit violation is observed in this case.

The results of these exciting papers probe into the nature of their samples’ superconductivity. It seems that the Pauli limit violation is intrinsic to the superconducting states and MAT2G is a special limit, suggesting that the superconductivity may be different from conventional spin-singlet superconductivity. To clarify this, measurements of the pairing symmetry are necessary. This will also give clarity on whether the mechanism is the same for all layer numbers or if there are subtle effects due to the slightly different symmetries between even and odd layer number stacks.

There are many additional questions that should be addressed. Twist angle disorder in the moiré superlattice plagues MAT2G samples, but the larger layer number systems surprisingly seem to lock into a common moiré despite their increased complexity. To ultimately obtain homogenous moiré devices, these relaxation mechanisms must be understood. Additionally, for more than two layers, the carrier density — which is extremely important in tuning the superconductivity — can no longer be uniformly controlled in all layers using conventional electrostatic gating techniques. Park and collaborators estimate the magnitude of this effect, but simultaneously solving for the inhomogeneity in the charge distribution and its effect on the electron–electron interactions will require very sophisticated modelling.