Stack two sheets of graphene and turn one very slightly. At about 1.1 degrees the pattern they make together slows the electrons almost to a standstill, so they start acting collectively – and the pair can even become a .
Going deeper
Twisting one layer against another creates a moiré pattern whose period is far longer than the atomic spacing – about 13 nm at 1.1°. That long period folds the bands into narrow moiré minibands, and at the magic angle the lowest ones become nearly flat.
Why a small twist makes a large pattern
Two identical lattices rotated by a small angle θ coincide only occasionally, and the pattern of coincidences repeats with a period of roughly the divided by θ in radians. For graphene, with a spacing of 0.246 nm, a twist of 1.1° gives about 13 nm, so one cell contains something like ten thousand carbon atoms.
That long period acts as a superlattice potential. The Brillouin zone shrinks accordingly, the original bands fold into many narrow minibands, and electrons now respond to a structure two orders of magnitude larger than the atomic one. The idea that interlayer tunnelling in such a superlattice could flatten bands entirely was set out in 2011, before the experiments.
What is magic about 1.1°
Flattening is not a smooth function of angle. In the continuum description, the ratio between interlayer tunnelling and the energy scale of the moiré momentum passes through special values at which the velocity of the Dirac carriers renormalises to nearly zero. The first and most accessible of these is near 1.1°, where the lowest two bands per and become nearly flat, isolated from the rest by gaps.
With kinetic energy almost switched off, Coulomb repulsion dominates. states appear at partial fillings of the moiré cell, and superconductivity appears beside them, both discovered in 2018. Whether the pairing is conventional remains debated, and related physics has since appeared in twisted trilayers, twisted and graphene.
The practical difficulty is the angle
The magic angle is a narrow target: deviations of a tenth of a degree change the bandwidth substantially, and the twist is not uniform across a real device. Layers relax, forming domains of stacking separated by walls, and varies from place to place, so a nominal 1.1° sample can be a patchwork.
This is why the field invested in assembly, in local probes such as scanning tunnelling and nano- to map the local angle, and in devices small enough to sit inside one uniform region. It is also why early reproducibility was poor: two devices with the same nominal angle could behave quite differently, and a reported twist angle now needs to come with evidence of how uniform it was.
For specialists
The twist angle (about 1.1° for graphene) at which interlayer tunnelling makes the lowest moiré bands nearly flat.