A way of making a : tear a single in two, rotate one half by a chosen angle and lay it back on the other. Because both halves come from the same crystal, the twist equals the rotation that was applied.
Going deeper
Tearing one flake in two and rotating one half gives a bilayer whose twist angle is known by construction, because both halves started with the same crystal axes. Everything after that is a fight to keep the angle where it was put.
Why tearing beats aligning
To build a twisted bilayer from two separate flakes, you have to know each flake’s crystal axes and align them on a rotation stage. Edges give a hint – a straight edge is usually a zigzag or armchair direction – but only to within a few degrees, and the two candidates differ by 30°. For physics, where a tenth of a degree matters, that is nowhere near good enough.
Tearing sidesteps the problem entirely. The stamp picks up part of a flake; the torn edge separates two pieces that were, a moment earlier, one crystal. Rotate the stage by θ and put the piece back down, and the misorientation between the halves is θ – not θ plus some unknown offset. The absolute crystal direction is still unknown, but for a twist angle that does not matter.
How well it works, and how it is checked
The same approach is what makes deliberately aligned stacks possible at all. Successive transfers of graphene can be used to build an artificial Bernal-stacked bilayer, and the evidence that it really is Bernal is worth listing because it is the standard checklist: a broad enough to need four Lorentzians, no moiré pattern visible under a , a flat in tunnelling spectroscopy, and a gap that opens with a transverse electric field. The same technique gives double-bilayer graphene stacks separated by boron nitride in which resonant tunnelling depends on rotational alignment.
For small twist angles, the moiré period itself is the measurement – a scanning probe or transmission electron image gives the angle directly. For transport devices the angle is often extracted afterwards from the at which the superlattice gaps appear, which is precise but tells you what you made rather than what you intended.
What the stack does next
A twisted bilayer is not in equilibrium. Aligned stacking is energetically preferred, so the layers relax: over time, and much faster when warm, twisted regions reconstruct into domains of stacking separated by walls, and the whole flake can creep back toward 0° or 60°. Any process step involving heat – including the used to keep interfaces clean – is in tension with keeping a twist angle.
The second problem is that the angle is not one number. applied during tearing and placement, bubbles, and local relaxation make the twist vary across a device, so a transport measurement averages over a distribution. Sample-to-sample and region-to-region variation in twisted bilayer graphene is a recognised difficulty and one reason results from nominally identical devices differ.
For specialists
Assembly of a twisted bilayer by picking up part of one flake, rotating it, and placing it on the remaining part.