Transmission Fast Atom Diffraction through 2D materials

What is measured

A beam of neutral hydrogen crosses a free-standing monolayer and drifts about 93 cm to a position-sensitive detector a few centimetres across. At 150, 300, 600 and 1200 eV the transmitted atoms arrive in a clear hexagonal pattern — the reciprocal lattice of the sheet.

Running the same beam on a monocrystalline sample and on a polycrystalline one separates them immediately. The polycrystal smears its orders into rings, because the detector is seeing several domains at once; the monocrystal gives discrete spots. The method reads out crystalline quality as a by-product.

Why the intensities are the measurement

Where the spots fall only repeats what a diffractometer already knows. The information is in how bright each order is.

In the eikonal approximation, the amplitude of an order is a Fourier component of the phase the atom accumulates while crossing the sheet — and that phase is the interaction potential integrated along the path. The pattern is therefore a fairly direct image of the projected atom–surface potential, and any calculation of it is only as good as the potential fed in.

Three potentials, and only one survives

The poster puts three descriptions of that potential side by side, in order of increasing accuracy and increasing cost. A binary sum treats the sheet as independent atoms and neglects the bonds between them. A scaled electron density takes the unperturbed density of the sheet and scales it, which neglects what the incoming atom does to the surface. Density functional theory neglects only the dynamics of the crossing.

For hydrogen through graphene, only the DFT-level potential reproduces the measured intensities. That is the result: the experiment is sharp enough to reject two standard approximations, which makes it a test of the potential rather than of the lattice.

hBN and LiF: where the sub-lattices show

Hexagonal boron nitride has graphene’s geometry but two different atoms on its two sub-lattices. The projectile does not see them: over the range of approach that matters, the boron and nitrogen potential curves stay close enough together that the computed pattern is very hard to tell from graphene’s.

Helium on lithium fluoride is the opposite case. The ionic lattice is rigid and highly ordered, the charge is strongly localised, the two sub-lattices come out resolved — and there, unlike graphene, a rescaled binary model does reproduce the result. How localised the charge is decides whether the cheap model is good enough.

The take-home

Transmission of fast atoms through a monolayer is an interaction spectroscopy: it measures the atom–surface potential instead of assuming one. Other surfaces and other projectiles follow the same recipe.

Next is time-dependent density functional theory, which propagates the electron cloud during the crossing rather than solving for a static ground state — the one approximation still standing in the list above.

This page is a summary, written for whoever scanned the code on the poster. The poster itself carries the data, the error bars and the conditions; the paper below carries the argument in full.