# 2D or not 2D? MARVEL algorithm answers the question

*Last modifications on March 8, 2018*

Two-dimensional materials, such as graphene, are a new and exciting class of materials. No more than a few atomic layers thick, they have the most extraordinary properties, making them attractive for all kinds of applications. However, despite high expectations, progress in identifying new 2D materials has been slow: to date, only a few dozen have been identified experimentally. In their just-out *Nature Nanotechnology* paper, which made the cover page, "Two-dimensional materials from high-throughput computational exfoliation of experimentally know compounds", a team led by MARVEL director Nicola Marzari takes a computational route towards improving that count.

* Fiorien Bonthuis, EPFL, NCCR MARVEL*

The team developed a screening algorithm to identify 3D materials with layered crystal structures such that a single layer can easily be stripped off to yield a 2D material. Applying this algorithm to large materials databases, they were able to identify — by simulations alone — close to 2000 well-known inorganic compounds that may be exfoliated into novel 2D materials. Together with a further characterization of the properties of those materials, this approach promises to greatly streamline and accelerate the experimental and technological effort for new applications based on 2D materials.

What's the difference between a pencil and a lollipop? A thin sliver of candy won't even get you a sugar rush, but a very thin sliver of graphite will get you a Nobel Prize. Really. In 2010 Andre Geim and Konstantin Novoselov received the Nobel Prize in Physics "for groundbreaking experiments regarding the two-dimensional material graphene". From a piece of graphite just like that found in ordinary pencils, and using a strip of regular adhesive tape, they managed to obtain flakes of carbon just one atomic layer thick: graphene. Graphene's properties are so exciting that soon the search was on for other 2D materials.

Progress in identifying new 2D materials has been slow, however: graphene was isolated more than a decade ago, and since then only a few dozen more 2D materials have been isolated experimentally. "There is a huge knowledge gap here," Marco Gibertini says. "For 3D crystals there are big databases collecting all the knowledge accumulated over the past hundred years. For 2D crystals there's hardly anything yet."

The first step towards closing this gap is to get a bigger portfolio of potential 2D materials, the MARVEL team decided. The idea is that there must be many more pairs like graphite and graphene: 3D materials with layered crystal structures, such that a single layer can easily be peeled off (exfoliated) to yield a 2D material (see Fig. below).

To find those materials, we can't very well repeat the Nobel Prize winning method, and go around sticking strips of adhesive tape to every known material to see if a single atomic layer comes off. The sticky tape method may have worked with a single material, but for the hundreds of thousands of known crystals, it is hopelessly inefficient. Moreover, it would help to know in advance which materials are worth trying, and which are not: if the sticky tape method doesn't work at first, it may be because you have to try a bit harder, or it may be because it's simply never going to work.

Nicola MarzariThis is a nice example of how computational methods can really speed up materials discovery. It used to be that to find a new material with specific properties, chemists had to just start somewhere and try and try again — a method that requires long hours in the lab plus a lot of luck. MARVEL's goal is to save laboratories much of this painstaking and often frustrating work by predicting, on the basis of calculations, which materials are worth trying out, thus narrowing down and focusing the search.

This is where MARVEL's high-throughput computational methods come into their own. Basically, the idea is this. Some 3D materials, such as the graphite in pencils, have the right crystal structure to yield a 2D material, whereas others, such as the candy in lollipops, do not. If we can find a computational method to figure out in silico which materials are the pencils and which ones are the lollipops, we are in a much better position when we start experiments: we know where to look for potential materials, and we know when it's worth persisting with the sticky tape (or whatever other method), or when there's no point even starting. "This is a nice example of how computational methods can really speed up materials discovery," Nicola Marzari says. "It used to be that to find a new material with specific properties, chemists had to just start somewhere and try and try again — a method that requires long hours in the lab plus a lot of luck. MARVEL's goal is to save laboratories much of this painstaking and often frustrating work by predicting, on the basis of calculations, which materials are worth trying out, thus narrowing down and focusing the search."

Nicolas MounetThe initial geometrical filtering allows us to downsize the number of candidate materials to compute. Next, the binding energy criterion puts the laws of physics back into the process and allows us to refine the screening very precisely.

The MARVEL team developed what is essentially a computational account of the difference between pencils and lollipops: an algorithm to screen for the structural properties that make graphite, but not candy, exfoliable. Their algorithm is based on two criteria, which together articulate the intuitive idea that the 2D layers must already be contained in the 3D parent material, and that, moreover, they must be relatively easy to separate from the rest of the material. The first is a geometric criterion: the 3D crystal structure has to somehow contain flat, chemically connected substructures; the second is a binding energy criterion: between the layers there can only be weak van der Waals interactions, and no strong chemical bonds. The two criteria are implemented in a two-step approach, Nicolas Mounet explains: "The initial geometrical filtering allows us to downsize the number of candidate materials to compute. Next, the binding energy criterion puts the laws of physics back into the process and allows us to refine the screening very precisely."

The team then used their algorithm to screen two of the largest materials databases (totaling over 500'000 entries). They identified a total of 1825 materials that may be exfoliable — a portfolio of potential 2D materials that represents an almost 50-fold increase of the number of 2D materials that are currently known.

A final and methodologically important feature of the work is that the researchers made sure that all calculations can be reproduced by any computational scientist in the world. To this end, they used the AiiDA computational materials discovery infrastructure. AiiDA stores the full provenance of every single step in the calculations, for all materials. "By making these AiiDA workflows publicly available, anybody in the world can not only redo any of our calculations, but also replace our 3D materials with their own favorite 3D materials to see whether they can be exfoliated," Giovanni Pizzi explains. He adds, "In fact, it is thanks to AiiDA that we could do this kind of calculations in the first place: without this software we would not have been able to combine so many different kinds of data in a single algorithm."

## Reference

Nicolas Mounet, Marco Gibertini, Patrick Schwaller, Davide Campi, Andrius Merkys, Antimo Marrazzo, Thibault Sohier, Ivano Eligio Castelli, Andrea Cepellotti, Giovanni Pizzi, and Nicola Marzari, *Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds*, Nature Nanotechnology **13**, 246 (2018). doi:10.1038/s41565-017-0035-5

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