## Wednesday, March 07, 2018

### Superconductivity in graphene bilayers - why is this exciting and important

As I mentioned here, the big story of this year's March Meeting is the report, in back-to-back Nature papers this week (arxiv pdf links in this sentence), of both Mott insulator and superconductivity in graphene bilayers.  I will post more here later today after seeing the actual talk on this (See below for some updates), but for now, let me give the FAQ-style report.  Skip to the end for the two big questions:
 Moire pattern from twisted bilayer graphene, image from NIST.

• What's the deal with graphene?  Graphene is the name for a single sheet of graphite - basically an atomically thin hexagonal chickenwire lattice of carbon atoms.  See here and here.  Graphene is the most popular example of an enormous class of 2d materials.  The 2010 Nobel Prize in physics was awarded for the work that really opened up that whole body of materials for study by the physics community.  Graphene has some special electronic properties:  It can easily support either electrons or holes (effective positively charged "lack of electrons") for conduction (unlike a semiconductor, it has no energy gap, but it's a semimetal rather than a metal), and the relationship between kinetic energy and momentum of the charge carriers looks like what you see for massless relativistic things in free space (like light).
• What is a bilayer?  Take two sheets of graphene and place one on top of the other.  Voila, you've made a bilayer.  The two layers talk to each other electronically.  In ordinary graphite, the layers are stacked in a certain way (Bernal stacking), and a Bernal bilayer acts like a semiconductor.  If you twist the two layers relative to each other, you end up with a Moire pattern (see image) so that along the plane, the electrons feel some sort of periodic potential.
• What is gating?  It is possible to add or remove charge from the graphene layers by using an underlying or overlying electrode - this is the same mechanism behind the field effect transistors that underpin all of modern electronics.
• What is actually being reported? If you have really clean graphene and twist the layers relative to each other just right ("magic angle"), the system becomes very insulating when you have just the right number of charge carriers in there.  If you add or remove charge away from that insulating regime, the system apparently becomes superconducting at a temperature below 1.7 K.
• Why is the insulating behavior interesting?  It is believed that the insulating response in the special twisted case is because of electron-electron interactions - a Mott insulator.  Think about one of those toys with sliding tiles.  You can't park two tiles in the same location, so if there is no open location, the whole set of tiles locks in place.  Mott insulators usually involve atoms that contain d electrons, like NiO or the parent compounds of the high temperature copper oxide superconductors.  Mott response in an all carbon system would be realllllly interesting.
• Why is the superconductivity interesting?  Isn't 1.7 K too cold to be useful?  The idea of superconductivity-near-Mott has been widespread since the discovery of high-Tc in 1987.  If that's what's going on here, it means we have a new, highly tunable system to try to understand how this works.  High-Tc remains one of the great unsolved problems in (condensed matter) physics, and insights gained here have the potential to guide us toward greater understanding and maybe higher temperatures in those systems.
• Why is this important?  This is a new, tunable, controllable system to study physics that may be directly relevant to one of the great open problems in condensed matter physics.  This may be generalizable to the whole zoo of other 2d materials as well.
• Why should you care?  It has the potential to give us deep understanding of high temperature superconductivity.  That could be a big deal.  It's also just pretty neat.  Take a conductive sheet of graphene, and another conducting sheet of graphene, and if you stack them juuuuuust right, you get an insulator or a superconductor depending on how many charge carriers you stick in there.  Come on, that's just wild.
Update:  A few notes from seeing the actual talk.
• Pablo painted a picture:  In the cuprates, the temperature (energy) scale is hundreds of Kelvin, and the size scale associated with the Mott insulating lattice is fractions of a nm (the spacing between Cu ions in the CuO2 planes).  In ultracold atom optical lattice attempts to look at Mott physics, the temperature scale is nK (and cooling is a real problem), while the spatial scale between sites is more like a micron.  In the twisted graphene bilayers, the temperature scale is a few K, and the spatial scale is about 13.4 nm (for the particular magic angle they use).
• The way to think about what the twist does:  In real space, it creates a triangular lattice of roughly Bernal-stacked regions (the lighter parts of the Moire pattern above).  In reciprocal space, the Dirac cones at the K and K' points of the two lattices become separated by an amount given by $k_{\theta} \approx K \theta$, where $\theta$ is the twist angle, and we've used the small angle approximation.  When you do that and turn on interlayer coupling, you hybridize the bands from the upper and lower layers.  This splits off the parts of the bands that are close in energy to the dirac point, and at the magic angles those bands can be very very flat (like bandwidths of ~ 10 meV, as opposed to multiple eV of the full untwisted bands).  Flat bands = tendency to localize.   The Mott phase then happens if you park exactly one carrier (one hole, for the superconducting states in the paper) per Bernal-patch-site.
• Most persuasive reasons they think it's really a Mott insulating state and not something else, besides the fact that it happens right at half-filling of the twist-created triangular lattice:  Changing the angle by a fraction of a degree gets rid of the insulating state, and applying a magnetic field (in plane or perpendicular) makes the system become metallic, which is the opposite of what tends to happen in other insulating situations.  (Generally magnetic fields tend to favor localization.)
• They see spectroscopic evidence that the important number of effective carriers is determined not by the total density, but by how far away they gate the system from half-filling.
• At the Mott/superconducting border, they see what looks like Josephson-junction response, as if the system breaks up into superconducting regions separated by weak links.
• The ratio of superconducting Tc to the Fermi temperature is about 0.5, which makes this about as strongly coupled (and therefore likely to be some weird unconventional superconductor) as you ever see.
• Pablo makes the point that this could be very general - for any combo of van der Waals layered materials, there are likely to be magic angles.  Increasing the interlayer coupling increases the magic angle, and could then increase the transition temperature.
• This is very exciting, and has great potential.  Really nice work.
• I wonder what would happen if they used graphite as a gate material rather than a metal layer, given what I wrote here.   It should knock the disorder effects down a lot, and given how flat the bands are, that could really improve things.
• There are still plenty of unanswered questions.  Why does the superconducting state seem more robust on the hole side of charge neutrality as well as on the hole side of half-filling?  This system is effectively a triangular lattice - that's a very different beast than the square lattice of the cuprates or the pnictides.  That has to matter somehow.  Twisting other 2d materials (square lattice MXenes?) could be very interesting.
• I predict there will be dozens of theory papers in the next two months trying to predict magic twist angles for a whole zoo of systems.

Anonymous said...

As someone not in the field, I am curious as to how these twisted bilayers are made. Naively, I would think if I take two sheets of graphene and stack them it would be energetically favorable for the two layers to be aligned rather than twisted with respect to one another. Is there some reason that is not the case and you can arbitrarily change their orientation?

Douglas Natelson said...

Anon, your intuition is correct. The bilayers are made by manual stacking (!), and at room temperature and large areas under typical conditions they will sit still, but if you elevate the temperature a bit (say 150C) they will try to snap back into Bernal stacking unless they're otherwise fixed.

Anonymous said...

In the talk, did Pablo address at all the influence of the network of topological modes, as imaged here: https://arxiv.org/abs/1802.02999 ? It seems that twisting can lead to different kinds of effects; do they co-exist, or do slight changes in angle change the physics drastically, or something else?

Thanks again for your great APS summaries!

Douglas Natelson said...

Anon@9:22, not explicitly, though the physics is related, in the sense that both have to do with hybridization between states in the upper and lower layers. I do think that slight changes in angle can change the physics a lot - the insulating states ascribed to Mott physics only exist in very narrow (fractions of a degree) ranges of twist angle around the "magic" angle. This questions are one reason why theorists are going to have a field day. (Thanks for the kind words.)

Andrey Antipov said...

Doug, thanks for a great review of Pablo's talk. I missed it and regret it, but this is a great substitute. I wanted to focus on one of the points you mentioned.
"This system is effectively a triangular lattice - that's a very different beast than the square lattice of the cuprates or the pnictides."
I believe this is what actually saves the high-Tc state. Single-band Hubbard model on a square lattice would show strong antiferromagnetic correlations (albeit not order thanks to Mermin-awagner), but those are killed anyway. Pnictides are multiorbital. Does the right angle stacking break valley degeneracy? (In other way how many orbitals in the effective model should I see)

Anonymous said...

Someone has to say it: this is by far the most important discovery made in graphene since its discovery 14 years ago. All the other findings made in this "promising" material were either repeats (with some variations) of effects observed in other high-mobility systems, or simpler single-electron effects predicted by the band structure. So I think there was some disappointment in what had been done so far, especially given the number of groups working on graphene. So I say: finally! Something interesting for the physics community! And kudos to the MIT group!

Anonymous said...

Pablo's talk was actually recorded, and can be found at https://www.youtube.com/watch?v=O2HVCjhuJlE