Magic angles to look at Moiré superlattices...

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 FLICK, PULSE AND SUPERCONDUCT

 

WHAT IS SUPERCONDUCTIVITY?

 

By definition, superconductivity is a state of matter that has no electrical resistance and does not allow magnetic fields to penetrate. For regular conductors, as we know, resistance decreases linearly with temperature and becomes 0 at absolute temperature (0 Kelvin). However, in the case of superconductors, they have a critical temperature — based on their physical properties — below which their resistance drops to 0 ohms.

Now, superconductors are of great influence due to their properties and hence find multitudes of applications. However, this also makes them expensive and difficult to obtain.

 

Graphene, an allotrope of carbon (which is more accessible than currently available superconductors) also acts as a superconductor. However, there is a twist





Source: www.maxpixel.net 

Graphene is a one-atom-thick layer of carbon atoms arranged in a hexagonal lattice. When multiple graphene layers are stacked on top of each other, free electrons are released due to the new covalent bonds formed, with ample space for electrons to flow freely between the layers. Thus graphene in its normal form is a conductor of electricity.

 

What if we could turn this conductor into a superconductor? Is it possible? It is. And not just by reducing the temperature to absolute zero, but by placing these graphene sheets on top of each other at a certain angle called the ‘magic angle’.

 

 



Source: www.everettyou.github.io

 

 

Two periodic lattices on top of each other with a relative ‘twist’, interfere to create a Moiré pattern. The periodic pattern forms a larger lattice called the Moiré superlattice. While such superlattices can be realized in materials such as graphene, hexagonal boron nitride (hBN), molybdenum disulphide (MoS₂) and others, we mainly focus on graphene in this article.

 

THE SCIENCE BEHIND

To understand how this twist enhances conductivity on such a scale, we take into consideration the behaviour of electronic matter waves in this environment.

The graphene layers generate a lattice, and as the scale of the lattice increases, the electronic matter wave of the free electrons propagates at longer wavelengths. Longer wavelength corresponds to lower momentum according to de Broglie’s relation p = h/λ.

Lower momentum thus implies reduced kinetic energy of the electrons (which, if you observe, is an effect similar to that caused by reduction of temperature in the case of regular superconductors).

Reduced kinetic energy makes the interaction energy relatively more important, resulting in enhanced interaction amongst the electrons.

Current, as we know, is basically the interaction of electrons as they pass on energy from one end of a substance to the other. As the interaction is enhanced, resistance reduces to a negligible value and we get a superconductor.

 

The main role of the ‘magic angle’ is to make the energy band of the material almost flat near the Fermi energy, creating the phenomenon of Van Hove's singularity. This satisfies the requirements for the Bardeen-Cooper-Schrieffer theory for superconductivity. According to this theory, electrons form Cooper pairs through interaction with lattice vibrations, which move in a coordinated manner, unlike in a random manner as in normal conductors which in effect allows electricity to flow with no resistance.




Source: www.pubs.acs.org

 

 

TWISTED BILAYER GRAPHENE

This magic angle is theoretically predicted to be 1.08° for graphene by a team of researchers at MIT led by Pablo-Jarillo Herrero.

The team discovered that a stable graphene structure at a 1.08° angle can be made using hexagonal boron nitride(hBN) and its superconductivity can be switched on and off at low temperatures by providing a simple electric pulse. The researchers aligned the first layer of hBN exactly with the top graphene sheet, while the second layer was offset by an angle of 30° with respect to the bottom graphene sheet. With this arrangement, they could engineer bistable behaviour in which the material can sit in one of two stable electronic states, allowing its superconductivity to be switched on or off with a short electrical pulse.

This structure is termed twisted bilayer graphene and is a pivotal step in the world of superconductors.

 

TWISTED TRILAYER GRAPHENE

Bilayer graphene has also directed research towards twisted trilayer graphene, which has better tunability of its electronic structure and superconducting properties than magic-angle twisted bilayer graphene. An intriguing point about twisted trilayer graphene is that it can be electrically tuned close to the crossover to a two-dimensional Bose–Einstein condensate.

 

Research on such Moiré superlattices is in progress taking its various applications into consideration. Moiré superlattices have immense potential and thus shall contribute to vastly improving the technical world.

 

 

 

 

CREDITS:

Aarya Kulkarni(112107001) SY ENTC

 

RESOURCES:

https://everettyou.github.io/2018/05/21/Moire.html

https://physicsworld.com/a/short-electrical-pulses-switch-superconductivity-on-and-off-in-magic-angle-graphene/

https://www.nature.com/articles/s41586-021-03192-0

 

NOTE:

This blog is meant for educational purposes only. We do not own any Copyrights related to images and information, all the rights go to their respective owners. The sole purpose of this blog is to Educate, Inspire, Empower, and create awareness in the viewers. The usage is non-commercial(Not For Profit) and we do not make any money from it.

 

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