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Analytical Expression Explains Bilayer Graphene's 1D Channels

Working in a theoretical group frequently entails having conversations in front of the data to clarify the narrative that nature is attempting to convey. An intriguing discovery was made at the Madrid-based IMDEA Nanociencia Institute recently.

Analytical Expression for the Synthesis of 1D Channels in Bilayer Graphene
Evolution of the energy landscape of twisted bilayer graphene as a function of the applied strain. Close to the critical strain the collapse of the Brillouin zone is appreciated. Image Credit: Physical Review Letters.

Two layers of graphene stacked on top of each other and slightly stretched apart by a minute force are known as strained bilayer graphene. Dr. Pierre Pantaleón, a researcher at the Group of Theoretical Modelling at IMDEA Nanociencia, was talking about this material with Prof. Paco Guinea, the group leader when Paco observed an irregularity that had missed the attention of everyone else; Pierre was demonstrating his animated depiction of strained graphene to the group.

It turns out that the Brillouin zone (the unit cell in the momentum space) of bilayer graphene is distorted and finally collapses in one direction when it is under strain. An inaccuracy in Pierre’s visualization program suggested the existence of a singularity due to the distortion at the collapsing point.

Singularities, such as the one the researchers were studying, call for serious consideration in physics. They might suggest that something is wrong, changing, or need more investigation. At that point, Paco’s study group included Dr. Andreas Sinner, a talented theoretical physicist who was working at Opole University in Poland, and they began investigating the singularity’s origin with Pierre.

What caught their interest was the simultaneous transformation in real space: the 2-dimensional material’s strained graphene led to the creation of nearly flawless one-dimensional moiré patterns, or one-dimensional channels.

Through the use of microscopes, scientists had previously observed similar occurrences and had written them off as design flaws like adhered materials or dislocations. Take the work of McEuen (Cornell University), Mendoza (Rio de Janeiro University), or Zhu (Columbia University) as examples.

However, the researchers now disclose masked impacts that were hidden behind what seemed to be artifacts. This is a natural phenomenon that occurs in hexagonal honeycomb lattices, such as those found in graphene, according to the study team at IMDEA Nanociencia. Specifically, strain is given to two layers that are placed at a minor twist angle.

The researchers’ most important finding is the analytical solutions they found for the necessary strain needed to produce these one-dimensional channels. This solution is surprisingly straightforward, depending only on two variables: the twist angle and the Poisson ratio, a constant unique to each material.

As a result of their research, they have developed a single mathematical formula that describes the phenomenon and provides information about its physical foundation.

Although the physics they explain in their study, which was published in Physical Review Letters, is not novel, their elegant and one-of-a-kind explanation of the phenomenon in such plain terms—a single analytical expression—is. The results pave the way for the engineering of new materials on surfaces with these types of one-dimensional channels.

Unlike their unrestricted mobility in the typical 2D graphene environment, electrons are constrained within these channels. These channels show a preferred direction of motion for the electrons.

This finding has far-reaching consequences, as its potential applications can be expanded to other materials, such as dichalcogenides, and different geometric arrangements.

The Group of Professor Guinea is presently engaged in a thorough investigation into the potential of graphene in both twisted and non-twisted bilayers, encompassing the detection of superconductivity. A thorough analysis was just released in the journal Nature Reviews Physics.

This work is the result of the Theoretical Modelling Group at IMDEA Nanociencia, which has received funding from the Spanish Program on Advanced Materials, the NMAT2D and MAD2D regional grants, and the EU’s Graphene Flagship.

Journal Reference:

Sinner, A., et al. (2023) Strain-Induced Quasi-1D Channels in Twisted Moiré Lattices. Physical Review Letters. doi:10.1103/PhysRevLett.131.166402

Pantaleón, P. A., et al. (2023) Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene. Nature Reviews Physics. doi:10.1038/s42254-023-00575-2

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