Researchers at Spain's IMDEA Nanoscience, Donostia International Physics Center, Ikerbasque and Poland's University of Opole have developed an analytical method to explain the formation of a quasi-perfect 1D moiré pattern in twisted bilayer graphene. The pattern, naturally occurring in piled 2D materials when a strain force is applied, represents a set of channels for electrons.
The team studied the effects of strain in moiré systems composed of honeycomb lattices. The scientists elucidated the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criterion for such collapse, they found a simple relation between the two quantities and the material specific Poisson ratio. The induced one-dimensional behavior is characterized by two, usually incommensurate, periodicities.
The team's results offer explanations for the complex patterns of one-dimensional channels observed in low angle twisted bilayer graphene systems and twisted bilayer dicalcogenides. Their findings can be applied to any hexagonal twisted moiré pattern and can be easily extended to other geometries.
The team shared the background for this work: Dr. Pierre Pantaleón, researcher at the Group of Theoretical Modeling at IMDEA Nanoscience, was talking with group leader Prof. Paco Guinea about strained bilayer graphene. Pierre was showing the group his animated visualization of strained graphene when Paco noticed an anomaly that had escaped everyone else's scrutiny. As it turns out, when bilayer graphene goes under strain, its Brillouin zone (the unit cell in the momentum space) distorts and eventually collapses in one direction. This distortion at the collapsing point caused an error in Pierre's visualization program suggesting the presence of some kind of singularity.
Singularities tend to indicate something requires a closer examination. Dr. Andreas Sinner, a theoretical physicist currently working at Opole University on Poland, joined Paco's research group and started looking together with Pierre on the origin of this singularity.
It was the concurrent transformation in real space that truly captivated their attention: strained graphene gave rise to the emergence of almost perfect one-dimensional moiré patterns—one-dimensional channels—within the 2-dimensional material.
Previously, scientists had glimpsed such phenomena through a microscope and had regarded them as design errors such as dislocations or adhered materials. But behind what appeared to be artifacts were masked effects. The research team confirmed that this is a natural occurrence within hexagonal honeycomb lattices—like those of graphene—specifically taking place when two layers are stacked at a slight twist angle and strain is applied.
The most significant contribution of the researchers lies in their discovery of analytical solutions for the critical strain required to generate these one-dimensional channels. Surprisingly, this solution is beautifully simple, relying on just two variables: the twist angle and the Poisson ratio—a material-specific constant. These findings lead them to create a single mathematical formula to describe the phenomenon, and this formula gives information on its physical origin.
The physics described in their work is not new, but the explanation of the phenomenon in such simple terms—a single analytical expression—is elegant and unique.
The findings open the door to engineering novel materials on surfaces capable of featuring these one-dimensional channels. Within these channels, electrons find themselves confined, in contrast to the free movement they exhibit in the standard 2D graphene landscape. Electrons within these channels also exhibit a preferential direction of movement.