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The concept of heterostrain was proposed in the context of materials science where two-dimensional materials can be stacked of top of each other and different strain applied to each layer. In addition to twist, heterostrain can have important consequences on the electronic and optical properties of the resulting structure. As such, the control of heterostrain is emerging as a sub-field of straintronics in which the properties of 2D materials are controlled by strain.

Etymology

The word heterostrain is constructed from the Greek prefix hetero- (different) and the noun strain. Il means that the two layers constituting the structure are subject to different strains. This is in contrast with homostrain in which the two layers as subject to the same strain. Heterostrain is designated as "relative strain" by some authors.

Manifestations and measurement of heterostrain

For simplicity, the case of two gaphene layers is considered. The description can be generalized for the case of different 2D materials forming an heterostructure.

In nature, the two graphene layers usually stack with a shift of half a unit cell. This configuration is the most energetically favorable and is found in graphite. If one layer is strained while the other is left intact, a moiré pattern is generated by the beating of the two atomic lattices. The shape of the moiré pattern depends on the type of strain.

• If the layer is deformed along one direction (uniaxial heterostrain), the moiré is one dimensional.
• If the layer is strained in the same way along two directions (biaxial heterostrain), the moiré is a two-dimensional superstructure.

Graphene layers in Bernal stacking

Graphene layers with biaxial heterostrain

Graphene layers with uniaxial heterostrain

In General, one layer can be deformed by an arbitrary combination of both types of heterostrain.

Heterostrain can be measured by scanning tunneling microscope which provides images showing both the atomic lattice of the first layer and the moiré superlattice. Relating the atomic lattice to the moiré lattice allows to determine entirely the relative arrangement of the layers (biaxial, uniaxial heterostrain and twist). Alternatively, if biaxial heterostrain is low enough, it is possible to determine twist and uniaxial heterostrain from the knowledge of the moiré period in all directions.

Origin and impact of heterostrain

Heterostrain is generated during the fabrication of the 2D materials stack. It can result from a meta-stable configuration during bottom up assembly or from the layer manipulation in the tear and stack technique. It has been shown to be ubiquitous in twisted graphene layers near the magic twist angle and to be the main factor in the flat band width of those systems. It explains some of the sample variability which had previously been puzzeling. Research is now moving towards understanding the impact of spatial fluctuations of heterostrain.

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