Stretching or squeezing a material. Because can be stretched much further than ordinary crystals before breaking, strain can be used as a knob to change their colour, conductivity or .
Going deeper
Strain is applied by bending, blistering or pressing. In monolayer MoS2, uniaxial tension lowers the emission energy by about 45 meV per percent, and near 1 % the gap changes from direct to indirect, so the emission weakens as well as shifts.
How far a 2D crystal can stretch
Ordinary crystals crack at a small fraction of a percent of strain, because cracks start at defects and . A small area of a 2D crystal can be almost free of both. Graphene suspended over holes and pressed with an tip showed a Young’s modulus of about 1 TPa and an intrinsic strength corresponding to strains of well over 10 % – the strongest material measured at the time. MoS2 breaks at roughly 6–11 %.
In practice, strain is applied by bending or stretching a flexible , which gives uniaxial strain of up to a few percent before the slips; by inflating a blister or bubble, which gives biaxial strain; or by transferring the layer onto patterned or thermally mismatched substrates.
What strain does to bands and vibrations
Stretching bonds changes how much neighbouring orbitals overlap, so band edges move. In monolayer MoS2, uniaxial tension lowers the emission energy by about 45 meV per percent, and near 1 % the direct gap gives way to an indirect one, so the emission dims; biaxial strain, pulling in both directions, shifts the gap about twice as fast.
Vibrations respond too. Under tension, bonds soften and peaks move to lower frequency, and uniaxial strain splits graphene’s G peak in two, which makes Raman a strain gauge. In graphene, strain that varies across the sheet acts on electrons like a magnetic field; in nanobubbles these pseudo-magnetic fields have been estimated at hundreds of tesla.
Strain nobody asked for
Most strain in real samples is accidental. Transfer leaves wrinkles and bubbles; layers grown at high temperature on a substrate that contracts differently on cooling keep a built-in strain; layers are stretched or compressed to fit the lattice underneath. Because strain shifts gaps, emission and Raman peaks, it can masquerade as a property of the material or change it from one spot to the next.
Strain and both move Raman peaks, so one peak alone cannot separate them. Plotting two peaks against each other – the G and 2D peaks of graphene, or the and A1′ modes of MoS2 – does, because the two effects move them in different proportions.
For specialists
Relative deformation of a lattice. 2D crystals sustain elastic strains of several percent, with graphene exceeding 10 % in nanoindentation, and strain shifts band edges, Raman modes and energies. Unintended strain from substrates, bubbles and transfer is a common confounder in measurements.