Researchers at Rice University, together with collaborators from the University of Manchester, the University of Brighton, the South Dakota School of Mines and Technology, the University of Sussex, and Pennsylvania State University, have shown that sub-nanometer-scale wrinkles in graphene can generate a strong electrical polarization simply by bending, without any added chemistry or dopants. The effect, known as flexoelectricity, was predicted theoretically in graphene in 2008 but had not previously been directly measured at this scale.
Flexoelectricity describes polarization induced by a strain gradient, and it can occur even in materials that would otherwise show no polarization at all. In three-dimensional materials, competing electromechanical effects tend to mask it, but atomically thin two-dimensional materials offer a cleaner setting to isolate strain-driven polarization. In principle, bending a two-dimensional sheet tightly enough can perturb the out-of-plane orbitals that carry its electrons, generating a "quantum" flexoelectric response distinct from classical charge separation across a deformed membrane. Confirming this quantum contribution experimentally has been difficult, since most prior work accessed curvatures several orders of magnitude gentler than the atomic-scale bending needed to perturb individual orbitals.
To reach that regime, the team grew graphene on a molybdenum disulfide (MoS2) substrate, where the mismatch in lattice constants and elastic properties between the two materials causes the graphene to spontaneously buckle into dense, sharply curved wrinkles as it settles. These self-assembled graphene nanowrinkles reached curvatures on the order of 10⁹ per meter, roughly three orders of magnitude sharper than curvatures probed in earlier flexoelectricity studies, while avoiding the external mechanical probing (such as AFM tip indentation) that can complicate interpretation of spontaneous, stable behavior.
Atomic force microscopy, Kelvin probe force microscopy, conductive atomic force microscopy, Raman spectroscopy, and density functional theory calculations were combined to characterize the wrinkles' geometry, local work function, and current response.
The measurements pointed to a large polarization effect concentrated at the sharpest points of the wrinkles. Kelvin probe force microscopy revealed pronounced, curvature-dependent shifts in local work function, and conductive atomic force microscopy detected a reproducible current onset at a threshold voltage of about 1 volt, closely matching a band offset of about 1.2 volts predicted by the density functional theory calculations. The current response tracked wrinkle sharpness rather than wrinkle height, with cells of differing height producing comparable currents of around 67 picoamps under a fixed 2-volt bias.
From these measurements, the researchers estimated polarization densities of roughly 4 coulombs per square meter theoretically and about 1 coulomb per square meter experimentally, exceeding values reported for mesoscale flexoelectric systems by five to seven orders of magnitude.
The researchers said the results point to a way of tuning a two-dimensional material's electrical behavior through geometry alone, rather than through added chemistry or doping, and that the self-assembled wrinkles offer a simple, scalable platform for further study. Pulickel Ajayan, co-corresponding author on the study, said the work shows that "even an ordinary wrinkle can become an extraordinary electronic feature when viewed at the atomic scale," adding that it "opens a new pathway for designing materials whose properties can be controlled through structure rather than chemistry." Lead author Sathvik Ajay Iyengar said that at the scale of the sharpest wrinkles, "the electrons in graphene shift slightly toward one side, creating two opposite electrical sides like the ends of a tiny battery."
The team said future work should aim to integrate the wrinkles into device architectures and explore pairing them with other two-dimensional materials, including wide-bandgap systems, potentially toward more sensitive sensors and ultrathin electronic devices.
