In recent years, researchers have used sophisticated nanostructuring techniques to make 2D thin-film materials that can be bent and curved into objects such as rolled-up nanotubes and nanohelices. These next-generation nanomaterials could be used in a host of electronics applications, from flexible displays to implantable medical devices that can conform to the soft, curved surfaces of the human body. They can also be used to study fundamental physics since the quantum mechanical properties of charge carriers in these nanomaterials are strongly affected by the curved environment in which they find themselves. Indeed, theoretical studies on such structures so far have revealed the existence of a series of unique electronic and transport properties, including winding-generated bound electronic states, strongly anisotropic ballistic magnetoresistance (MR) in non-magnetic semiconducting nanotubes and snaking states in the transport properties of core-shell nanowires, to name but three.

Rippled or wrinkled nanostructures are one of the most important types of deformed nano-objects made to date and they are produced by applying external strain to a thin film material. Researchers have already succeeded in ripple retexturing graphene, for instance, and making wrinkled semiconducting nanomembranes and multilayer black phosphorus flakes with ripples.

Structural wrinkles can produce periodic electronic potentials that can induce mini band gaps and topological end states such as Shockley end modes. Creating ripples in a material can thus also be a way to modulate its electronic properties without having to resort to chemical doping. This strategy has an added advantage in that the system remains chemically pristine.

Weiss oscillations are strongly anisotropic

Carmine Ortix and Ching-Hao Chang of Utrecht University and IFW Dresden have now shown that the magnetotransport properties of a 2DEG placed in a rippled nanostructure could naturally display the Weiss oscillations already observed in conventional 2DEGs that are subjected to periodic electric or magnetic field potential. This is because electrons contained in a rippled structure behave as though they have been subjected to a periodically modulated magnetic field even though they have only been exposed to a homogenous one.

“More importantly, since we can tune the ratio between the homogenous and inhomogeneous components of the magnetic field on demand by simply rotating the externally applied homogenous magnetic field, we find that the Weiss oscillations are strongly anisotropic (that is, they are strongly dependent on the magnetic field direction),” say the researchers. “This means that the directional dependence of the magnetoresistance, which depends on the angle at which the homogenous magnetic field is applied, also contains these anisotropic Weiss oscillations.”

To understand the magnetotransport of a wrinkled 2DEG, the researchers first derived the effective magnetic field felt by an electron confined on a nanocorrugated surface when subject to a homogenous magnetic field. “We then determined the magnetic quantum states coming from this effective field,” explains Chang. “By inserting these states into the so-called Kubo mathematical formula for diffusive conductivity, we were then able to observe how the behavior of the MR in the material changes in the diffusive transport regime as we change the angle of the applied magnetic field.”

Where do the Weiss oscillations in the corrugated 2DEG come from?

The Weiss oscillations in the MR are caused by the interplay between the two characteristic length scales present in a nanocorrugated 2DEG subject to a homogenous magnetic field, he tells The first is the wavelength of the periodic corrugations and the second the radius of the electron cyclotron orbit (the closed trajectory travelled by an electron in a homogenous magnetic field).

“When the radius of the cyclotron orbit has a multiple value of the geometric corrugations, the electron largely drifts, which leads to the Weiss oscillations we observed in the MR.

“Our observations of angle-dependent Weiss oscillations in a corrugated 2DEG is just one important geometry-induced effect in a series of such effects,” adds Ortix. “These effects can be used to investigate novel transport properties in 2DEGs and to develop next-generation electronic devices with novel functionalities by tailoring the local geometry of the materials.”

Full details of the research are reported in Nano Futures 1 035004.