A team of researchers from Harvard University, the National Institute for Materials Science in Tsukuba, Japan, and École Polytechnique has demonstrated a device made of graphene and a carbon nanotube for coherently guiding electrons. As reported in a recent issue of Physical Review Letters, the device could be used for transmitting electron wavepackets for quantum information processing.  

Researchers are interested in creating confined versions of graphene, which is usually a two-dimensional (2D) sheet, for guiding electrons. In a sheet of graphene, the electronic states are a continuum, whereas the electronic states in a confined graphene are quantized into discrete energy levels. Previously, researchers had attempted to create one-dimensional (1D) nanostructures of graphene by cutting them into nanoribbons. Cutting graphene, however, often introduces disorder, particularly in the edges of the nanoribbon. “To study the quantum properties of materials like graphene, it’s important to eliminate disorder, because any amount of disorder will cause the electrons to scatter,” says Cory Dean of Columbia University, who was not connected with this study. Instead of creating graphene nanostructures, researchers have tried creating 1D channels inside graphene sheets. 

To reduce the effects of disorder, the research team created a 1D channel in graphene far from its edges. First, the researchers assembled a heterostructure of graphene sandwiched between two layers of hexagonal boron nitride (h-BN). Then lithography was used to create trimetallic (chromium, palladium, and gold) electrodes on top of the graphene heterostructure that were electrically isolated from the graphene. In the final step, a single carbon nanotube was transferred atop the isolated electrodes but separated from the graphene by the upper layer of h-BN. 

The geometry of the circuit allowed the researchers “to apply a large voltage on the single nanotube without flowing any current to the graphene,” says Jean-Damien Pillet of École Polytechnique, who was the corresponding author of the article.

Pillet and his collaborators applied a voltage to the carbon nanotube which induced a potential well in the graphene directly below the nanotube. The width of the potential well is controlled both by the distance between the nanotube and graphene, which can be controlled by the thickness of the upper h-BN layer, and the voltage applied to the carbon nanotube. “You have a lot of versatility in the system,” says Dean, “and you can vary things dynamically.”

To characterize the potential well, the researchers measured the quantum capacitance in the carbon nanotube as a function of applied voltage. In this system, the quantum capacitance describes the change in the carrier concentration due to the shift in Fermi level caused by the voltage difference between the nanotube and graphene. The appearance of resonances in the quantum capacitance corresponded to the existence of guided modes, or potential well whose width is smaller than the wavelength of the electrons it is expected to transmit.

The researchers also observed how the depth and shape of the well changed across a range of voltages. Under certain applied voltages, the observed guided modes were well-separated from other energy levels, which will be important for transmitting an electron wavepacket.

Moving forward, the researchers would like to use the guided modes in their device to transmit an electron wavepacket, which could make it useful for future quantum computing applications. Pillet says that additional electrodes need to be added to the circuit to transport electrons. In addition to changes in circuit geometry, Dean expects that the cleanliness of the graphene layer will need to be improved by enhancing the quality of the h-BN sandwich layers.

Beyond applications for the specific device itself, “[t]his is a beautiful demonstration of integrating a manifestly 1D material with a manifestly 2D material,” Dean says. A combination of different techniques for assembling 1D and 2D structures could be expanded to create additional devices that combine these two regimes.

Read the abstract in Physical Review Letters.