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Stacking-dependent properties of trilayer graphene

A particular example of few-layer graphene shows unexpected electronic properties, such as band-gap opening, related to the order in which the sheets are stacked.
15 February 2012, SPIE Newsroom. DOI: 10.1117/2.1201201.004068

Graphene, a single atomic layer of graphite, consists of carbon atoms arranged in a honeycomb lattice. Since its experimental isolation on insulating SiO2 (silica) substrates in 2004,1 it has quickly taken the scientific and technological communities by storm. It has been dubbed as a ‘carbon flatland,’ ‘carbon wonderland,’ and a new ‘wonder material’ because of its extraordinary material properties. For instance, it is the ultimate 2D system: it is softer than silk yet stronger than steel; it conducts heat better than copper; and it conducts electricity better than silicon. It is also transparent and elastic, yet as a capping layer it is impermeable to even the smallest molecules. These and other material properties continue to astound. The 2010 Nobel Prize in physics was awarded to Andre Geim and Konstantin Novoselov for their groundbreaking experiments on graphene.

The initial flurry of activity following discovery mainly focuses on single-layer graphene. Its few-layer cousins were largely ignored, since they are assumed to be similar to graphite, a well-studied material. More recently, however, researchers have realized that few-layer graphene (FLG) hosts a wealth of fascinating physics and potential applications.2–5 For instance, band structures are more amenable to band-gap engineering and application in digital electronics, while allowing stronger electron interactions that lead to novel correlated phenomena. Equally fascinating is the dependence of their properties on the manner in which successive graphene layers are stacked.6–9

Figure 1. (a) Schematics of ABA (Bernal)- and ABC (rhombohedral)-stacked three-layer graphene (TLG), respectively. (b) Resistance (R) vs. charge density n (in log-linear scales) for suspended ABA (red curve) and ABC (blue curve) TLG devices. Upper inset: Scanning electron microscopy image of a suspended TLG graphene device. Scale bar: 2μm.

Most FLG and graphite are Bernal-stacked. In other words, one corner of the hexagons of the top sheet is located above the center of the hexagons of the bottom sheet. Because the adjacent atoms in each graphene sheet are considered crystallographically inequivalent, there are up to 2n−2 distinct stacking sequences in n-layer graphene, with different band structures. Stacking order thus provides an important yet rarely explored degree of freedom for tuning the electronic properties of FLG. Here we start from a simple case: trilayer graphene (TLG) has two stacking orders, ABA (Bernal) and ABC (rhombohedral), their only difference being the position of the top layer, which is shifted by a distance of just one atom: see Figure 1(a). This seemingly small difference leads to entirely different band structures: the energy-momentum relation of ABA-stacked TLG consists of two branches, a linear branch and a quadratic branch; that of ABC-stacked TLG, in contrast, is a single cubic branch,6 though both are expected to be metal-like.10

To investigate the intrinsic electrical properties of TLG free of influences from the substrate, we use a lithography-free technique11 to fabricate clean, suspended TLG devices. The device mobility is exceedingly high, up to 280,000cm2/Vs (in comparison, standard silicon devices have mobility 500–2000cm2/Vs). Each device behaves as a field effect transistor: its resistance changes with the number of electrons on the graphene sheet, which can be tuned by gate voltages. At the so-called charge neutrality point (CNP), the TLG sheet has zero doping, and its resistance reaches a maximum.

We studied close to a hundred devices. Much to our surprise, they displayed two distinctly different behaviors at the CNP.12 Most devices are metallic and conductive at the CNP, with resistivity ∼5–10kΩ. A small percentage of devices become insulating (1–10MΩ): see Figure 1(b). After examining the devices using Raman spectroscopy,13 we found that the conductive devices are ABA-stacked TLG, and the insulating ones ABC-stacked. Thus, different stacking orders significantly modify TLG's electrical properties, despite the seemingly minute difference in structure.

The insulating state in ABC-stacked TLG is particularly interesting. Our measurement reveals a band gap of ∼6meV (likely to be even larger in cleaner samples), whereas theoretical calculations of band structure predict a gapless semiconductor with resistivity of a few kilo-ohms.10 This band gap arises from electronic interactions that are enhanced due to the charges' quantum confinement to two dimensions, in conjunction with the particular band structure of the ABC-stacked layers. It also suggests spontaneous ordering of electrons, a consequence of the fascinating many-body physics in this 2D system. This spontaneous gap opening, though small, has important implications for band-gap engineering for graphene electronics.

The impact of stacking order is also revealed in the different quantum Hall (QH) effects exhibited by the devices.6, 14 In high magnetic fields, the cyclotron orbits of electrons coalesce into highly degenerate states, and the devices' Hall conductivity is quantized at integer values of e2/h or (25.9kΩ )−1, where e is electron charge and h is Planck's constant. Unique to ABC-stacked trilayers, the QH plateaus split into three branches, reflecting a topological change in the Fermi surface, a process known as the Lifshitz transition. This is the first time that the Lifshitz transition is observed in graphene or its few-layer cousins.12

Our findings demonstrate that just a tiny difference in stacking produces the difference between metals and insulators at low temperature. This is a rich topic of which we and other researchers have barely scratched the surface. For example, under an out-of-plane electric field, ABA-stacked TLG is expected to exhibit band overlap and become less resistive, whereas ABC-stacked TLG is expected to open a band gap up to 350meV.6, 15,16 FLG with different stacking orders is speculated (but not experimentally proven) to host different chemical and mechanical properties. Controllable synthesis of FLG with different stacking orders is yet another possibility. Thus, FLG's material properties can be tuned, in principle, by simply changing the stacking order of the layers. As immediate next steps, we plan to further study the insulating state in ABC-stacked TLG to establish the specific type of electron ordering, and to explore the different electronic properties of FLG under applied electric and magnetic fields

This work was supported by the National Science Foundation, the Office of Naval Research, University of California Lab Fees, and the Focus Center on Functional Engineered Nano Architectonics.

Chun Ning (Jeanie) Lau
University of California
Riverside, CA

Chun Ning (Jeanie) Lau is an associate professor of physics. She received her BA from the University of Chicago and her PhD from Harvard University, and has been a research associate at Hewlett-Packard Laboratories. Her research interests center on properties of carbon nanomaterials.

Wenzhong Bao
Department of Physics
University of Maryland, College Park
College Park, MD

Wenzhong Bao graduated from Nanjing University with a BS in physics (2006). He received his PhD from the University of California, Riverside (2011), having studied in the Department of Physics and Astronomy. He is currently a postdoctoral researcher in Michael Fuhrer's group at the University of Maryland, College Park.

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