Charge-density waves discovered on graphene sheets

Graphene consists of a 2D network of carbon atoms just one atom thick. This simple network of atoms results in remarkable physical properties: graphene has higher strength, better thermal conductivity, and greater intrinsic mobility than any other material known.¹ These properties translate into huge technological potential, for example, in transparent electrodes for flatscreen TVs, in fast, energy-efficient transistors, and in ultrastrong composite materials. Hence an enormous global effort is focused on understanding and controlling graphene's properties with the aim of tailoring them for specific applications.

The electronic properties of graphitic materials—including graphene, graphite, and carbon nanotubes—can be readily tuned by adding charge carriers, a process known as doping. The usual method for doping graphene is through the electric-field effect. However, 10 times as many charge carriers can be added by chemical doping, i.e., decorating the graphene surface with atoms.² In bulk graphite, high levels of doping can lead to superconductivity. The highest doping of graphite is achieved by inserting arrays of calcium atoms between the graphene sheets to form the superconductor CaC₆ (calcium-intercalated graphite).³

We used scanning tunneling microscopy (STM) and spectroscopy (STS) to investigate the graphene-terminated surface of CaC₆ at the atomic scale.⁴ STM exploits the sensitive dependence of quantum tunneling on the distance between a probe (a metal tip culminating in a single atom) and the sample. Normally, one would expect the electrons added to the graphene sheets by the calcium dopants to spread out uniformly. In contrast, when we imaged the surface of CaC₆, we found nanometer-scale 1D stripes (see Figure 1). These stripes are superposed on top of the hexagonal lattices of the graphene atoms and the calcium atoms below, which rules out any atomic reordering. The stripes were commensurate with the underlying atoms, and the stripe-stripe distance was 1.125nm. Using STS, we measured an energy gap in the electronic structure that could be directly correlated to stripe periodicity. This provided strong evidence that the stripes correspond to a charge-density wave (CDW): the first substantiated direct detection of a CDW in a graphitic system.

Figure 1. Charge-density wave on the graphene sheets of CaC₆ (calcium-intercalated graphite). Ball-and-stick model showing the graphene carbon atoms (red) and dopant calcium atoms (green) in the layer below. Above this is a 3D rendering of a scanning tunneling micrograph showing the expected surface atoms with additional stripes. (Image courtesy K. Adam Rahnejat.)

CDWs form spontaneously in some low-dimensional systems below a critical temperature, when the energy saved in reorganizing some of the electrons into long-range modulations overcomes the cost of moving the atoms to electrostatically compensate. This reorganization leads to the energy gap observed in our STS measurements. We found that the electronic stripes in CaC₆ only involved electrons in the graphene planes. Furthermore, despite measuring a large movement of the calcium atoms below the surface from their typical positions (∼0.6nm), we detected no movement of the carbon atoms.

Electronic stripes and superconductivity are often found in close proximity in low-dimensional systems, e.g., in cuprate (copper ion-containing compounds) or dichalcogenides (sulfur, selenium, and tellurium ion-containing). Indeed, understanding the relationship between these two states is thought by some to be of vital importance to understanding superconductivity itself. The observation of stripes in the very simple system of graphene offers an excellent test bed for studying the relationship between two important phenomena. Our observation that the stripes are localized on graphene sheets suggests the tantalizing possibility that CDWs and superconductivity can be achieved in a graphene-based field-effect transistor at high enough electron doping. This would open up new applications for graphene, for example, in making nano-SQUIDs (superconducting quantum interference devices).

In summary, we have discovered electronic stripes on the highly doped graphene surface of the graphitic superconductor CaC₆ and shown that the stripes correspond to a CDW. This is not only important for studying the relationship between stripes and superconductivity, but also suggests routes for driving graphene superconducting. So far, the CDW phase in CaC₆ has been observed only at 78K, well above the superconducting transition temperature (T_c) of 11.5K. In the future, we plan to explore CaC₆ above and below T_c to see whether the CDW phase competes with or coexists with the superconducting phase. In addition, our results suggest novel ways of encoding and manipulating information in graphene: binary zeros and ones would correspond to stripes running in different directions.

We would like to thank the UK Engineering and Physical Sciences Research Council for funding.