Supplementary Information

Supplementary Figures

Supplementary Figure S1: No distortion observed in the graphite lattice. (a) Drift corrected and re-

orientated topographic STM image recorded at +300 mV with off-stripe [A] and on-stripe [B] line profiles

marked in the graphitic (110) direction . (b) cross-correlation of line profiles shown in (a) displaying no

systematic distortion in the graphite lattice.

A B

a b

Supplementary Figure S2: Additional CITS data. Topography image, recorded at the CITS set point +800

mV, 50 pA, shows the surface area where CITS data was collected. Remaining FT images are g(q,V) plots at the

sample bias indicated.

Supplementary Figure S3: Constant current STM imaging of the stripe phase (a) A 50 nm x 50 nm region

of the CaC6 stripe surface recorded at +800 mV and 50 pA set point, (b) A second 50 x 50 nm region showing

the CaC6 stripe phase (recorded at 300 mV 50 pA set point), (c) A higher resolution scan taken from bottom left

region of (a) showing the stripes in more detail, (d) Scan taken undertaken on a different part of the surface

recorded at +600 mV and 50 pA set point. (e) Stripes imaged at +600 mV 50 pA under a different tip condition.

a b

c d e

Supplementary Notes

Supplementary Note 1. Correlation Analysis of Graphite Lattice

For completeness we have included a cross-correlation analysis of the carbon atom positions in the stripe

direction, analogous to that of the Ca atom positions in Fig. 3. A topographic STM image taken at +300 mV

sample bias was used for this purpose since the Ca atoms are topographically small at this bias. The stripe

direction is not parallel to any of the STM-visible graphite directions so the line profiles are taken in the

graphitic (110) direction as illustrated in Supplementary Fig. S1a. Supplementary Fig. S1b displays the

correlations of the on-stripe and off-stripe profiles. We measure no distortion of the carbon lattice away from its

ideal configuration. The data are noisier than those in Fig. 3b, which follows because the interatomic spacing in

the graphite (110) direction is greater than in the (100) or (010) directions and also because there are fewer data

points per carbon atom than per Ca atom since carbon atoms are closer together and smaller (meaning that there

is a lower signal to noise ratio out of plane as well). In short, close examination of the carbon lattice by line

profiles, lattice overlays and cross correlation of line profiles (as shown here) reveals no longitudinal or

transverse distortions to within the STM in-plane resolution of 0.01 nm.

Supplementary Note 2. Additional CITS data

Further to the CITS data presented in the main text we also present (in Supplementary Fig. S2) the topographic

location used for CITS measurements and g(q,V) images at a number of biases to visually demonstrate that the

Ca lattice and stripe periodicity are both non-dispersive.

Supplementary Note 3. Additional STM imaging

To prove that our findings are generic and reproducible, we show in Supp. Figs. S3a and S3b images of stripes

over larger areas of the CaC6 surface than presented in the main text. The stripes are uniform and regular for at

least 300 nm in every direction. Our search did not extend beyond this range for fear of tip contamination,

however the stripes showed no sign of degrading over this range and were not interrupted by the terrace edges

seen in both images. Therefore it is probable that the stripe phase spanned the entire crystal. In-plane HOPG is

somewhat polycrystalline so the crystal size is likely to be in the 1 – 10 µm range. A number of small

discontinuities in the stripes can be seen, particularly in Supplementary Fig. S3a, these have the appearance of

small kinks where a given stripe ‘moves’ laterally by one stripe-lattice position. This is shown more clearly in

Supplementary Fig S3c, a zoomed in, higher resolution scan taken from bottom left region of Supplementary

Fig. S3a. The phenomenon can be seen clearly across the centre of the image and also in the top left.

Furthermore, a particularly high density of dark and light patches or defects can be seen around these

discontinuities although the reason for this is not entirely clear. Supplementary Fig. S3d is a topographic image

measured with the same tunnelling parameters as Fig. 4a but on a different part of the surface, this demonstrates

a reproducibility of the stripe appearance. The apparent rotation in stripe direction between the two figures is

real. Finally, Supplementary Fig. S3e shows the stripes imaged with a different tip shape. In this case the stripes

are less strongly defined. However, they still match the stripe phase unit cell exactly and both the carbon and

calcium lattices are present as before. This image was recorded on the same sample but for a different surface

region to the images presented in the main text.

Supplementary Note 4. A note on the bulk nature of the stripe

STM is a local and surface sensitive probe, and behaviour of the bulk cannot necessarily be extrapolated from

the appearance of the surface. Here we discuss two possible scenarios:

The first scenario is that the bulk structure matches the surface we have measured and the CDW and distortion

are both seen throughout the sample below the critical temperature given by Fig. 1 in the main manuscript.

However, in other similar systems where CDWs have been observed by STM subsequent confirmation by X-ray

scattering has not always been trivial, e.g. in the case of some cuprates.42

The second scenario is that the CDW in the bulk is of different character to that which we have seen at the

surface. For example, this is the case in NbSe343

, NbSe2 44

, and BixCa1-xMnO3.45

The bulk CDW could differ in

a number of ways; for example the symmetry, length scale or temperature dependence. Recently it has been

shown that the stripes in TiSe2,46

whilst apparently unidirectional at the surface, in fact rotate between

successive layers of the sample, and furthermore that the rotation can occur clockwise or anticlockwise.

Supplementary References

42 Wise, W.D. et al. Charge-density-wave origin of cuprate checkerboard visualized by scanning tunnelling

microscopy. Nature Phys. 4, 696 - 699 (2008). 43

Brun, C. et al. Surface Charge Density Wave Phase Transition in NbSe3. Phys. Rev. Lett. 104, 256403 (2010).

44 Murphy, B. M. et al. Phonon Modes at the 2H-NbSe2 Surface Observed by Grazing Incidence Inelastic X-Ray

Scattering. Phys. Rev. Lett. 95, 256104 (2005).

45 Renner, C. et al. Atomic-scale images of charge ordering in a mixed-valence manganite. Nature 416, 518 –

521 (2002).

46 Ishioka, J. et al. Chiral Charge-Density Wave. Phys. Rev. Lett. 105, 176401 (2010).