Supplementary Information
Carbon Monoxide Stripe Motion Driven by Correlated Lateral Hoppingin 1.4 × 1.4 Monolayer Phase on Cu(111)Nana K. M. Nazriq1, Peter Krüger1,2, and Toyo Kazu Yamada1,2*
1. Department of Materials Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan.
2. Molecular Chirality Research Centre, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan.

Author Information,Corresponding Author: Toyo Kazu Yamada *E-mail: toyoyamada@faculty.chiba-u.jp

CO sub-monolayer coverages on Cu(111) at cryogenic temperatures in UHV

BA
0.1 LC0.5 L√3 x √3 R30order

3.0nm

3.0nm

disorderFigure S1. STM images (15 × 15 nm2, Vs = ‒40 mV, I = 1 nA) of a Cu(111) surface with (A) 0.1 L and (B)0.5 L CO adsorption in UHV at 20 K. All STM images were taken at 4.6 K. In (A), CO single molecules
are observed as dark spots as a metal W tip was used to scan. In (B), ordered √3x√3 R30 domains and otherdisordered domains are mixed. (C) Enlarged image in (B).

Silver mean discussion
Fig. S2 shows STM topographic images of the CO rows on Cu(111). We can see the rows has asequence of D S D S D S S D S S D S. The S -/D sequence is not periodic. Thus, once we thought thisis just a random sequence. As shown in the FFT image in Fig .2 in the main text, the sub-main peakhas the ration of 0.405, and this value is comparable to the irrational numbers of 0.414 = 1/(√2 + 1).
These numbers have been known as factors of the silver mean value [1-3], which is related to a quasicrystal-like behaviour [1]. Smith et al. discussed on the formation of a “silver mean” quasi-periodic
Ag films on GaAs.
A quasi-crystal is a crystal that has a non-periodic sequence in the arrangement of the atoms or unit
lattice. Non-periodicity requires a material parameter to follow a certain sequence related to theFibonacci sequence or bronze-Fibonacci sequence, etc. These are sets of metallic mean or ratios foundin shapes and structures of natural occurrence.
The silver mean is in analogy to the well-known golden mean or the Fibonacci sequence. A golden
mean sequence is a sequence where each term is the sum of previous term and the term before that.
i.e; Fn = Fn-1 + Fn-2 . The golden mean sequence ABAABABAAB…, can be formed by the iteration of
Sn+1 = {Sn, Sn-1} from the seeds (building blocks) of S1 = A, S2 = {A, B}.
However, for a silver mean sequence, each term is the sum of twice the previous term and the number
before that. i.e; Fn = 2Fn-1 + Fn-2. The silver mean sequence can be formed by the iteration Sn+1 = {Sn,Sn, Sn-1}, with the same building blocks of A and B which result in the sequence
ABAABABABAABABAA….
The real space arrangements of the CO chain sequence were found to be in good agreement with thesilver mean sequence. From Fig. S2A, the sequence of the single and double rows are as follows;
DSDSDSSDSSDS… The first half of the sequence DSDSDSSD follows the silver mean sequence ofBABABAAB. The second half of the sequence SDSSDSD also follows the silver mean sequence
ABAABAB. Analysis of a strip of the STM image shows that the sequence follows exactly of thesilver mean until a certain coherence length. This would also occur in other strips of the STM image.
These positions are where the silver mean sequence is broken (limited coherence length of less than 7nm).

silver mean

AB

A

B

A

B

A

A

B

A

A

B

A B

silver mean
DS

DS

DS

S

D

1 nm

B

7 nm

C

Figure S2. Possibility of “Silver mean” sequence in CO rows on Cu(111). (A) BABABAA or AABAABAB
denote “Silver mean” sequence, which partially correspond to DSDSDSSD sequence in CO rows, whike
the sequence ended within 7 nm. (B) and (C) denote before and after the hopping, where DSSDSSSDDSSD
changed to DSSDSDSSDSSD.

However, this does not occur regularly and are different for some areas of the CO monolayer. This canbe seen from Fig. S2B to Fig. S2C. To avoid confusion, we will discuss the strip marked with a yellow
box. The first half sequence in Fig. S2B follows DSSDSS (silver mean). It is followed by a SSSDSSD.
After scanning, the next image (Fig. S2C), the S changes to a D (red circle). This makes another silver
mean sequence of DSSDSDSS in Fig. S2C. We concluded that, this occurrence does not provide
enough evidence to support the argument that this is a silver mean sequence.
Note: Golden mean value = 1.618… Silver mean value = 2.414… = √2 + 1. Bronze = 3. 302…

References[1] Smith, A. R.; Chao, K.-J.; Niu, Q.; Shih, C.-K. Formation of Atomically Flat Silver Films onGaAs with a Silver Mean Quasi Periodicity. Science 1996, 273, 226–8.
[2] Ali, M. K.; Gumbs, G. Quasiperiodic dynamics for a generalized third-order Fibonacci series.
Phys. Rev. B 1988, 38, 7091–7093.
[3] Gumbs, G.; Ali, M. K. Dynamical maps, Cantor spectra, and localization for Fibonacci andrelated quasiperiodic lattices. Phys. Rev. Lett. 1988, 60, 1081–1084.

Successive STM topographic images showing continuous hopping

Figure S3. Successive 30 STM topographic images (t = 0 – 45 min) showing continuous correlated COhopping on Cu(111) at 4.6 K in UHV.

Figure S4. Successive 30 Inverse FFT images (t = 0 – 45 min) using the two sub-main peaks, clearly showing
continuous CO stripe formation wave motion on Cu(111) at 4.6 K in UHV.

Spectroscopy measurements on CO rows on Cu(111)

A Lower row (bridge site)0.255-0.255

0.255

dI/dV [nA/V]

dI/dV [nA/V]

B Higher row (top site)

-0.5

-0.8

0.0

0.5

0.0 0.8
E - EF [eV]

-0.5

-0.8

0.0

0.5

0.0 0.8
E - EF [eV]

Figure S5. STS grid mode results obtained on (A) lower rows and (B) higher rows. Experimentally obtained
scanning tunneling spectroscopy dI/dV curves (setpoint: Vs = ‒40 mV, I = 1 nA), which are proportional tosample LDOS. Upper panels denote STM topographic image and dI/dV curves (right panels) were measured
Topography
at dotted points. Lower panelsTopography
show dI/dV plots along the row. x and y axes denote thesample bias voltage -0.051
and position on the row respectively.

Schematic diagram of the CO unit lattice on Cu(111)AB

Cu latticeyx

CO lattice

Figure S6. Schematic diagram depicting the Cu lattice unit vectors and the corresponding CO unit lattice.

Scanning tip effect: comparison between forward and backward scan images
Scratches: Forward scan image
tip effect

3.0nm

Backward scan image

Scratches:
tip effect

3.0nm

Figure S7. STM topographic images obtained on the CO 1.4 × 1.4 array at 4.6 K (Vs = 40 mV, I = 0.73 nA).
Right panel images were obtained when the STM tip scanned from left to right direction (forward scan).
Left panel images were obtained when the STM tip scanned from right to left direction (backward scan).
Scratches are marked by the arrows.