Extinction, σ/area 1.5 1.0 t = t 0 t = 0.7 t 0 t = t 0 t = 1.3 t 0 t = 1.5 t 0 0.7 0.9 1.1 Energy (ev) = 20 nm t 1.3 Supplementary Figure 1: Plasmon epenence on isk thickness. We show classical calculations for isks of ifferent thicknesses (t in units of t 0 = a 0 / 3 = 0.236 nm, see legen) an = 20 nm in iameter. The valence electron ensity is ajuste to have the same number of electrons in all cases. These results show that the plasmon energies an absorption profiles are rather inepenent on isk thickness, provie this is small compare with the iameter, which corroborates the robustness of our calculations with respect to the choice of film thickness. 1
y/ Without -ban screening (a) (b) (c) -1 1 Inuce charge ensity (arb. units.) Classical (g) - - = 3 nm - y/ Incluing -ban screening () = 9 nm - x/ = 15 nm (f) (e) y/ - - - - = 3 nm - x/ = 9 nm - x/ = 15 nm Supplementary Figure 2: Maps of inuce charge ensity corresponing to the lowest-orer ipolar plasmon of single-monolayer gol isks of ifferent iameters, as obtaine from our quantum mechanical escription (a-c,-f), compare with a classical, local calculation (g). The upper (lower) row shows results calculate without (with) inclusion of -ban electron screening. The classical calculation (g) is obtaine from the solution of Poisson s equation for a isk escribe by a resonant permittivity 1 1 /t, where t is the isk thickness. The ipolar patttern exhibits raial oscillations of a perio similar to the Frieel oscillations. The inclusion of -ban screening (2f) results in more complex patterns riven by the iscrete character of the backgroun ipoles. In all cases consiere, the ipolar character is clearly preserve an the inuce charge accumulates at the borer of the nanoisk as the iameter increases, thus approaching the behavior of a classical, local escription of the isk. 2
Fermi energy, E F (ev) Electronic ensity (nm -2 ) 3.7 3.6 3.5 3.4 3 6 9 12 15 100 = 3 nm 50 100 0 50 100 0 50 iameter, (nm) = 9 nm = 15 nm 0-8 -4 0 4 8 (a) (b) Position along iameter (nm) 1.17 1.14 1.11 Fermi velocity, v F (10 6 m/s) Supplementary Figure 3: Filling of electron energy levels in a metallic isk. (a) Fermi energy E F relative to the bottom of the parabolic s-ban (left scale) an Fermi velocity v F = 2E F /m e (right scale) as a function of singlemonolayer gol isk (SMG) iameter. We consier a single (111) atomic layer of an fcc metal of lattice constant a 0 (e.g., a 0 = 0.408 nm in gol). In practice, a single-layer isk of iameter has (π/ 3)(/a 0 ) 2 electrons that fill states of increasing energy up to a level that efines the Fermi energy E F. (b) Unperturbe valence electron ensity profiles for SMGs of ifferent iameters. 3
0.13 Absorbance, A 0.26 = 1.5 = 2 = 3 = 8nm l max = 1 l max = 4 l max = 6 0 1.00 1.35 1.70 Energy (ev) Supplementary Figure 4: Multipolar effects in the interaction of isk arrays. We examine the valiity of the ipole approximation to represent each isk in the arrays consiere in the main paper. For simplicity, we present classical results, as we expect that the conclusions shoul be irectly applicable to quantum calculations as well. We use a layer KKR approach 2,3 to calculate the absorbance of perioic hexagonal arrays of = 8 nm gol isks with ifferent lattice parameters, with each isk represente through its scattering matrix, which is obtaine with the bounary-element metho (BEM). 4 We inclue multiples of orbital angular momentum l l max. The results are remarkably converge alreay with l max = 1 (ipolar approximation) for the two larger spacings uner iscussion, whereas for a perio equal to 1.5 times the isk iameter multipolar corrections are rather small. Therefore, we conclue that the ipolar approximation use in the main paper provies quantitatively correct results for the geometrical parameters uner consieration. 4
Absorbance, A 0.45 0.30 0.15 = 30 nm Au Cu = 45 nm Ag oping charge ensity (10 13 cm -2 ) -5 0 +5 0 0.7 0.9 1.1 Energy (ev) Supplementary Figure 5: Electrical moulation of the absorbance of hexagonal perioic arrays forme by single atomic-layer isks mae of silver, gol, an copper. The structures are similar to those of Fig. 5 of the main paper, but now the isks are larger, leaing to lower-energy plasmons in the 0.7-0.8 ev region. Silver is the less lossy of these three materials, an consequently, the optimum choice to maximize the optical tunability because its plasmons are narrower. Although the valence electron ensity is very similar in these metals, their plasmons occur at ifferent energies ue to variations in -ban screening. The geometrical an oping parameters are inicate by labels. The spectra are obtaine from classical calculations. 5
Energy (ev) 2.5 1.9 1.3 0.7 light-line 1000 100 10 1 layer 10 layers layers Plasmon wavelength (nm) 1 Supplementary Figure 6: Plasmons an tunability of thin homogeneous gol layers. We represent the plasmon ispersion relations of layers consisting of 1 an 10 atomic monolayers oriente along the (111) irection. The results are obtaine from classical electromagnetic theory, using optical ata for the ielectric function, 5 moifie as escribe in the main paper to inclue electrical oping. The plasmons of unope layers (soli curves) are compare with those preicte for an aitional ensity of 10 14 cm 2 electrons (ashe curves). The light line an the ispersion of surface plasmons in a semi-infinite gol layer are shown for comparison. We conclue that the single-layer gol film can unergo similar electrical tunability as the nanostructures consiere in the main paper. The plasmons of the single layer are relatively far from the light line, although they have sizable wavelengths of 100 s nm in the NIR spectral region. Like in graphene, the in/out-coupling of light to these plasmons represents a serious challenge, which can be overcome by ecorating the layer with aitional structures or by placing it near a grating of perio comparable to the plasmon wavelength. 6
Supplementary References [1] Fang, Z.; Thongrattanasiri, S.; Schlather, A.; Liu, Z.; Ma, L.; Wang, Y.; Ajayan, P. M.; Norlaner, P.; Halas, N. J.; García e Abajo, F. J. Gate tunability an hybriization of localize plasmons in nanostructure graphene. ACS Nano 2013, 7, 2388 2395. [2] Stefanou, N.; Yannopapas, V.; Moinos, A. Heterostructures of photonic crystals: Frequency bans an transmission coefficients. Comput. Phys. Commun. 1998, 113, 49 77. [3] Stefanou, N.; Yannopapas, V.; Moinos, A. MULTEM 2: A new version of the program for transmission an ban-structure calculations of photonic crystals. Comput. Phys. Commun. 2000, 132, 189 196. [4] García e Abajo, F. J.; Howie, A. Retare fiel calculation of electron energy loss in inhomogeneous ielectrics. Phys. Rev. B 2002, 65, 115418. [5] Johnson, P. B.; Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 1972, 6, 4370 4379. 7