Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ; (e) mv, pa,.. m ; (f) mv, pa, m ; (g) mv, pa, m ; (h) mv, pa, m. All the scale bars are m.
Supplemetary Figure S Height ad strai estimatios at boudaries. (a) STM image same as Fig. b. (b) Lie profile ivestigated from the lie show i (a). The axes at right side show the differet estimated heights based o differet strais i the slope regio. (c) Schematic image for the projectio effect. (d) Relatioship betwee the estimated height ad the assumed strai. (e) ad (g) STM images of a potassium-free regio of the K-HOPG surface without ad with oe overlappig of potassium-free domais. (f) ad (h) Lie profiles i (e) ad (g), where the height is estimated based o the atomic arragemet aalysis i (a) (c). STM coditios: (a) - mv, pa,.. m ; (e) mv, pa,. m ; (g) mv, pa, m. (i) The calculated C C distace as a fuctio of the positio. The maximum stretchig was calculated to be about.%.
He io itesity (arb. uits) E He io =. MeV Top C layer Top K positio About Layer..... Eergy (MeV)... Supplemetary Figure S Rutherford backscatterig result shows that K is itercalated ito the graphite. The eergy of the icidet He io was. MeV.
a b c d Supplemetary Figure S STM images from the same regio reveal clear overlappig ad evolutio of dark patter (slightly drifted). Note how the shapes chaged at the areas surrouded by the white, blue ad gree borders. (a) (d) mv, pa, m. All the scale bars are m. Durig the experimet at. K, the evolutio of patters (e.g. idicated by the coloured rectagles) was observed.
STS peak eergy (mev) STS peak eergy (mev) STS peak eergy (mev) Pearso s Pearso's r r... (a) Max for ( + ) ) Max Max for for (best fittig)........ ( + ). - - - - - Assumed Ladau Assumed idex Ladau of the idex st peak of the from st peak the left from (-. left i Fig.d mv) i Fig. d (b) (c) Max Pearso s r for ( ) + (d) Max Pearso s r for - - - - Pearso's r:. a = -. ±. b =. ±. - Pearso's r:. a = -. ±. b =. ±. - Pearso's r:. a = -. ±. b =. ±. ( ( ) + ).. Supplemetary Figure S Aalysis of quatized peaks i Fig. d i the mauscript for determig the depedece ad the Dirac poit. (a) Examiiatio of the peak eergies as a liear fuctio of the Ladau idex,, ad. (b) Oe of the fittig results for relatioship. (c) ad (d) show the best fittig for ad relatioship, respectively.
Derived DP (mev) Pearso's r di/dv (arb. uits) STS peak eergy (mev) a b f....... - -... g - - -... c e Supplemetary Figure S STM images ad STS spectra of K-HOPG show LLs are frequetly observed ear the boudary. (a) (e) STM images with dark patters; (f) STS results from the positios idicated i (a) (e); (g) Fitted results of peak eergy to correspodig to the spectra i (f), error bar of each poit is below +/ mev i each case; (h) The accuracy of fit (Pearso s r) of the STS peaks to the LLs; (i) Derived DPs ad pseudomagetic fields (B S ). STM measuremet coditios: (a) mv, pa,.. m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ; (e) mv, pa, m. d...... - - - - - - h Positio Number Positio Number Positio umber i. - -..... - -..... - -..... - -...... - -...... - -...... - -.... -.... - Bs (T) Sample bias (mv). - - -. - - -. - - -. - - - - - - -......................
Pearso's r STS Peak eergy (mev) - -.... - -.... - -.... - - - - - - - - - -.................... - - - - - - - -.... - -................ - -. - - - -................. Positio Number Supplemetary Figure S Liear fittig betwee peak eergies i the STS spectra Fig. b versus. The umber of each figure correspods to the STS spectrum i Fig. b. Error bar is below +/ mev i each case. The fittig accuracy (Pearso s r) of the STS peaks to the LLs is also show.
di/dv (arb. uits) a c e b d f x - x - boudary dark bright ---.......... --- - - - -.... - - - -............... - - - -....... - - - - Sample Bias (mv) - - Supplemetary Figure S STM images with dark patters ad STS spectra obtaied from the boudaries, dark patters ad bright regios. At the boudary regios, asymmetric LL peaks as well as the parabolic features (U-shape) were observed i the STS spectra (STS, No., ). I the potassium-free domais, the U-shape (or with LL peaks) was ofte observed (No., ). I the bright regios, bad gaps (No. ) ad LL-like peaks i the STS (No. ) were observed. STM measuremet coditios: (a) mv, pa,.. m ; (b) mv, pa, m ; (c) mv, pa,. m ; (d) mv, pa,.. m ; (e) mv, pa,.. m ; (f) mv, pa,.. m.
Supplemetary Methods Height ad strai estimatios at boudaries. STM images are kow to be iflueced by the local desity of states (LDOS) ear E F of the surface. Therefore, the height measured by STM at the boudary of the potassium-itercalated regio is apparet rather tha real if LDOS is o-uiform o the surface. It is however possible to roughly estimate the height by aalyzig the atomic arragemet i the STM top view image. I this sectio, we first estimate the heights with assumig differet magitudes of strais based o the atomic arragemet i the STM images at the boudary. The we compare those heights with that expected from the iterlayer distaces of KC ad graphite ad fially estimate the strai at the boudary. I the lie profile of the STM image i Supplemetary Fig. Sb, the legth of seve corrugatio periods at the boudary regio (. m, a) is shorter tha that of the flat dark regio (. m, c). As show i the schematic image (Supplemetary Fig. Sc), legth a could be cosidered as the projectio of legth c. The, the heights could be estimated with assumig stretchig strai levels s = %, %, %, %, %, ad % by the followig equatio (equatio (S)): h s = (S) The heights were thus obtaied as h =., h =., h =., h =., h =. ad h =. m, respectively, as show i Supplemetary Fig. Sb ad d. O the other had, the height at the boudary was assumed to be. m from the differece of iterlayer distaces betwee HOPG (. m) ad KC (. m). The depth of the dark regio (potassium-free domais) i K-HOPG should be comparable to. m. If the dark patters overlap, the height differece will be a itegral multiple of. m, i.e.. or. m. The estimated height of h (. m) or h (. m) i Supplemetary Fig. Sa correspods to three dark patters overlappig,. m. This idicates that the stretchig at the boudary is ot sigificat o the surface of K-HOPG (below %). This is cosistet with the maximum value of.% C-C stretchig calculated by DFT as show i Supplemetary Fig. Si. Supplemetary Fig. Se ad g show examples of the potassium-free regio without ad with overlappig of dark patters, where the height differeces were estimated to be. m (Supplemetary Fig. Sf) ad. m (Supplemetary Fig. Sh), respectively. The height differeces are i good agreemet with the itegral multiple of. m. Rutherford backscatterig of K-HOPG shows that K is itercalated. To examie the presece of potassium ear the HOPG surface, ex-situ Rutherford back-scatterig spectroscopy (RBS) was coducted after the etire set of STM experimets (Supplemetary Fig. S). Two broad peaks at low ad high eergies are origiated from carbo ad potassium atoms i the
K-HOPG sample, respectively. The broad peaks idicate that the scattered He ios are at differet eergies due to scatterig by atoms at differet depths. As idicated by the arrows i Supplemetary Fig. S, the highest eergy positio i the peak compoet correspods to the He ios scattered by the top layer of the correspodig elemet. Because of the broad potassium peak, the potassium is estimated to be distributed through at least approximately layers of the HOPG. That is, the RBS experimet cofirms that potassium is itercalated ito the deep layers of the HOPG sample. Determiatio of depedece ad the Dirac poit. We first assume that the eergies of peaks follow the liear relatioship with (equatio (S)), (equatio (S)), or (equatio (S)), correspodig to ormal two dimesioal electroic gas, bilayer graphee ad graphee, respectively. = E ± ± =,,,. (S) = -, -,,,, (S) = -, -,,,, (S) Withi each relatioship, we further assume a Ladau idex for each peak. The we examie the liearity by the Pearso s method ad select the coditio with the best liearity. I this method, the liearity was evaluated by the Pearso correlatio coefficiet (equatio (S)): r (S), where N is the umber of the pairs, XY is the product of XY (multiply) ad XY is multiply each X times each Y, the sum the products. I our aalysis, X correspods to,, or, ad Y correspods to the peak eergy. The results were summarized i Supplemetary Fig. Sa for the peak eergies obtaied from STS spectrum i Fig. d i the mauscript as a example. For the relatioship, the peak eergies always deviate from the liear relatioship. Here, the Pearso s r is idepedet of the Ladau idex. As for the relatioship, the maximum Pearso s r was obtaied whe the first peak from the left (. mv) i Fig. d is assumed to be Ladau level =. I this case, the Pearso s r is.. While, the best fittig (Pearso s r =.) was obtaied for the relatioship whe the peak at. mv i figure d is assumed to be Ladau level = as show i Supplemetary Fig. Sa ad d. We have repeatedly aalyzed the liearity i such a way. The best fittig has bee always obtaied for the relatioship whe the first peak from the left was assumed to be =. So we are sure that the STS peaks are due to Ladau levels of graphee ad the derived Dirac poit locates at the deep positio aroud -. ev. The shift of the Dirac poit is cosistet with the shifted Dirac coe for KC (-. ev) measured by ARPES.
Differet type of electroic structures depedig o the STS measurig positios. At the boudary regios, asymmetric LL peaks as well as the parabolic features (U-shape) were observed i the STS spectra, as show i Supplemetary Fig. S (STS, No., ). I the dark areas (potassium-free domais), the U-shape (or with LL peaks) was ofte observed (No., i Supplemetary Fig. S). I the bright regios, bad gaps (No. i Supplemetary Fig. S) ad LL-like peaks i the STS (No. i Supplemetary Fig. S) were observed. Here we otice that parabolic structures cotai a dip at E F betwee arrows idicated i Supplemetary Fig. S (STS No., -), which may be ascribed to the electro-phoo couplig i partially potassium-itercalatd graphite. These differet types of electroic structures i Supplemetary Fig. S may be ascribed to the complexity of the K i-plae structure. I particular, the asymmetric features may be due to Coulomb impurity effects ad the gaps could be ascribed to the specific alkali superstructure. I additio, mixed electroic structures such as LLs + parabolic feature are observed, which may be due to the propagatio of the states. This may be resposible for the o-eergy-shift feature of the gaps ad parabolic structures. I other words, STS spectrum may cotai the iformatio of o-doped regio, such as deep layer or potassium-free regio. Supplemetary Refereces:. Pereira, V. M., Nilsso, J. & Castro Neto, A. H. Coulomb Impurity Problem i Graphee. Phys. Rev. Lett., (). Farjam, M. & Rafii-Tabar, H. Eergy gap opeig i submoolayer lithium o graphee: Local desity fuctioal ad tight-bidig calculatios. Phys. Rev. B, ().