Introduction

Since the controlled positioning of 35 single Xe adatoms on a single crystal Ni(110) surface in the work by Eigler and collaborators1, scanning tunneling microscopy (STM) has been considered not only an imaging and spectroscopic technique but also as a unique instrument capable of fabricating designer structures at the atomic scale2,3. Over the years, STM manipulation of surface adsorbates4,5,6,7,8,9,10 and surface atom vacancies11,12,13 has progressed from both technical and conceptual points of view (Fig. 1a). Particularly, the design of specific systems facilitating reliable STM operation has shown the fabrication of unprecedently complex structures through thousands of controlled manipulation events. For example, carbon monoxide molecules adsorbed on Cu(111) at cryogenic temperatures were arranged in hierarchies performing basic logic operations5 or in artificial lattices expressing highly tunable electronic bands8,14,15. Even higher stability of surface vacancies in the Cl layer on Cu(110) enabled the atom-by-atom realization of a one-kilobyte memory12, establishing state-of-the-art status for STM manipulations.

Fig. 1: Buried interface under epitaxial bilayer graphene on SiC(0001).
figure 1

a Schematics of scanning tunneling microscopy (STM) -based manipulation procedures and corresponding physical mechanism involved (F: force; I: inelastic tunneling; E: electric field)2,3. In the cases of surface atoms and adsorbates, the surface atomic layer gives the manipulation plane, where the corresponding surface reconstructions define the in-plane manipulation sites. This work introduces material and experimental protocols for an analogous manipulation platform consisting of covalent Si-C bonds at the atomically sharp, buried interface. b Calculated charge density distribution across the regular interface of epitaxial bilayer graphene (BLG) and SiC substrate. AB-stacked BLG on top is decoupled from SiC by the graphene buffer layer (Cbuffer). Red dashed ellipses mark examples of covalent sp3 bonds (shared charge density) between Cbuffer and interface Si atoms. c Calculated charge density distribution at ~0.1 nm above BLG atoms along (0001)SiC plane. Black and white dashed rhombuses mark two corresponding SiC unit cells, which are the same size as in d. The color bar is the same in b, c. d, e STM constant-current topographies (sample bias, \(U=-10\) mV, and tunneling current, \(I=500\) pA). Note that low-bias STM topography of AB-stacked BLG exhibits atomic contrast of only one sublattice from the top layer70. White arrows mark examples of protrusions on the regular, quasi-hexagonal moiré interface structure. The area marked by a white line rectangle is presented in e. f Cross-section along the hexagonal path marked in panel e. Atomic-contrast corrugation (black line) is removed by a low-pass Gaussian filter (red line).

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However, the transfer of such accomplishments from metal substrates to more application-relevant systems is challenging. It requires a careful combination of STM manipulation protocols with material design, synthesis, and processing. Hydrogenated Si(100)11,13 is one of the most successful examples, where Simmons and collaborators used STM-stimulated desorption of single H atoms to fabricate devices realizing single-atom transistors16 or coupled qubits17. For these applications, the synthesis and processing steps are indeed critical, as STM lithographic patterns form the only chemically active sites for phosphine molecule adsorption, from which phosphorous dopants are subsequently incorporated into the crystalline lattice, thermally activated, and finally protected by a few layers of post-deposited Si.

The larger band-gap semiconductor, silicon carbide (SiC), constitutes another technologically important material with applications varying from high-power microelectronics18 to quantum information processing19,20. Controlled thermal decomposition of the top SiC layers also allows for precise growth of epitaxial graphene-SiC heterostructures21,22,23,24,25,26. Due to their high mesoscale quality and compatibility of the SiC(0001) substrate with general semiconductor processing strategies, these epitaxial graphene-based systems attract significant attention27,28,29,30,31. In this case, the interface between the first epitaxial graphene layer (buffer layer; Cbuffer) and SiC are primarily responsible for their unique electronic properties32,33,34,35. Controlling over this interface tunes the graphene electronic states, which leads to a rich variety of systems manifesting graphene-based physics of fundamental interest. Particularly, they include ballistic transport in topological edge states of graphene nanoribbons28,29,31,36, graphene flat bands34,35, strain-induced pseudo-magnetic fields30, or superconductivity via intercalation of the interface37,38,39,40. On the other hand, epitaxial graphene is routinely used as a model material system, e.g., to study electric-field-dependent single-atom chemical bonding between metal and graphene41, or structural dislocations of graphene42 and their dynamics43. Finally, improved synthesis methods of a high-quality, long-range ordered interface between Cbuffer and SiC have recently enabled semiconducting graphene, a long-standing challenge44,45,46.

In epitaxial graphene, Cbuffer consists of sp2 hybridized C atoms a arranged in quasi-hexagonal (6 × 6)SiC moiré pattern. This graphene-like network is separated by sp3 hybridized C atoms covalently bonded to Si from the substrate. It was also shown that Cbuffer and the underlying top SiC layer form incommensurate lattices45, slightly deviating from the (6\(\sqrt{3}\)×6\(\sqrt{3}\))R30°SiC reconstruction model47. The resulting local stress additionally modulates the interface structure by producing larger patches of decoupled graphene. Importantly, the breaking of covalent bonds between Cbuffer and SiC is associated with charge redistribution across the interface, as shown globally by rapid cooling synthesis25 or hydrogenation48,49.

Here, we use the above properties of the epitaxial graphene to design a platform for STM manipulation of bilayer graphene (BLG) and monolayer graphene (MLG) heterostructures on the SiC(0001) substrate. We show that the inherent local stress from the incommensurate lattices forming the Cbuffer-SiC interface under the epitaxial graphene creates a fine balance for local covalent coupling of Cbuffer to the SiC substrate; which consequently could be reversibly controlled by the application of an electric field with the use of STM setup. The charge separation resulting from covalent bonds’ redistribution is used to pull or push the interface atoms depending on the polarity of the tip-sample bias voltage. The reported effect allows us to pattern the otherwise chemically inert epitaxial graphene with remarkable lateral precision, reaching single unit cells of the interface moiré lattice (~1.8 nm). Similar electric-field-induced manipulation procedures for graphene heterostructures on hexagonal boron nitride (hBN) have provided highly tunable control over graphene local doping levels at the nanometer-scale50,51,52,53. Moreover, subsurface atom manipulations with STM electric field have also been achieved in other semiconducting systems like GaAs54,55,56,57, ZnO58, or PdSe259 by redistribution of single charged defects (dopants or vacancies). However, in contrast to these investigations, our system provides a more defined subsurface STM manipulation landscape by synthesizing a buried two-dimensional interface expressing ferroelectric-like switching behavior60.

Results

The interface of the graphene buffer layer and SiC

Figure 1b displays a cross-section of the epitaxial BLG interface in the form of a charge density map modeled by our density functional theory (DFT) calculations (see Methods for details). It consists of three layers of C atoms atop a SiC bilayer. The top two layers of purely sp2 hybridized C form the AB-stacked BLG. In contrast, the hybrid third layer (Cbuffer) possesses some sp3 hybridized atoms, which are covalently bonded to the underlying Si as manifested by the shared charge densities (red ellipses). The Cbuffer and SiC lattices are rotated by 30° creating a complex moiré pattern of these covalent bonds, and thus the effective corrugation of the whole BLG heterostructure exhibits a faint, quasi-hexagonal (6 × 6)SiC periodicity (Fig. 1c). The proposed (6\(\sqrt{3}\)×6\(\sqrt{3}\))R30°SiC and (13 × 13)Cbuffer supercell, which is used in our calculations, still includes a small tensile strain (~0.4%)61 in comparison to the unit cell of freestanding graphene. As a result, part of the quasi-hexagonal moiré pattern in the relaxed DFT structure is more protruded (green color in Fig. 1c) due to the breaking of additional covalent bonds between Cbuffer and SiC (Supplementary Fig. 1).

The above model corresponds well to our low-bias STM topography of the ultra-high vacuum synthesized epitaxial BLG (for synthesis details see Methods and ref. 62) presented in Fig. 1d (all STM experiments were performed at ~78 K). Positions of the protruded parts of the BLG interface, exemplified by the white arrows, are spanned by the (6 × 6)SiC lattice unit vectors. They may occupy any of the three alternating corners of the quasi-hexagonal pattern (Fig. 1e). Cross-section of the high-resolution STM in Fig. 1f shows that these protrusions extend only about 25 pm from the regular moiré corrugation. This small value supports the findings of our DFT and points to the local changes of covalent coupling within the buried interface between Cbuffer and SiC as a natural origin of the observed protrusions63. Moreover, due to the difference in thermal expansion coefficients of graphene and SiC25, the covalent coupling between Cbuffer and SiC should depend on kinetic conditions during synthesis. In this work, extended annealing times at the SiC graphitization step (1 h at ~1570 K for BLG and 1 h at ~1470 K for MLG) followed by progressive two-step cooling under ultra-high vacuum resulted in protrusion surface densities of about 0.4 per one (6 × 6)SiC unit cell [~1.2 per (6\(\sqrt{3}\)×6\(\sqrt{3}\))R30°SiC], matching the DFT model predictions.

Evidence of electric-field-induced interface manipulation

Interestingly, stable configurations of the moiré pattern protrusions change upon STM imaging performed with larger bias voltages, as seen in Fig. 2a under the atomically resolved top BLG lattice. The observed dynamic behavior depends on the polarity of the applied voltage. Particularly, large negative sample biases decrease the average number of protrusions, while large positive biases increase it (Fig. 2b). This manipulation process is reversible. Additionally, imaging at low sample biases and tunneling currents (soft STM scanning conditions) exhibits hysteresis effects depending on the previously used conditions, so the density of the protrusions can be controlled (Supplementary Fig. 2). These results particularly exclude the origination of these features from heteroatoms, i.e., Si, consistent with former studies showing a chemically homogenous interface64.

Fig. 2: Evolution of bilayer graphene-SiC interface during scanning tunneling microscopy (STM) experiments.
figure 2

a, b STM constant-current (\(I=100\) pA) topographies of two surface regions (a 10 nm × 10 nm and b 25 nm × 25 nm) obtained for larger sample biases as indicated above each panel. c Surface densities of the protrusions as a function of STM sample bias (\(I=500\) pA). The data set was obtained in the same surface region. Due to hysteresis effects, the area was imaged with negative sample bias (\(U=-1.5\) V, \(I=500\) pA) before starting each voltage ramp (arrows). Insets present representative STM images (20 nm × 20 nm). d Surface densities of the protrusions as a function of STM current for three different positive sample biases. The experiments were not performed in the same surface regions. Note the logarithmic scale of the tunneling current. Error bars in c and d represent standard error calculated assuming a Poisson distribution of protrusions.

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Figure 2c presents a quantitative analysis of the protrusion density as a function of STM sample bias voltage for a given area of BLG/SiC and tunneling current. The experiment consisted of two datasets of STM images obtained for sequentially increasing negative and positive sample bias voltages (Supplementary Fig. 3). Before collecting each set, the area was imaged with a large negative voltage, which, due to the hysteresis effect, resulted in low starting surface densities of protrusions [~0.2/(6 × 6)SiC]. For the negative sample biases, the number of protrusions initially increases up to the level close to native surface densities [~0.4/(6 × 6)SiC], and then progressively decreases to the initial, low value. In contrast, for the positive voltages, we observe a monotonic, close to linear, increase in surface densities up to the level reaching about one protrusion per (6 × 6)SiC unit cell. For the positive voltages, the density also increases linearly with the logarithm of the tunneling current (Fig. 2d). Such a weak tunneling current dependence, together with the above bias voltage polarity dependences, point to the STM-induced, local electric field50,59,65,66 as a source of the manipulation.

Small effective electric fields during soft STM scanning conditions, e.g., \({|U|} < 0.4\)V and \(I < 100\) pA, do not modify metastable configurations of the interface protrusions, i.e., for densities close to equilibrium (but high-density phases are stabilized by large positive voltages). This fact enables nanometer-scale STM patterning of BLG/SiC heterostructure, as exemplified in Supplementary Fig. 4, where a manipulation protocol involving large bias constant-current imaging increases the surface density of protrusions.

The experiments performed on MLG/SiC show that the densities of the observed protrusions also depend on the bias voltage used for STM imaging (Supplementary Fig. 5a–c). As in the BLG case, soft STM imaging conditions preserve different metastable configurations of protrusions. Consequently, we also performed nanometer-scale patterning of MLG using large bias constant-current STM conditions (Supplementary Fig. 5d, f). Quantitative agreement in the results for MLG and BLG independently supports the buried interface modification as the origin of manipulation.

Downscaling of STM manipulation to single moiré sites

Observation of metastable configurations of protrusions under soft STM scanning conditions could be further used to scale down our manipulation protocols to reach lateral precision of a single moiré (6 × 6)SiC lattice site. In this case, we stabilize the position of the STM tip above a certain corner of the moiré pattern on BLG/SiC (Fig. 3a). Then, to create a protrusion under constant-height STM operation conditions, we initialized a positive sample bias voltage ramp loop (Fig. 3b). An abrupt rise of the tunneling current signal, followed by a clear hysteresis, manifests the formation of a protrusion underneath (due to decrease of distance between the tip and the top graphene layer). This is proven by a subsequent STM scan (Fig. 3a, middle panel). This manipulation process is not only reversible, as shown by a similar procedure performed for negative voltage (Fig. 3c), but also highly reproducible (Supplementary Fig. 6 and Supplementary Movies 1–3). It allows local control of the protrusion arrangement, forming predefined structures. However, often, a single voltage ramp creates or annihilates additional protrusions in the vicinity of the targeted location. Nevertheless, as the process is easily reversible, a series of consecutive manipulations could create an intended pattern. The same manipulation strategy applies to the MLG/SiC system (Supplementary Fig. 7 and the corresponding Supplementary Movie 4).

Fig. 3: Reversible, single-site interface manipulation by local scanning tunneling microscopy (STM) electric field.
figure 3

a Sequence of three consecutive STM constant-current (\(U=+0.3\) V, \(I=25\) pA, 10 nm × 10 nm) topographies of the same surface region of the epitaxial bilayer graphene (BLG) heterostructure. Due to soft scanning conditions, an atomic contrast of top BLG is not registered. The white, dashed circles mark lateral positions of the STM tip during constant-height (STM feedback loop is open) sample bias voltage ramps. b Tunneling current signal registered during positive voltage ramp loop (see arrows). Vertical tip-sample distance is defined by \({U}_{0}=+0.3\) V and \({I}_{0}=10\) pA. The total temporal scale of the ramp loop \(t=2048\) ms. The rapid increase in signal relates to the creation of a single protrusion underneath the STM tip. c Tunneling current signal registered during negative voltage ramp loop (\({U}_{0}=-0.3\) V, \({I}_{0}=20\) pA, \(t=2048\) ms). Rapid decrease in the absolute value of current relates to the annihilation of a single protrusion underneath the STM tip. Note the negative sign of tunneling current. d Local variation of scanning tunneling spectroscopy differential conductance \({{\mbox{d}}}I/{{\mbox{d}}}V(U)\) data (constant-height, \({U}_{0}=-0.45\) V, \({I}_{0}=300\) pA). Corresponding spectra are collected at corners of the moiré pattern hosting a regular interface (black) and two protrusions (red and blue). Each spectrum is averaged over 49 (7 × 7) single curves spanning the square regions marked on the inset STM topography. Note that the limited range of voltages and tunneling currents used for \({{\mbox{d}}}I/{{\mbox{d}}}V(U)\) spectroscopy did not modify the interface structure. e Schematic presenting a manipulation mechanism based on the charge redistribution across the interface of the graphene buffer layer and SiC for two different voltage polarities.

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To determine the influence of the interface protrusions on the electronic properties of BLG, we also performed a scanning tunneling spectroscopy experiment (Fig. 3d). Differential conductance \({{\mbox{d}}}I/{{\mbox{d}}}V\) spectra obtained above the corners of the moiré interface pattern match closely to the former STM reports of epitaxial BLG on SiC(0001)62,67,68,69,70, particularly featuring a n-doped BLG system with a Dirac point located about 0.33 eV below the Fermi level. Comparison between spectra above protrusions and a regular interface shows consistent shift of about 10 mV towards positive voltages for the \({{\mbox{d}}}I/{{\mbox{d}}}V\) spectra of protrusions. Due to efficient screening by the large density of electronic states from the top BLG layers, such small changes are expected50,69. The shift of spectra towards a neutral graphene electronic configuration directly above the protrusions supports the mechanism of electric-field-induced charge redistribution at the interface, which accompanies the detachment of Cbuffer from the SiC substrate (Fig. 3e). This interpretation is also consistent with the photoelectron spectroscopy experiments performed after global decoupling of epitaxial graphene25,48, presenting the same trend of p-doping towards a neutral, freestanding system.

Interface structural changes upon manipulation from DFT

Our DFT calculations performed for the \(6\sqrt{3}{a}_{{{\mbox{SiC}}}}\times 6\sqrt{3}{a}_{{{\mbox{SiC}}}}\) slab of BLG on SiC(0001) found degenerate configurations with a single protrusion, whose position depends on the initial configuration of atoms. Figure 4 depicts the results from such two configurations, A and B, for each of which the protrusion position is separated by a distance of about (6 × 6)SiC, matching the experimental findings about their possible locations. These configurations mimic the transition between two metastable states upon STM manipulation. A comparison of the calculated charge densities across the interface plane shows a change in covalent coupling between Cbuffer and terminal Si atoms associated with annihilation or formation of the protrusion (Fig. 4a, b and Fig. 4e, f, respectively). Figure 4c, g presents the exact C-Si covalent bond distributions at the interface in the form of charge density difference (CDD) maps. Here, CDD is defined as \(\triangle \rho ={\rho }_{{{\mbox{GSiC}}}}-{\rho }_{{{\mbox{G}}}}-{\rho }_{{{\mbox{SiC}}}}\), where \({\rho }_{{{\mbox{GSiC}}}}\), \({\rho }_{{{\mbox{G}}}}\) and \({\rho }_{{{\mbox{SiC}}}}\) are charge densities of whole BLG-SiC slab, freestanding trilayer graphene slab, and freestanding Si-terminated SiC(0001) slab, respectively. Our model shows that the annihilation or formation of a single protrusion affects several C-Si bonds at the interface, i.e., the annihilation of the protrusion region presented in the top right part in Fig. 4g creates eleven new C-Si covalent bonds, while two previously present bonds in Fig. 4c are broken. As the change of sp2 hybridization of the Cbuffer atoms into sp3 increases the bond lengths within the graphene buffer layer (sp3 bonds are longer than sp2), this complex behavior is associated with the release of a tensile strain created upon the formation of new C-Si covalent bonds45,71.

Fig. 4: Redistribution of C-Si covalent bonds and charge upon switching of a protrusion site.
figure 4

a Calculated charge density distribution across a regular interface of the epitaxial bilayer graphene (BLG) in configuration A along the protrusion location as marked by the dashed lines in panels b–d. b Calculated charge density distribution of the \(6\sqrt{3}{a}_{{{\mbox{SiC}}}}\times 6\sqrt{3}{a}_{{{\mbox{SiC}}}}\) supercell at ~0.1 nm above BLG top atoms along (0001)SiC plane as indicated by the blue arrow in a. c Calculated charge density difference (CDD) at the interface plane as indicated by the red arrow in a. The bright features in c (larger CDD values) correspond to C-Si covalent bonds (see Supplementary Fig. 1d for the exact locations of atoms). d Charge accumulation (red) and depletion (green) at the interface are displayed as a top view of the corresponding CDD isosurfaces with a magnitude of 0.002 e bohr-3 (arbitrarily chosen to present data in three-dimensional space). For a perspective view see Supplementary Fig. 8. e–h Same as a–d but for BLG/SiC in configuration B. The C-Si bonds affected by the manipulation of the upper right protrusion are indicated by two black arrows in c and eleven white arrows in g. The color scale for a–c and e–g is the same.

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Moreover, the CDD isosurfaces presented in Fig. 4d, h help to visualize a charge redistribution upon formation or annihilation of a protrusion site. Due to the lack of C-Si covalent bonds, there is minimal charge transfer between SiC and Cbuffer directly below the protrusion site around the area of ~0.75 nm in diameter (see also Supplementary Fig. 8). In contrast, in the same region without the protrusion, when Cbuffer is covalently coupled to SiC, the charge transfer from SiC to Cbuffer occurs34. These results rationalize the mechanism presented schematically in Fig. 3e.

Local STM tip position dependence

Finally, we investigated a detailed position dependence of our local manipulation protocol for the formation of protrusions on the BLG/SiC system (Fig. 5a). To probe different lateral locations of the moiré corrugation pattern, we set a series of positive sample bias voltage ramps over a grid consisting of 86 × 86 points spanning an area of 10 × 10 nm2. First, from the fragmented STM image collected during the experiment (Fig. 5b), we obtain a distribution of the metastable protrusion locations. It is important to note that since soft imaging conditions were used in between positive voltage ramps, the local structure is not stabilized by the STM-induced electric field. The protrusions closely follow the (6 × 6)SiC lattice, but the corresponding sites are not equivalent. Moreover, the interplay between local stress within the heterostructure precludes the formation of a complete lattice, i.e., the formation of a dense protrusion pattern in one part, annihilates them in the other. This effect is clearly seen via analysis of the single voltage ramp spectra performed away from the (6 × 6)SiC lattice sites. In this case, as the tip is in between two or three switchable interface locations, we often observe multiple switching events caused by inherent instabilities (Fig. 5c). In contrast, for locations directly above protrusions, we generally do not register any switching events, because once a protrusion is formed, it is stable under positive voltage conditions.

Fig. 5: Tip position dependence for local scanning tunneling microscopy (STM) manipulations.
figure 5

a STM constant-current topographies (\(U=+0.3\) V, \(I=25\) pA) of the same surface region of the epitaxial bilayer graphene obtained before and after a position-dependent manipulation experiment. b STM constant-current topography (\(U=+0.3\) V, \(I=25\) pA) obtained during a position-dependent manipulation experiment. The image is built from 86 fragmented vertical datasets registered after each line of 86 single-point I–V dependences collected along the fast scan direction (see the blue arrows). c Two-dimensional map showing the distribution of protrusion switching counts obtained from a grid of 86 by 86 point I–V dependences for positive sample bias voltage ramps from \(+0.3\) V to \(+0.7\) V (constant-height is defined at each point from \({U}_{0}=+0.3\) V, \({I}_{0}=25\) pA, temporal scale of one ramp \(t=1024\) ms). A single count is defined as a rapid increase or decrease of the tunneling current signal (>15% of its previous value). The thin white lines in b and c are (6 × 6)SiC grids guiding the eye for positions of the moiré pattern exhibiting protrusions. d, e Examples of single I–V curves from the experiment showing single (d) and multiple (e) switching events. Arrows point to the lowest threshold voltages that induce switching. f Histogram presenting the distribution of switching threshold voltages. Colors are associated with corresponding switching counts in panel c.

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Figure 5d, e presents examples of single-point spectra from the experiment for single and multiple switching events, respectively. The single events dominate (apart from zero events), they generally exhibit larger changes in tunneling current signals and larger threshold voltages (Fig. 5f). This behavior is caused mainly by the lateral distribution of single switching events close to the locations of expected protrusions. These results clarify the reproducibility of the previously described manipulation protocol by presenting its limitations, which are particularly strongly related to the position of the STM tip with respect to the (6 × 6)SiC moiré lattice. On the other hand, the reversibility of the processes opens a possibility for the implantation of autonomous STM patterning procedures and their further optimization.

Conclusions

In summary, we have developed an ultimately precise buried manipulation platform for model two-dimensional heterostructures: epitaxial bilayer and monolayer graphene grown on SiC(0001). It consists of an atomically sharp moiré interface underneath the top graphene layer(s). We have shown that the application of an electric field from the scanning tunneling microscope controls the attachment of the underlying buffer layer to the SiC substrate in locations laterally defined by their (6 × 6)SiC moiré lattice vectors, resulting in the formation of defined and metastable patterns of protrusions on the epitaxial graphene heterostructures. We have quantitatively investigated the corresponding STM manipulation conditions on the epitaxial bilayer graphene, while the epitaxial monolayer graphene qualitatively has shown the same behavior. Our DFT modeling explains that this highly reversible and local ferroelectric-like switching is due to the charge redistribution associated with breaking and restoring the corresponding C-Si covalent bonds. The intrinsic, tensile interface strain enhances this process.

The results present an architecture for local patterning of epitaxial graphene heterostructures with the precision of single (6 × 6)SiC moiré lattice vectors (see Fig. 6a). Due to the complex electric-field-related mechanism and the interplay between structural stress at the interface, in the formation of designer structures, this lateral precision must be accompanied with limitations in their local densities. However, for densities close to the thermodynamic equilibrium, the protrusions could be locally arranged in ordered superstructures (Fig. 6b, c). This opens perspectives for locally tunable graphene superstructures formed directly within the epitaxial graphene systems. In contrast to STM-based manipulation platforms on metallic4,5,8,12,14,15 or semiconducting10 substrates, the inherent graphene Dirac electrons and low density of states from the silicon carbide create an opportunity for exploring rich quantum phases in low-energy electronic excitations of tailored graphene superlattice minibands72,73,74.

Fig. 6: Buried interface manipulation perspectives.
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a Series of scanning tunneling microscopy (STM) constant-current topographies (\(U=+0.5\) V, \(I=100\) pA) presenting the formation of closely packed protrusions on the epitaxial bilayer graphene (BLG), forming the “\(\Lambda\)” pattern from the (6 × 6)SiC moiré lattice sites. b, c STM constant-current topographies (\(U=+0.3\) V, \(I=25\) pA) presenting examples of 12 protrusions forming the (3 × 4) lattice of the (13 × 13)Cbuffer supercells on the epitaxial monolayer graphene (MLG, b) and BLG (c), respectively. Note specific interface electronic states contrast in the STM topography of MLG in b, similar to previous reports41,68,80.

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Methods

Synthesis

The epitaxial monolayer graphene (MLG) and bilayer graphene (BLG) synthesis for the majority of the work was performed at the Ames National Laboratory in two custom-made ultra-high vacuum systems with base pressures below 1 × 10-10 mbar. Our 6H-SiC(0001) substrates (n-type, 330 μm, 0.02-0.2 Ω∙cm) were purchased from University Wafers Inc or Cree Inc and diced into 9 mm × 1.5 mm samples. After an introduction to ultra-high vacuum, samples were outgassed for several hours at temperatures up to ~870 K. Epitaxially grown MLG/BLG on Si-face were synthesized by thermal annealing for 1 h at ~1470 K and ~1570 K, respectively. The temperature was monitored by an infrared pyrometer. During annealing, the pressure in the chamber was kept below 3 × 10-10 mbar. Annealing was performed by direct current heating followed by a two-step cooling process. At first, samples were cooled down to room temperature by slow thermalization on a sample stage, followed by their introduction to a cryostat hosting a scanning tunneling microscope (STM) operating at liquid nitrogen temperature. To confirm the generality of the results, we reproduced the main findings of the work on a high-quality BLG/SiC(0001) heterostructure synthesized by BeeGraphene via Si beam-assisted graphitization of SiC24,26. In this case, the external samples were shipped to the Ames National Laboratory, outgassed for several hours at ~570 K under ultra-high vacuum, and subsequently introduced to STM cryostat for characterization.

STM experiments

All STM experiments were performed at the Ames National Laboratory under liquid nitrogen conditions (~78 K) in the commercial Scienta-Omicron low-temperature STM. Tungsten STM tips were obtained by electrochemical etching of W wire (99.95%, 0.25 mm) in NaOH solution. Before experiments, the tips were in situ prepared and tested on the Au(111) surface. Scanning tunneling spectroscopy data were collected with an external lock-in amplifier (MFLI, Zurich Instruments) with a frequency of 691 Hz and VAC = 15 mV. Data from the externally prepared samples are presented in Supplementary Fig. 2 and Supplementary Fig. 3c, d (Sample type B).

DFT calculations

The first-principles calculations were performed based on density functional theory (DFT). We use the VASP code75 with PAW pseudopotentials76 and the optB88-vdW functional77. The supercell \(13{a}_{{{\mbox{G}}}}^{* }\times 13{a}_{{{\mbox{G}}}}^{* }\) matches \(6\sqrt{3}{a}_{{{\mbox{SiC}}}}\times 6\sqrt{3}{a}_{{{\mbox{SiC}}}}\) (see Supplementary Fig. 1), where the lattice constant of 6H-SiC is \({a}_{{{\mbox{SiC}}}}=3.09545\mathring{\rm A}\) and the lattice constant of top graphene is \({a}_{{{\mbox{G}}}}^{* }=\sqrt{3}{a}_{{{\mbox{SiC}}}}/2\approx 2.681\mathring{\rm A}\)61. Thus, the top graphene has a tiny tensile strain of 0.4% relative to the underlying SiC(0001) substrate by considering the pristine graphene or graphite lattice constant \({a}_{{{\mbox{G}}}}=2.465\mathring{\rm A}\)61. During relaxation, the bottommost C single-atom-thick layer is fixed with the dangling bonds passivated by pseudo-H atoms. The \(k\) mesh is taken to be \(1\times 1\times 1\) due to the sufficiently large supercell size. The vacuum thickness along the direction perpendicular to the slab surface is 2 nm. The energy cutoff is set to be 550 eV. Spin polarization and dipole corrections are always considered, while spin-orbit coupling is not considered in this work78. The force convergence tolerance is set to be no greater than 0.005 eV/\(\mathring{\rm A}\). In the calculation for configuration A, we initially chose a slab with all atomic planes being flat. To obtain configuration B, we relax an initial structure in which the top three graphene layers are arranged to be mirror-image symmetric to those in the fully relaxed configuration A. All charge density and CDD plots are generated by the VESTA program79.