Intercalant-induced Kekule ordering and gap opening in quasi-free-standing graphene

TL;DR

This work investigates how Sn intercalation at the buffer-layer/SiC(0001) interface induces Kekulé ordering and opens a band gap in graphene. A combined experimental/theoretical approach using LT-STM/STS, SPA-LEED, and DFT (VASP) reveals two graphene phases: conventional quasi-free-standing graphene and Kekulé-O graphene, with the latter showing a ∼90 meV gap and Γ-point backfolding, driven by local Sn(1×1) intercalant strain and inhomogeneity. The DFT results reproduce the main spectroscopic features and identify Sn-derived states ($S_1$–$S_3$) and their hybridization with graphene, consistent with the measured STS. The findings highlight intercalant homogeneity and strain as key levers for tuning graphene’s structural and electronic properties, with Pb intercalation not producing Kekulé order, underscoring the species-specific nature of intercalant-induced stability and gap formation.

Abstract

We present a comprehensive investigation of the structural and electronic properties of Sn intercalated buffer layers on SiC(0001) using low-temperature scanning tunneling microscopy and spectroscopy (LT-STM/STS), spot-profile analysis low-energy electron diffraction (SPA-LEED), and density functional theory (DFT) calculations. Sn intercalation effectively decouples the buffer layer, yielding quasi-free-standing monolayer graphene (QFMLG) while introducing local lattice distortions. Bias-dependent STM imaging revealed the coexistence of conventional and Kekule-ordered graphene domains, governed by the underlying Sn(1x1) reconstruction at the SiC interface. The measured STS spectra exhibit good agreement with DFT results. However, achieving homogeneous Sn(1x1) domains remains challenging, apparently, due to strain within the Sn monolayer, which drives the emergence of Kekule distortions and the associated electronic band-gap opening omogeneously in graphene. These findings highlight the crucial role of intercalant homogeneity and strain in tuning graphene`s structural and electronic properties.

Figures (5)

• Figure 1: (a) STM topographic image of a large Sn-intercalated area, showing bubble-like features (+1.5 V, 250 pA). (b) Height profile extracted along the red line in Fig. \ref{['Figure1']}(a), in comparison to the height profile across a SiC step with buffer layer (blue). (c) Atomically resolved STM image of a 7 × 7 $\rm nm^2$ area outlined by the green dashed rectangle in Fig. \ref{['Figure1']}(a) (+1.2 V, 300 pA). (d) A zoomed-in STM image of the area marked by the blue dashed rectangle (Fig. \ref{['Figure1']}(c)), exhibiting the graphene (blue hexagon) and O-shape Kekulé structure (green circle). (e) Corresponding FFT image of Fig. \ref{['Figure1']}(c), showing the diffraction spots of the graphene (blue circles, $a = 2.46$ Å) and Kekulé-O (green circles, $a = 4.25$ Å). (f-g) SPA-LEED images of the clean BL (f) and after the Sn intercalation (g), recorded with 100 eV primary energy at 300 K. The pink circles represent the diffraction spots of the intercalated Sn(1$\times$1) phase. All STM images were acquired at 77 K.
• Figure 2: Bias-dependent STM images showing the topography of two different Sn-intercalated BL regions. (a-d) Region I: STM images of Sn-induced free-standing MLG. (a) +0.1 V - 380 pA, (b) +0.05 V - 360 pA, (c) -0.1 V - 370 pA. (d) A closed-up STM image of the area marked by the red dashed rectangle in Fig. \ref{['Figure2']}(c), showing the graphene honeycomb lattice. (e-f) Corresponding FFT images of Fig. \ref{['Figure2']}(a) (e), and of Fig. \ref{['Figure2']}(b) (f). (g-j) Region II: STM images of Sn-induced distorted graphene structure. (g) +1 V - 300 pA, (h) +0.02 V - 280 pA, (i) -0.12 V - 300 pA. (j) Zoomed-in STM image of the area marked by the purple dashed rectangle in Fig. \ref{['Figure2']}(h), showing the Kekulé-O graphene lattice (+0.05 V, 400 pA). (k-l) Corresponding FFT images of Fig. \ref{['Figure2']}(g) (k) and of Fig. \ref{['Figure2']}(h) (l). Blue and green circles represent the diffraction spots of graphene and Kekulé-graphene ($\sqrt{3}$Gr). Schematic representations of the graphene and Kekulé-O graphene lattices are also shown in Figs. \ref{['Figure2']}(d)-(j). The green lines represent the distorted C-C bonds. All STM images were acquired at 4.5 K.
• Figure 3: (a) DFT calculations of the band structure (left) and density of states (right) for Sn-intercalated BL/SiC. (b) Comparison between the calculated (DFT) and experimental (STS) electronic structure of EG/Sn(1$\times$1)/SiC. (Top) Calculated DOS within an energy range (-1 eV to +0.5 eV) extracted from Fig. \ref{['Figure3']}(a). (Middle) STS of the Sn-induced QFMLG recorded at $V_b$ = 1 V, $I_t$ = 350 pA (blue curve). The spectrum was fitted with a Gaussian function. (Bottom) STS of the Sn-induced Kekulé-O graphene recorded at $V_b$ = 1 V, $I_t$ = 400 pA (green curve). $S_1*$ and $S_3*$ represent the modification of the Sn-electronic bands. The brown dashed lines represent the zero DOS. The inserted STM images display the probed positions. (c) Structural model for EG/Sn(1$\times$1)/SiC with $(\sqrt{3} \times \sqrt{3})$ supercell: top view (left) and side view (right). The STS data were recorded at 4.5 K.
• Figure 4: (a) Topographic STM image of a Sn-intercalated BL/SiC (region I) ($V_b$ = 0.1 V, $I_t$ = 380 pA). (b) Line scan of d$I$/d$V$ ($V_b$, x) spectra measured at different positions along the black dashed line in the STM image ($V_b$ = 0.2 V, $I_t$ = 400 pA). (c) Corresponding d$I$/d$V$ spectra (STS) extracted from the specific position as indicated by the colored circles in the STM image. (d) Set-point current-dependent d$I$/d$V$ spectra recorded at $V_b$ = 0.2 V, and $I_t$ = 450 pA, 550 pA, 650 pA, 750 pA. The inserted STM image shows the probed position. All STM/STS data were acquired at T = 4.5 K.
• Figure 5: (a) (Top) STM image of a Sn-intercalated BL/SiC (region II) showing the appearance of Kekulé-O ordered graphene at a bias of +0.02 V, as presented in Fig. \ref{['Figure2']}(g)-(i). (Bottom) d$I$/d$V$ line scan ($V_b$, x) taken along the black dashed line ($V_b$ = 0.4 V, $I_t$ = 350 pA, T = 4.5 K). (b) The corresponding d$I$/d$V$ spectra extracted from the positions marked by the colored circles in the STM image (Fig. \ref{['Figure5']}(a). (c) Current-dependent d$I$/d$V$ spectra of the Kekulé-O graphene, exhibiting a band gap of 90 meV ( $V_b$ = 0.4 V, $I_t$ = 350 pA, 450 pA, 550 pA). The inserted STM image shows the probed position. (d) Tunneling d$I$/d$V$ spectra of monolayer graphene (MLG) at 77 K (blue, 0.4 V, 350 pA), buffer layer at 4.5 K (red, 0.4 V, 350 pA), and Kekulé-O graphene at 77 K (pink, 0.5 V 300 pA) and at 4.5 K (green, 0.4 V, 350 pA).