Quasiperiodic modulation of electronic states at edges of tellurium nanoribbons on $\mathrm{graphene}/6H\text{−}\mathrm{SiC}\left(0001\right)$

Trigonal tellurium with helical structure exhibits intriguing properties due to its inherent chirality, which has attracted considerable research interest recently. Using cryogenic scanning tunneling microscopy/spectroscopy and density functional theory calculations, we investigated quasiperiodic defects at particular edges of Te nanoribbons grown on graphene/SiC(0001) substrate. The detailed topography of edge defects reveals the chirality of Te nanoribbon, and the defects induce a quasiperiodic modulation of the electronic states along the edge. The average period of the edge defects varies with the twist angle between Te nanoribbon and substrate, implying the electronic modulation can be tuned by the interfacial interaction. Based on the morphology analyses and modeled calculations, we further propose the growth mechanism of the Te nanoribbons.

Figure 1

Chiral structures of the helical Te layers. (a) Two tellurium layers with opposite chirality in space groups $P{3}_{1}21$ (upper panel) and $P{3}_{2}21$ (lower panel), respectively. Their helical directions are marked by grey helixes with the atomic chains pointing into the page. (b) The top and side views of the structures in (a), with the unit cells indicated by black rectangles. ${\mathrm{R}}_2$ and ${\mathrm{L}}_2$ (${\mathrm{R}}_{1,3}$ and ${\mathrm{L}}_{1,3}$) denote the edges terminated by ${\mathrm{Te}}_2$ (${\mathrm{Te}}_1$ and ${\mathrm{Te}}_3$) atoms. R and L represent the right-handed and left-handed chiralities, respectively. (c) High-resolution STM image ($V_b=-0.50\mathrm{V}$, $I_t=200\mathrm{pA}$, thickness ∼3.4 nm) and the corresponding simulated image by DFT calculation. The atomic structure of Te layer is superposed on the images. In structural models the ${\mathrm{Te}}_1$, ${\mathrm{Te}}_2$, and ${\mathrm{Te}}_3$ atoms are represented by green, yellow, and brown spheres, respectively.

Figure 2

(a) Large scale STM image of a typical Te nanoribbon ($V_b=-1\mathrm{V}$, $I_t=10\mathrm{pA}$). The height profile along the orange dashed arrow is shown in Fig. 5. The white arrows indicate the quasiperiodic defects along the edge. (b) and (c) STM images of ${\mathrm{L}}_2$ and ${\mathrm{R}}_2$ edges ($V_b=-1\mathrm{V}$, $I_t=20\mathrm{pA}$). The blue and yellow arrows indicate type-I and type- II defects, respectively. Insets: High-resolution STM images resolving the chirality of the nanoribbons. (d) and (e) The DFT optimized structures and simulated images of type-II defects in left-handed and right-handed ribbons.

Figure 3

The $dI/dV$ measurements on the ${\mathrm{R}}_2$ edge of a Te nanoribbon (thickness $\sim 4.63\mathrm{nm}$, representing 12 layers Te). (a) STM image ($V_b=-1\mathrm{V}$, $I_t=10\mathrm{pA}$) of the nanoribbon. The contrast of the image is adjusted to make the defects clear. (b) The $dI/dV$ spectra measured at the indicated sites in (a), following the same color code. (c) and (d) The line $dI/dV$ mapping results along the black and white dashed arrows in (a), respectively. (e) The calculated PDOS at the site of the defect (blue curve) and a site away from the defect at the edge (red curve) of the bilayer Te nanoribbon (see Fig. S2 in Ref. [46] for details).

Figure 4

The origination of the edge defects in tellurium nanoribbons on Gr/SiC. (a) The sketch of the angle between the screw axis of Te nanoribbon and the close-packed direction of the (6 × 6) corrugation of Gr/SiC substrate. θ is the twist angle. (b) STM image ($V_b=-1\mathrm{V}$, $I_t=20\mathrm{pA}$) of the monolayer Te nanoribbon on Gr/SiC, the white rectangle marked the edge defects of the nanoribbon. (c) Twist angle dependence of the period of the edge defects of Te nanoribbon.

Figure 5

(a) The height profile along the dashed orange arrow in Fig. 2. (b) The growth mechanism of Te layers in a nanoribbon on Gr/SiC substrate, with their ${\mathrm{Te}}_2$-atom terminated edges aligned together. (c) and (d) The adsorption energy of a single Te adatom (grey circles) at different sites above the nanoribbon (sticks) without and with edge defects, respectively. (Note: The color bar indicates the adsorption energy with “low” being the favored site.)