Emergence of a Helical Metal in Rippled Ultrathin Topological Insulator Sb\textsubscript{2}Te\textsubscript{3} on Graphene

TL;DR

The paper investigates ultrathin Sb$_2$Te$_3$ on graphene to understand how nanoscale corrugations driven by substrate strain influence electronic structure. Using LT-STM, DFT, and a moiré ladder framework, it shows that the intrinsic hybridization gap in the flat 1QL system is closed by ripple-induced buckling, yielding a gapless metallic state with complex spin texture. The authors reveal a Helical Metal, where spin–orbit coupling is redistributed across a dense miniband spectrum, enhancing helicity beyond simple Rashba behavior. This work suggests that controlled geometric modulation in TI/graphene heterostructures can unlock dense helically polarized states with potential spintronic implications.

Abstract

The integration of topological insulators (TIs) with graphene offers a pathway to engineer hybrid quantum states, yet the impact of strain at the 2D limit remains a critical open question. Here, we investigate the structural properties of ultrathin (1 quintuple layer) Sb$_2$Te$_3$ grown on single-layer graphene and, motivated by the structural modulations observed at the TI surface, explore theoretically how such nanoscale corrugations may influence the electronic behavior of the system. Using low-temperature scanning tunneling microscopy (LT-STM), we observe a periodic rippling of the heterostructure with a wavelength of ~$\sim8.7$ nm. Energetic analysis reveals that these ripples are not intrinsic but are driven by strain from the substrate during cooling. Density functional theory (DFT) calculations show that while the ideal flat heterostructure exhibits a hybridization gap of $\sim40$ meV, the ripple-induced structural modulation closes this gap, restoring a metallic state. This gapless phase is not a trivial metal. By combining an effective moiré ladder model with spin-resolved DFT, we find that the proximity-induced spin-orbit coupling is redistributed across a dense manifold of minibands. The resulting ``Helical Metal'' has a complex spin-texture beyond a simple Rashba splitting. Remarkably, while the flat system is effectively spinless in this ultrathin limit due to hybridization, the ripples actively restore the spin polarization. Our findings suggest that rippled TI/graphene heterostructures provide an interesting platform to develop spintronics, where geometric modulation unlocks dense helical states that are inaccessible in the pristine flat limit.

Figures (8)

• Figure 1: (a) Crystal structure of Sb$_2$Te$_3$. The rhombohedral primitive cell is denoted by the inner black lines, and the quintuple layers are separated by dotted red lines. Each QL is nearly 1 nm wide. Along the article Te, Sb, C atoms are colored orange, cyan and black, respectively. (b) Top and lateral view of the primitive cell of 1 QL of Sb$_2$Te$_3$ on graphene (vacuum space is trimmed). (c) orthogonal cell of the heterostructure used to calculate buckling.
• Figure 2: (a) STM topography of the modulated pattern found in the surface of a 1QL Sb2Te3 nanoplatelet grown on single-layer graphene. (b) Angle-dependent correlation function for the stripes in (a). The color scale on the right-hand side plots represents the value of $<$G$\theta$(r)$>$. This quantity is plotted as a function of $|r|$ (vertical axis) and the angle $\theta$ with the horizontal axis. The angle-dependent correlation functions reveal clear arcs of intensity, associated with the stripe-like modulation on the surface of Sb2Te3 nanoplatelet. Solid and dashed lines represent the best fits to $Nd/\cos[(\alpha–90^\circ)–\theta]$ and $(2N–1)w/\cos[(\alpha–90^\circ)–\theta]$ for the local maxima and minima, respectively, as described in the main text. (c) and (d) STM topography of uniaxial ripples found in CVD SLG transfer onto SiO2, after the cooling-down process. (e) Optical microscope image of Sb2Te3 nanoplatelets grown on graphene/SiO2 where optical contrast shows nanoplatelets are in the range of a few quintuple layers (light purple) up to several QLs (yellowish) thick
• Figure 3: Band structure of a single QL of Sb$_2$Te$_3$: freestanding (top) and on graphene (bottom). SOC is included. The Dirac cone from graphene is folded to $\Gamma$. At this energy scale, the bands appear spin-degenerate; the Rashba spin texture becomes visible only at much higher magnification.
• Figure 4: (a) Top and lateral views of the supercell used to model the electronic structure of the ripples. (b) Band structure of the rippled supercell; X and Y correspond to directions perpendicular to and along the ripples, respectively. (c) Zoom of the low-energy bands near the Fermi level.
• Figure 5: Spin-texture close to the Dirac cone of the system with ripples. The spin projection axes ($S_x,S_y,S_z$) coincides with the Cartesian axes.