Imaging Quantum Well States of Dirac Electrons in Exfoliated 3D Topological Insulators

TL;DR

The paper demonstrates mechanical exfoliation of the 3D topological insulator (Bi0.1Sb0.9)2Te3 into atomically clean ultrathin flakes (3–10 QL) and directly resolves quantum well states (QWS) of Dirac electrons via STM/STS. The observed QWS energies evolve with thickness and are well described by a Nearly Free Electron model, while a phase accumulation approach reconstructs the bulk $\Gamma$–$L$ dispersion in agreement with DFT calculations; the QWS persist despite surface defects, indicating robust, intrinsic confinement. The work integrates experimental exfoliation, spectroscopy, Raman thickness calibration, and first-principles calculations to reveal thickness-dependent interlayer coupling and the emergence of quasi-bulk bands, paving the way for quantum-confined topological devices and engineered surface-state phenomena.

Abstract

We present a controlled mechanical exfoliation technique for bulk 3D topological insulators that yields atomically clean ultrathin flakes, enabling quantum well states (QWS) of Dirac electrons to be clearly resolved. Achieving reliable fabrication of pristine, high-quality two-dimensional layers suitable for atomic-scale spectroscopy remains a central experimental challenge in uncovering their emergent quantum states and realizing device-relevant functionalities. Atomically resolved scanning probe microscopy and micro-Raman spectroscopy reveal a strong correlation between Raman intensity and film thickness, enabling rapid identification of (Bi\textsubscript{0.1}Sb\textsubscript{0.9})\textsubscript{2}Te\textsubscript{3} flakes with desired thickness. High resolution scanning tunneling spectroscopy on exfoliated flakes with atomically flat terraces reveals QWS, driven by quantum confinement of Dirac electrons. This effect is rarely observed due to the electrons resistance to electrostatic confinement caused by Klein tunneling. The standard phase accumulation model accurately captures the characteristics of QWS and extracts the electronic band dispersion, showing excellent agreement with density functional theory calculations. Band structure calculation reveals that with increasing quantum-layer thickness, the interlayer coupling enhances the electronic dispersion, progressively reducing subband splitting and giving rise to bulk-like continuous bands. Spatially resolved spectroscopy around surface defects further confirms that QWS of Dirac electrons in topological insulators remains robust against defect scattering. This work paves the way for exploring diverse quantum phenomena and device applications through quantum confinement, surface-state engineering, and tunable topological phases.

Figures (7)

• Figure 1: (a) Schematic of layered atomic structure of (Bi0.1Sb0.9)2Te3 portraying quintuple layer sequence and the cleaving planes, single unit cell consists of three QLs. (b) Top view of the crystal structure. (c) X-ray diffraction spectrum of the as-grown (Bi0.1Sb0.9)2Te3 (0001) single crystal plotted on a logarithmic intensity scale. The vertical axis represents the raw detector counts (no normalization was applied), while the horizontal axis denotes the diffraction angle ($2\theta$). (d) Schematic of the mechanical exfoliation and dry-transfer technique for fabrication of ultra-thin (Bi0.1Sb0.9)2Te3 flakes: exfoliation from bulk crystal onto polydimethylsiloxane (PDMS) film to avoid adhesive contamination, transfer of flakes onto conductive Si substrate using a 2D transfer system with controlled heating for conformal contact, secondary transfer of selected thickness single flake onto another conductive Si substrate having Au cross as reference markers, using polycarbonate (PC)-coated PDMS handles for STM measurements, followed by PC removal with toluene.
• Figure 2: Quintuple layer (QL) number-dependent apparent colors of exfoliated (Bi0.1Sb0.9)2Te3 flakes transferred to conductive Si-substrates: (a) AFM measurements of TI flakes with thicknesses ranging from 3 nm ($\sim$3 QL) and its integral multiples to 96 nm (96 QL). (b) Optical microscopy images of the corresponding flakes.
• Figure 3: (a) Raman spectra of exfoliated (Bi0.1Sb0.9)2Te3 flakes with different thicknesses showing the evolution of characteristic phonon modes with the inset illustrating their vibrational schematics and corresponding crystallographic directions. (b) Thickness dependence of the Raman peak intensity ratio $A^1_{1g}$ to $E^2_g$ for flakes ranging from a few QLs to bulk, (inset) Peak intensity ratio vs flake thickness for flakes $\leq$ 15 QL highlighting their linear dependency in low thickness regime.
• Figure 4: (a–f) STM topographic images of exfoliated flakes with different thicknesses, ranging from 3 QL to 10 QL. All the topographic scans acquired at constant current mode with setpoint U = 500 - 800 mV, I = 100 pA (the colorbar represents relative height). The corresponding line profiles (shown below each image) show the step heights of the flakes relative to the substrate.
• Figure 5: (a) A series of LDOS spectra (vertically shifted) acquired on flakes of 3 QL to 10 QL height portray the quantization of electrons in 2D limits, and the arrows indicate the position of the corresponding QWS peaks of each layer. (b) Projected density of states (PDOS) at the $\Gamma$ point, resolved by QL number from 1 to 10, showing progressive peak sharpening and energy shifts. (c) Quantized energies of the QWSs as a function of flake thickness for different n-values (n=1-5, as shown with different colored triangles). The experimental data (top) are fitted using Nearly free electron model. (d) Energy spacing between adjacent dI/dU peaks as a function of the number of layers in 3-10 QLs (Bi0.1Sb0.9)2Te3. Different color markers represent the energy separations between successive quantum well states ($n_1-n_2$, $n_2-n_3$, and $n_3-n_4$). (e) Subband energy splitting at $\Gamma$ as a function of the number of QLs, indicating quantum confinement and interlayer coupling. (f) QWS energies vs momentum plot giving $|v_g|= 1.6\times10^5$ m/s as calculated from the slope of the nearly linear fit.