STM imaging of electronic waves on the surface of Bi$_2$Te$_3$: topologically protected surface states and hexagonal warping effects

Abstract: Scanning tunneling spectroscopy studies on high-quality Bi$_2$Te$_3$ crystals exhibit perfect correspondence to ARPES data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear which disperse with a particular wave-vector that may result from an unconventional hexagonal warping term.

• The paper demonstrates that topological protection suppresses backscattering, evidenced by damped Friedel oscillations on Bi₂Te₃ surface states.
• It reveals that hexagonal warping initiates near -100 meV, transforming energy contours and enabling new scattering channels.
• The study rigorously cross-compares STM/STS LDOS data with ARPES findings to validate theoretical predictions in topological insulators.

STM Imaging of Electronic Waves on Bi$_2$Te$_3$: Insights into Topological Protection and Hexagonal Warping

The paper investigates the electronic properties of the topologically protected surface states of Bi$_2$Te$_3$ using Scanning Tunneling Microscopy (STM) and Spectroscopy (STS). It builds on existing work identifying Bi$_2$Te$_3$ as a three-dimensional (3D) topological insulator (TI) with a protected surface state derived from the Quantum Spin Hall Effect. The study seeks to elucidate the topological protection mechanisms and the effects of hexagonal warping on these surface states, with cross-verification using Angle Resolved Photoemission Spectroscopy (ARPES).

Key Findings

The research demonstrates a strong alignment between STS spectra and ARPES data, substantiating that the observed local density of states (LDOS) precisely maps onto surface state characteristics. A major focus is on Friedel oscillations observed near step defects on Bi$_2$Te$_3$ surfaces. The paper delineates distinct regimes in the surface state band; in the main part of the band, oscillations are significantly damped, indicating robust protection against backscattering due to the TI's topological nature. Beyond these energies, related to the hexagonal warping of the surface band, oscillations become apparent with specific dispersing wave vectors.

The study uses a meticulous approach to compare the LDOS variations to ARPES-derived electronic band structures. It identifies the onset of hexagonal warping at approximately -100 meV, where the constant energy contours of the surface state band transition from convex to a concave hexagram shape, which allows new scattering processes. The presence of non-dispersive peaks hitherto in the Dirac regime suggests complex dynamics, potentially indicative of bound state formations near step edges.

Implications and Future Directions

The observations reinforce the notion that Bi$_2$Te$_3$ exhibits well-protected surface states within certain energy domains, where suppression of backscattering is evident. The intricate changes in the LDOS and the emergence of oscillations attributable to hexagonal warping elucidate the complexity and richness of topologically nontrivial surfaces.

As a practical implication, understanding these phenomena can inform the design of TI-based electronic devices that exploit low-dissipation surface states. The mapping of surface band warping reinforces predictions and may guide further theoretical and computational models addressing spin-momentum locking and nesting in TIs.

Future explorations may expand on the interaction of surface states with bulk states to comprehend their joint effect on surface scattering phenomena. Moreover, conducting similar STM studies under varying external conditions like magnetic fields could unravel further insights into the protection mechanisms and the influence of magnetic perturbations on surface states of TIs.

In conclusion, this paper offers a comprehensive examination of the surface electronic phenomena on Bi$_2$Te$_3$ and positions itself as a significant contribution to the nuanced understanding of topological insulators. The analytical correlation between STM results and theoretical expectations provides a robust framework for future empirical explorations in the domain of topological quantum materials.