[Paper Review] Band Topology and Dichroic Signature of Bismuth

Guang Bian, Tay‐Rong Chang+4 more|arXiv (Cornell University)|Oct 2, 2017

Photorefractive and Nonlinear Optics3 citations

TL;DR

This study establishes an experimental criterion for detecting the band topology of bismuth using angle-resolved photoemission spectroscopy (ARPES) and circular dichroism, showing that surface band responses to perturbations differ fundamentally between topological and trivial phases. The key result is a spectroscopic method to directly probe the $β_2$ topological invariant in Bi, resolving long-standing ambiguity about its topology, while CD-ARPES reveals complex spin textures on Bi(111) surfaces with a maximum dichroism of ~0.12.

ABSTRACT

Bismuth has been the key element in the discovery and development of topological insulator materials. Previous theoretical studies indicated that Bi is topologically trivial and it can transform into the topological phase by alloying with Sb. However, recent high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements strongly suggested a topological band structure in pure Bi. To address this issue, we study the band structure of Bi and Sb films by ARPES and first-principles calculations. By tuning tight binding parameters, we show that Bi quantum films in topologically trivial and nontrivial phases response differently to surface perturbations. Therefore, we establish an experimental route for detecting the band topology of Bi by spectroscopic methods. In addition, our circular dichroic photoemission illuminates the rich surface states and complex spin texture of the Bi(111) surface.

Motivation & Objective

• To resolve the long-standing debate on whether pure bismuth is topologically trivial or nontrivial by establishing a direct experimental criterion for band topology detection.
• To investigate how surface band dispersions in Bi and Sb thin films respond to surface perturbations, linking this response to bulk band topology.
• To map the spin texture of Bi(111) surfaces using circular dichroism ARPES, identifying multiple spin-polarized surface states relevant for spintronics.
• To overcome the challenge of probing the small bulk gap at the L point in bulk Bi by using quantum confinement in thin films to enhance detectable topological signatures.

Proposed method

• Employed molecular beam epitaxy (MBE) to grow high-quality, epitaxial Bi and Sb films on Si(111) substrates with controlled thicknesses.
• Conducted high-resolution angle-resolved photoemission spectroscopy (ARPES) using 22 eV photons and 15 meV energy resolution to map bulk and surface electronic structures.
• Performed circular dichroism ARPES (CD-ARPES) with left- and right-handed circularly polarized light to probe spin-polarized surface states, defining dichroism as $I_{DICH} = (I_{LCP} - I_{RCP}) / (I_{LCP} + I_{RCP})$.
• Used first-principles calculations within the projector augmented wave (PAW) method in VASP and GGA functional to simulate band structures and spin textures.
• Tuned tight-binding parameters to simulate the response of surface bands to surface perturbations in both topological and trivial phases.
• Compared experimental ARPES and CD-ARPES data with first-principles simulations to validate the topological nature of Bi and the origin of spin textures.

Experimental results

Research questions

• RQ1 Can the band topology of pure bismuth be experimentally determined despite its small bulk gap at the L point?
• RQ2 How do surface band dispersions in Bi and Sb thin films respond differently to surface perturbations when the bulk is topologically trivial versus nontrivial?
• RQ3 What is the role of quantum confinement in thin films in enabling the detection of topological band structure in Bi?
• RQ4 What spin-polarized surface states are present on the Bi(111) surface, and how can they be probed using circular dichroism ARPES?
• RQ5 Can CD-ARPES distinguish between Rashba-type surface states and additional surface resonances in Bi?

Key findings

• Sb films with thickness ≤21 atomic layers exhibit topological surface states that connect to bulk bands similarly to topological insulators, confirming Sb's topological nature in thin films.
• The response of surface bands to surface perturbations—such as chemical terminations—differs fundamentally between topological and trivial phases, providing a direct experimental criterion for detecting band topology.
• A critical thickness exists beyond which the hybridization gap from quantum confinement exceeds the intrinsic bulk band gap, allowing the true band topology of Bi to be revealed in freestanding films.
• CD-ARPES measurements on Bi(111) films show a maximum dichroism of ~0.12, confirming the presence of spin-polarized surface states, including a cross-shaped surface resonance and two additional surface bands.
• The experimental dichroic map matches first-principles calculations, resolving three distinct spin features: two Rashba-like surface states and a surface resonance overlapping the bulk band.
• The study demonstrates that spectroscopic techniques like ARPES and CD-ARPES can overcome the technical challenge of probing the small L-point gap in bulk Bi, enabling direct detection of its topological invariant.