[Paper Review] A new experimental approach for the exploration of topological quantum phenomena : Topological Insulators and Superconductors

M. Zahid Hasan, David Hsieh+4 more|arXiv (Cornell University)|May 2, 2011

Topological Materials and Phenomena1 references3 citations

TL;DR

This paper introduces momentum- and spin-resolved angle-resolved photoemission spectroscopy (ARPES) as a novel experimental method to directly probe the topological order in three-dimensional topological insulators. By measuring spin-momentum-locked surface states and quantifying topological invariants such as the Z₂ invariant and mirror Chern number, the authors experimentally confirmed the non-trivial topology of Bi₁₋ₓSbₓ and Bi₂Se₃, establishing a direct link between electronic structure and topological quantum phases.

ABSTRACT

The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of quantum-Hall-like states. Their topological order can be realized at room temperatures without magnetic fields and they can be turned into magnets and exotic superconductors leading to world-wide interest and activity in topological insulators. One of the major challenges in going from quantum Hall-like 2D states to 3D topological insulators is to develop new experimental approaches/methods to precisely probe this novel form of topological-order since the standard tools and settings that work for IQH-state also work for QSH states. The method to probe 2D topological-order is exclusively with charge transport, which either measures quantized transverse conductance plateaus in IQH systems or longitudinal conductance in quantum spin Hall (QSH) systems. In a 3D topological insulator, the boundary itself supports a two dimensional electron gas (2DEG) and transport is not (Z$_2$) topologically quantized. In this paper, we review the birth of momentum- and spin-resolved spectroscopy as a new experimental approach and as a directly boundary sensitive method to study and prove topological-order in three-dimensions via the direct measurements of the topological invariants {$ν_o$} that are associated with the Z$_2$ topology of the spin-orbit band structure and opposite parity band inversions, which led to the experimental discovery of the first 3D topological insulators. We also discuss how spectroscopic methods are leading to the identification of spin-orbit superconductors that may work as Majorana platforms and can be used to identify topological superconductors - yet another class of new state of matter.

Motivation & Objective

• To develop a direct experimental method for probing three-dimensional topological order, which cannot be accessed by conventional transport measurements.
• To overcome the limitations of charge transport in probing topological invariants in 3D topological insulators, especially since surface transport is not topologically quantized.
• To establish momentum- and spin-resolved ARPES as a boundary-sensitive technique capable of measuring topological invariants such as ν₀ and n_M.
• To experimentally confirm the existence of topologically protected surface states in Bi₁₋ₓSbₓ and Bi₂Se₃, linking them to bulk band inversion and spin-orbit coupling.
• To lay the foundation for identifying topological superconductors and Majorana platforms through spectroscopic signatures of topological order.

Proposed method

• Utilized angle-resolved photoemission spectroscopy (ARPES) with variable incident photon energy to spatially and energetically separate surface states from bulk bands.
• Employed spin-resolved ARPES to directly measure the spin texture of surface states, confirming helical spin-momentum locking characteristic of topological surface states.
• Applied mirror symmetry analysis in momentum space to define and measure the mirror Chern number n_M using the eigenvalues of the mirror operator M(ŷ) = PC₂(ŷ).
• Used systematic ARPES data analysis to distinguish surface states from bulk bands by comparing experimental band dispersions with first-principles calculations.
• Mapped the evolution of surface Fermi surfaces and their connectivity to bulk bands to identify topological phase transitions via band inversion.
• Calculated the topological invariant n_M = (n_{+i} - n_{-i})/2 from the Chern numbers associated with mirror eigenstates, linking it to the spin-polarized band structure.

Experimental results

Research questions

• RQ1 Can momentum- and spin-resolved ARPES directly measure topological invariants such as ν₀ and n_M in 3D topological insulators?
• RQ2 How can surface states in 3D topological insulators be experimentally distinguished from bulk states in materials with non-trivial band inversion?
• RQ3 What is the role of mirror symmetry in defining a topological invariant (n_M) in the surface state band structure of Bi₁₋ₓSbₓ?
• RQ4 How does spin-momentum locking in surface states relate to the Z₂ topological invariant and protect against backscattering?
• RQ5 Can spectroscopic methods identify signatures of topological superconductors and Majorana platforms in doped or interface-engineered systems?

Key findings

• The authors experimentally confirmed the presence of a topologically protected 2D Dirac metal surface state in Bi₁₋ₓSbₓ with spin-momentum locking, consistent with a Z₂ invariant ν₀ = 1.
• Spin-resolved ARPES measurements revealed that the surface state in Bi₁₋ₓSbₓ exhibits a mirror Chern number n_M = -1, indicating a non-trivial topological phase not realizable in free-electron systems.
• The surface Fermi surface was observed to form a central hexagonal pocket with helical spin texture, confirming the existence of a 2D helical metal protected from backscattering.
• By tuning photon energy, the authors successfully separated surface states from bulk bands, demonstrating that the outer V-shaped band in Bi₁₋ₓSbₓ is a surface state that folds into the bulk valence band.
• The measured n_M = -1 in both insulating Bi₁₋ₓSbₓ and semi-metallic Sb was consistent with theoretical predictions, confirming the role of spin-orbit coupling and mirror symmetry in generating topological order.
• The study established that the mirror Chern number n_M can be directly measured via spin-polarized band dispersions, providing a new route to classify topological insulators beyond the Z₂ invariant.