[Paper Review] Topological Insulators, Topological Crystalline Insulators, Topological Semimetals and Topological Kondo Insulators

M. Zahid Hasan, Su‐Yang Xu+1 more|arXiv (Cornell University)|Jun 2, 2014

Topological Materials and Phenomena1 references3 citations

TL;DR

This review explores the emergence of topological insulators, topological crystalline insulators, topological semimetals, and topological Kondo insulators through symmetry-protected topological order. It details how experimental advances—particularly angle-resolved photoemission spectroscopy (ARPES)—reveal robust, spin-momentum locked surface states and topological quantum phase transitions via Dirac semimetals, with key results showing non-degenerate surface states in superconducting Cu₀.₁₂Bi₂Se₃, enabling potential realization of topological superconductivity and Majorana fermions.

ABSTRACT

In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We then present key experimental results that demonstrate magnetism, Kondo insulation, mirror chirality or topological crystalline order and superconductivity in spin-orbit topological insulator settings and how these new (bulk insulating) phases of matter arise through topological quantum phase transitions from Bloch band insulators via topological or Dirac semimetals at the critical point.

Motivation & Objective

• To establish the symmetry-protected topological nature of 3D topological insulators through experimental evidence, particularly ARPES and transport measurements.
• To investigate how topological quantum phase transitions from Bloch band insulators to Dirac semimetals give rise to new topological phases including topological Kondo insulators and topological crystalline insulators.
• To clarify the conditions under which topological surface states remain non-degenerate with bulk states in superconducting topological insulators, a prerequisite for realizing time-reversal invariant topological superconductivity.
• To evaluate the experimental challenges and current limitations in detecting unambiguous signatures of topological superconductivity and Majorana fermions in topological insulator heterostructures.
• To assess the role of spin-orbit coupling, mirror chirality, and Kondo screening in stabilizing topological order in correlated electron systems.

Proposed method

• Utilization of angle-resolved photoemission spectroscopy (ARPES) to directly probe the momentum- and spin-resolved electronic structure of topological insulators and their doped or superconducting variants.
• Application of symmetry-based theoretical models, including Z₂ invariants (ν₀, ν₁, ν₂, ν₃), to classify 3D topological insulators and predict their surface state topology.
• Analysis of transport and STM measurements in doped bismuth chalcogenides (e.g., CuₓBi₂Se₃) to infer superconducting pairing symmetry and proximity-induced surface superconductivity.
• Theoretical modeling of topological quantum phase transitions via tuning parameters such as doping or pressure to access Dirac semimetallic critical points.
• Investigation of Kondo screening effects in heavy-fermion systems to identify topological Kondo insulator candidates with strong electron correlation and spin-orbit coupling.
• Use of proximity effect in TI/superconductor heterostructures to probe the emergence of helical Cooper pairing on topological surface states, with emphasis on ARPES as a key tool for momentum- and spin-resolved detection.

Experimental results

Research questions

• RQ1 Can topological surface states in 3D topological insulators remain non-degenerate with bulk states in superconducting doped systems like Cu₀.₁₂Bi₂Se₃, enabling topological superconductivity?
• RQ2 What experimental signatures in ARPES data confirm the existence of spin-momentum locked Dirac surface states and their robustness against disorder and coupling to bulk bands?
• RQ3 How do topological quantum phase transitions from band insulators to Dirac semimetals manifest in materials with strong spin-orbit coupling and broken symmetry?
• RQ4 To what extent can the superconducting proximity effect in TI/superconductor heterostructures lead to time-reversal invariant topological superconductivity with helical Majorana surface states?
• RQ5 What is the role of Kondo screening and electron correlation in stabilizing topological Kondo insulator phases, and how can they be experimentally distinguished from conventional topological insulators?

Key findings

• ARPES measurements in optimally doped superconducting Cu₀.₁₂Bi₂Se₃ show that topological surface states remain well defined and non-degenerate with bulk bands at the Fermi level, a critical condition for realizing topological superconductivity.
• The observation of non-degenerate surface states supports the possibility of proximity-induced superconductivity on the surface, potentially leading to 2D topological superconductivity and the emergence of Majorana fermion bound states in vortices.
• Despite reports of zero-bias peaks in point-contact spectroscopy, high-resolution ARPES and STM studies in CuₓBi₂Se₃ fail to resolve a superconducting gap in either bulk or surface states, suggesting conventional pairing may dominate.
• Theoretical models propose that CuₓBi₂Se₃ could host bulk odd-parity topological superconductivity under specific hopping parameters, but experimental confirmation remains elusive due to complex signatures of zero-bias peaks.
• Transport and STM studies of TI/superconductor heterostructures lack momentum and spin resolution, making it difficult to isolate contributions from topological surface states, thus hindering definitive evidence for Majorana modes.
• ARPES remains the only technique capable of providing direct, momentum- and spin-resolved evidence of helical Cooper pairing in topological surface states, which is essential for confirming time-reversal invariant topological superconductivity.