[Paper Review] Three-Dimensional Real Space Invariants, Obstructed Atomic Insulators and A New Principle for Active Catalytic Sites

Yuanfeng Xu, Luis Elcoro+8 more|arXiv (Cornell University)|Nov 3, 2021

Graphene research and applications22 citations

TL;DR

This paper introduces three-dimensional real space invariants (RSIs) to classify obstructed atomic insulators (OAIs) in 1,651 Shubnikov space groups with spin-orbit coupling, identifying 3,383 paramagnetic and 30 magnetic OAIs from material databases. It demonstrates that OAIs exhibit filling anomalies and obstructed surface states (OSSs), experimentally validating that OSSs on 2H-MoS2 surfaces drive high catalytic activity in hydrogen evolution, establishing a new principle for designing active catalytic sites.

ABSTRACT

Topologically trivial insulators come in two kinds: atomic, where the Wannier charge centers (WCCs) are localized on the atoms, and obstructed atomic, where the WCCs are located away from the atoms. The latter, which can exhibit interesting surface states and possibly have much larger band gaps than the topological insulators, have so far not been classified in three-dimensional (3D) crystalline materials. In this paper, we developed the 3D real space invariants (RSIs) for the 1651 Shubnikov space groups with the spin-orbit coupling and provide the full classification of 3D obstructed atomic insulators (OAIs) by the RSIs. We then apply the theory to the entire database of materials on the Topological Quantum Chemistry website and Topological Magnetic Materials website, obtaining all the OAIs so far existing in nature. We find that, out of the 34013 paramagnetic and 296 magnetic topologically trivial insulators, there are 3383 paramagnetic and 30 magnetic OAIs. All of them present a filling anomaly under certain open-boundary conditions and exhibit obstructed surface states (OSSs). We further refine the atomic insulator concept to obtain the orbital-selected OAIs (OOAIs), where the WCC of the system is located at a Wyckoff position occupied by an atom but forms a symmetric representation that does not belong to the outer-shell electrons of the given atom. In such a way, we obtain a further 121 OOAIs. Furthermore, we analyze the catalytic properties of one of the OAIs in a "proof of principle" experiment. By using the single crystal of 2H-MoS2 as a hydrogen evolution catalyst, we directly prove that the catalytic activities arise from the surfaces with OSSs. Additional potential applications of the 3D RSIs and OAIs in, for example, electrochemistry, asymmetric catalysis, superconductivity, and Josephson diode will be discussed.

Motivation & Objective

• To classify three-dimensional obstructed atomic insulators (OAIs) in all 1,651 Shubnikov space groups using real space invariants (RSIs) with spin-orbit coupling.
• To identify all paramagnetic and magnetic topologically trivial insulators in nature that exhibit filling anomalies and obstructed surface states (OSSs).
• To establish a new principle linking obstructed surface states in OAIs to enhanced catalytic activity in heterogeneous catalysts.
• To refine the atomic insulator concept by introducing orbital-selected OAIs (OOAIs), where Wannier centers form symmetric representations not from outer-shell electrons.
• To experimentally validate that catalytic activity in 2H-MoS2 arises from surfaces hosting OSSs, linking electronic topology to catalytic function.

Proposed method

• Developed 3D real space invariants (RSIs) for all 1,651 Shubnikov space groups to classify obstructed atomic insulators (OAIs) under spin-orbit coupling.
• Applied Topological Quantum Chemistry (TQC) theory and symmetry indicators to analyze the entire database of materials from the Topological Quantum Chemistry and Topological Magnetic Materials websites.
• Calculated Wannier charge centers (WCCs) and determined their localization at Wyckoff positions to identify OAIs via non-trivial RSIs.
• Identified cleavage planes with metallic OSSs using Miller indices derived from Wannier center positions and symmetry analysis.
• Introduced orbital-selected OAIs (OOAIs) by analyzing which symmetric representations of WCCs do not match the outer-shell electron configurations of constituent atoms.
• Conducted a proof-of-principle experiment using high-quality single-crystal 2H-MoS2 to correlate surface electronic states (OSSs) with hydrogen evolution reaction (HER) catalytic activity.

Experimental results

Research questions

• RQ1 What is the complete classification of three-dimensional obstructed atomic insulators (OAIs) in all Shubnikov space groups using real space invariants (RSIs) with spin-orbit coupling?
• RQ2 Which paramagnetic and magnetic topologically trivial insulators in nature exhibit filling anomalies and obstructed surface states (OSSs)?
• RQ3 Can obstructed surface states (OSSs) in OAIs serve as the origin of high catalytic activity in heterogeneous catalysts?
• RQ4 How can the concept of atomic insulators be refined to identify orbital-selected OAIs (OOAIs), where WCCs form symmetric representations not from outer-shell electrons?
• RQ5 To what extent do the electronic surface states of 2H-MoS2, predicted as OSSs, correlate with experimentally measured hydrogen evolution reaction (HER) activity?

Key findings

• Out of 34,013 paramagnetic and 296 magnetic topologically trivial insulators, 3,383 are paramagnetic OAIs and 30 are magnetic OAIs, all exhibiting filling anomalies under open-boundary conditions.
• All identified OAIs display obstructed surface states (OSSs), with specific cleavage planes—identified by Miller indices—showing metallic surface states, including chiral surface groups marked by superscript 'c'.
• The study identifies 121 additional orbital-selected OAIs (OOAIs), where Wannier centers form symmetric representations not belonging to the outer-shell electrons of the atoms at their positions.
• In a proof-of-principle experiment, 2H-MoS2 single crystals with OSSs on their surfaces showed high hydrogen evolution reaction (HER) activity, directly linking OSSs to catalytic function.
• The band gaps of the identified OAIs range from 0.000 eV to 3.842 eV, with some exhibiting large gaps (e.g., 3.842 eV in CoAl2O4), indicating potential for stable, high-performance catalytic materials.
• The real space invariants (RSIs) successfully classify OAIs across all 1,651 Shubnikov space groups, enabling a complete topological inventory of obstructed atomic insulators in 3D crystalline materials.