[Paper Review] Spin Hall effect in 2D metallic delafossite PtCoO$_2$ and vicinity topology

Sota Kitamura, Hidetomo Usui+10 more|arXiv (Cornell University)|Nov 7, 2018

Copper-based nanomaterials and applicationsMaterials Science3 citations

TL;DR

This paper identifies a strong intrinsic spin Hall effect in the 2D metallic delafossite PtCoO₂, driven by six strongly tilted Dirac cones near the Fermi level whose nodes are gapped by large spin-orbit coupling. The system exhibits 'vicinity topology'—a metastable topological phase protected by approximate crystalline symmetries—revealed through Wilson loop analysis and mirror Chern number calculations, positioning PtCoO₂ as a platform for spintronics and topological quantum phenomena.

ABSTRACT

The two-dimensional (2D) metal PtCoO$_2$ is renowned for the lowest room temperature resistivity among all oxides, close to that of the top two materials Ag and Cu. In addition, we theoretically predict a strong intrinsic spin Hall effect. This originates from six strongly-tilted Dirac cones that we find in the electronic structure near the Fermi surface, where a gap is opened by large spin-orbit coupling (SOC). This is underpinned by rich topological properties; in particular, the phenomenology of a mirror Chern metal is realized not exactly, but very accurately, on account of an approximate crystalline symmetry. We expect that such 'vicinity topology' to be a feature of relevance well beyond this material. Our Wilson loop analysis indicates further elaborate features such as fragile topology. These findings highlight PtCoO$_2$ as a promising material for spintronic applications as well as a platform to study the interplay of symmetry and topology.

Motivation & Objective

• To understand the origin of the strong intrinsic spin Hall effect in the 2D metallic oxide PtCoO₂.
• To investigate the topological nature of the electronic structure, particularly the role of spin-orbit coupling and crystalline symmetries.
• To explore the emergence of 'vicinity topology'—topological features protected by approximate symmetries—beyond exact topological classifications.
• To connect the observed electronic structure to measurable transport and surface phenomena, such as edge states and Wannier center flows.
• To establish PtCoO₂ as a model system for studying the interplay between symmetry, topology, and electron correlation in 2D materials.

Proposed method

• First-principles density functional theory (DFT) calculations using the WIEN2K package with PBE-GGA exchange-correlation functional and scalar relativistic approximation.
• Construction of a nine-band tight-binding model on a triangular lattice using maximally localized Wannier functions derived from DFT bands.
• Explicit inclusion of spin-orbit coupling (SOC) as an on-site term with λ ≈ 0.55 eV, calibrated to reproduce ARPES data.
• Computation of Wilson loop eigenvalues along high-symmetry paths to probe the flow of Wannier centers and detect topological invariants.
• Analysis of mirror Chern numbers and $C_{2z} ilde{ au}$ symmetry to identify stable and metastable topological indicators.
• Simulation of slab geometry to compute edge states and probe surface-sensitive topological responses.

Experimental results

Research questions

• RQ1 What is the origin of the strong intrinsic spin Hall effect in PtCoO₂, and how does it relate to its electronic band structure?
• RQ2 How do the six Dirac cones near the Fermi surface contribute to topological transport properties despite being gapped by spin-orbit coupling?
• RQ3 To what extent can topological invariants like the mirror Chern number be realized in systems with approximate, rather than exact, crystalline symmetries?
• RQ4 What is the role of orbital-momentum locking in modifying electron scattering and transport in PtCoO₂?
• RQ5 Can surface probes detect metastable topological states protected by approximate symmetries, such as $C_{2z} ilde{ au}$?

Key findings

• PtCoO₂ hosts six strongly tilted Dirac cones near the Fermi level, which are robust under crystalline symmetry but gapped by large spin-orbit coupling (λ ≈ 0.55 eV), opening a gap of ~0.43 eV.
• The system realizes a 'vicinity topology' phase, where the mirror Chern number is preserved with high accuracy due to approximate mirror symmetry, despite breaking at surfaces.
• Wilson loop analysis reveals fragile topology and Wannier center crossings at 0 and ±π, indicating a metastable $ ilde{b Z}$ classification protected by $C_{2z} ilde{ au}$ symmetry.
• The orbital character on the Fermi surface is not pure $d_{3z^2-r^2}$ but has significant $d_{3x^2-r^2}$-like character, locked to momentum, which may reduce impurity scattering.
• Surface-sensitive probes may access a state where only the metastable topology (via $C_{2z} ilde{ au}$) is realized, enabling experimental study of fragile and approximate topological phases.
• The combination of strong SOC, 2D metallic character, and rich topological structure makes PtCoO₂ a promising candidate for spintronic devices and topological quantum research.