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Topological Nature of Orbital Chern Insulators

Yueh-Ting Yao, Chia-Hung Chu, Arun Bansil, Hsin Lin, Tay-Rong Chang

Abstract

Ground state topologies in quantum materials have unveiled many unique topological phases with novel Hall responses. Recently, the orbital Hall effect in insulators has suggested the existence of orbital Chern insulators (OCIs) in which the orbital angular momentum drives the Hall response. Studies on OCIs, however, have so far been restricted to valley-locked or spinful systems, but candidate materials for systematic studies of OCIs are lacking. Here we discuss a framework for investigating OCIs using the feature-spectrum topology approach. To characterize the ground-state topology in the orbital degree of freedom, we introduce the orbital Chern number and orbital-feature Berry curvature and demonstrate the bulk-boundary correspondence and orbital Hall response. We also uncover a parameter-driven topological phase transition, which would offer tunability of the OCIs. In this way, we identify monolayer blue-phosphorene (traditionally considered topologically trivial) as the primal 'hydrogen atom' of OCIs as a spinless, valley-free OCI material. Our study gives insight into the nature of orbital-driven topological phases and reveals a new facet of blue-phosphorene, and provides a new pathway for advancements in orbitronics and the discovery of novel topological materials.

Topological Nature of Orbital Chern Insulators

Abstract

Ground state topologies in quantum materials have unveiled many unique topological phases with novel Hall responses. Recently, the orbital Hall effect in insulators has suggested the existence of orbital Chern insulators (OCIs) in which the orbital angular momentum drives the Hall response. Studies on OCIs, however, have so far been restricted to valley-locked or spinful systems, but candidate materials for systematic studies of OCIs are lacking. Here we discuss a framework for investigating OCIs using the feature-spectrum topology approach. To characterize the ground-state topology in the orbital degree of freedom, we introduce the orbital Chern number and orbital-feature Berry curvature and demonstrate the bulk-boundary correspondence and orbital Hall response. We also uncover a parameter-driven topological phase transition, which would offer tunability of the OCIs. In this way, we identify monolayer blue-phosphorene (traditionally considered topologically trivial) as the primal 'hydrogen atom' of OCIs as a spinless, valley-free OCI material. Our study gives insight into the nature of orbital-driven topological phases and reveals a new facet of blue-phosphorene, and provides a new pathway for advancements in orbitronics and the discovery of novel topological materials.

Paper Structure

This paper contains 4 equations, 4 figures, 1 table.

Figures (4)

  • Figure 1: (a) Crystal structure of honeycomb pnictogen monolayers, with the top and bottom panels showing the side and top views, respectively. (b-c) Band structure and orbital contributions in (b) buckled and (c) planar monolayer blue-phosphorene. (d) $\hat{L}_z$-projected feature spectrum of buckled monolayer blue-phosphorene, where the inset highlights the $\mathbb{I}_0$ sector. (e) $\hat{L}_z$-resolved Wilson loop for sectors. (f) $\hat{L}_z$-feature Berry curvature $\Omega^\mu$ of $\mathbb{I}_{\pm}$.
  • Figure 2: (a) Armchair-edge energy band with the orbital texture $\langle\hat{L}_z\rangle$. (b) Edge $\hat{L}_z$-feature spectrum. (c) Orbital (blue line) and spin (red line) Hall conductivity as a function of the chemical potential in monolayer blue-phosphorene.
  • Figure 3: (a) Evolution of the band gap at the $\Gamma$ point in monolayer $\beta$-bismuthene as a function of SOC strength. (b,e) Band structure and orbital contributions at points (b) A and (e) B marked in panel (a). (c,f) $\hat{L}_z$-projected feature spectrum at points (c) A and (f) B marked in panel (a). (d,g) $\hat{L}_z$-resolved Wilson loop at points (d) A and (g) B marked in panel (a).
  • Figure 4: (a-c) Edge transport behavior for (a) CIs, (b) SCIs, and (c) OCIs. (d-f) Edge energy band structures corresponding to (d) chiral edge states in CIs, (e) helical edge states in SCIs, and (f) floating edge states in OCIs.