Discovery of higher-order topological insulators using the spin Hall conductivity as a topology signature

Costa, Marcio; Schleder, Gabriel R.; Acosta, Carlos Mera; Padilha, A. C. M.; Cerasoli, Frank; Nardelli, Marco Buongiorno; Fazzio, Adalberto

doi:10.1038/s41524-021-00518-4

Cited by 22 publications

(11 citation statements)

References 48 publications

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“…They show that triangular nanoflakes with armchair edges present in-gap corner states with fractional charge, protected by C 3 symmetry. Besides being one of the striking features of a 2D-HOTI [39][40][41][42][43], they explain the presence of metallic edge states in the zigzag edges and connect them to the topology of the 2D material.…”

Section: Introductionmentioning

confidence: 88%

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Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides

Costa¹,

Focassio²,

Cysne³

et al. 2022

Preprint

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Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTI), protected by C3 rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H-TMDs and reveal that 1T-TMDs are identified by a Z4 topological invariant. As a result, when cut along appropriate directions, they host conducting edge-states, which cross their bulk energy-band gaps and can transport orbital angular momentum. Our linear response calculations thus indicate that the HOTI phase is accompanied by an orbital Hall effect. Using general symmetry arguments, we establish a connection between the two phenomena with potential implications for spin-orbitronics.

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Section: Introductionmentioning

confidence: 88%

“…Refs. [37,38] have recently revealed that some 2H-TMDs are 2D higher-order topological insulators (2D-HOTIs), not previously identified by the SHE signature [39]. They show that triangular nanoflakes with armchair edges present in-gap corner states with fractional charge, protected by C 3 symmetry.…”

Section: Introductionmentioning

confidence: 96%

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides

Costa¹,

Focassio²,

Cysne³

et al. 2022

Preprint

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“…Once the PAO Hamiltonian H PAO (k) is constructed we can calculate the orbital responses to an applied electric field using linear−response theory. This method have been used to investigate several other systems, ranging from topological to timedependent properties [62][63][64][65] 3. Electronic spectra of both models…”

Section: Ab-initio Simulationsmentioning

confidence: 99%

Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides

Cysne¹,

Guimarães²,

Canonico³

et al. 2022

Preprint

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The orbital magnetoelectric effect (OME) generically refers to the appearance of an orbital magnetization induced by an applied electric field. Here, we show that nanoribbons of transition metal dichalcogenides (TMDs) with zigzag (ZZ) edges may exhibit a sizeable OME activated by an electric field applied along the ribbons' axis. We examine nanoribbons extracted from a monolayer (1L) and a bilayer (2L) of MoS2 in the trigonal (H) structural phase. Transverse profiles of the induced orbital angular momentum accumulations are calculated to first order in the longitudinally applied electric field. Our results show that close to the nanoribbon's edge-state crossings energy, the orbital angular momentum accumulations take place mainly around the ribbons' edges. They have two contributions: one arising from the orbital Hall effect (OHE) and the other consists in the OME. The former is transversely anti-symmetric with respect to the principal axis of the nanoribbon, whereas the latter is symmetric, and hence responsible for the resultant orbital magnetization induced in the system. We found that the orbital accumulation originating from the OHE for the 1L-nanoribbon is approximately half that of a 2L-nanoribbon. Furthermore, while the OME can reach fairly high values in 1L-TMD nanoribbons, it vanishes in the 2L ones that preserve spatial inversion symmetry.The microscopic features that justify our findings are also discussed.

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“…, where for the SH conductivity X η = ŝη and for the OH conductivity (OHC) X η = ˆ η ; ŝη and η represent the η-components of the spin and of the atomic angular momentum operators, respectively. This is implemented in the Paoflow code [40] that been successfully used o study topological materials [41,42], time dependent spin dynamics [43], among other topics. For our conductivity calculations we have increased the sampling to 200×200×1 k-points in the 2D B.Z.…”

Section: Introductionmentioning

confidence: 99%

Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides

Cysne,

Costa,

Canonico

et al. 2020

Preprint

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It has been recently shown that monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase exhibit relatively large orbital Hall conductivity plateaus within their energy band gaps, where their spin Hall conductivities vanish [1,2]. However, since the valley Hall effect (VHE) in these systems also generates a transverse flow of orbital angular momentum it becomes experimentally challenging to distinguish between the two effects in these materials. The VHE requires inversion symmetry breaking to occur, which takes place in the TMD monolayers, but not in the bilayers. We show that a bilayer of 2H-MoS2 is an orbital Hall insulator that exhibits a sizeable OHE in the absence of both spin and valley Hall effects. This phase can be characterised by an orbital Chern number that assumes the value CL = 2 for the 2H-MoS2 bilayer and CL = 1 for the monolayer, confirming the topological nature of these orbital-Hall insulator systems. Our results are based on density functional theory (DFT) and low-energy effective model calculations and strongly suggest that bilayers of TMDs are highly suitable platforms for direct observation of the orbital Hall insulating phase in two-dimensional materials. Implications of our findings for attempts to observe the VHE in TMD bilayers are also discussed.

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Discovery of higher-order topological insulators using the spin Hall conductivity as a topology signature

Cited by 22 publications

References 48 publications

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides

Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides

Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides

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