A monolayer transition-metal dichalcogenide as a topological excitonic insulator

Varsano, Daniele; Palummo, Maurizia; Molinari, Elisa; Rontani, Massimo

doi:10.1038/s41565-020-0650-4

Cited by 91 publications

(70 citation statements)

References 47 publications

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“…Second, the exciton condensate is naively expected to exhibit a charge density wave (CDW) with wavevector k Λ , but CDWs are not seen in tunnelling microscopy 20,24,33 and our detailed temperature-dependent Raman spectra show no evidence of any CDW transition (Supplementary Section 3). One possible explanation is that the condensate is made of direct excitons having q = 0, as predicted 25 for the T′ phase of monolayer MoS 2 . We have checked that this leads to no substantial symmetry breaking, due to the anisotropic character of the WTe 2 band structure (Methods and Supplementary Fig.…”

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confidence: 79%

“…This band structure immediately invokes the possibility that excitons could occur in equilibrium in monolayer WTe 2 , and therefore that the insulating state might not be a simple band insulator [25][26][27][28] . In this Article we argue that the behaviour of the conductivity and the electron chemical potential, even well above 100 K, is impossible to reconcile with an independent particle picture and strongly indicates the presence of excitons in the equilibrium state.…”

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Evidence for equilibrium exciton condensation in monolayer WTe2

et al. 2021

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We present evidence that the two-dimensional bulk of monolayer WTe2 contains electrons and holes bound by Coulomb attraction—excitons—that spontaneously form in thermal equilibrium. On cooling from room temperature to 100 K, the conductivity develops a V-shaped dependence on electrostatic doping, while the chemical potential develops a step at the neutral point. These features are much sharper than is possible in an independent-electron picture, but they can be accounted for if electrons and holes interact strongly and are paired in equilibrium. Our calculations from first principles show that the exciton binding energy is larger than 100 meV and the radius as small as 4 nm, explaining their formation at high temperature and doping levels. Below 100 K, more strongly insulating behaviour is seen, suggesting that a charge-ordered state forms. The observed absence of charge density waves in this state is surprising within an excitonic insulator picture, but we show that it can be explained by the symmetries of the exciton wavefunction. Therefore, in addition to being a topological insulator, monolayer WTe2 exhibits strong correlations over a wide temperature range.

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Evidence for equilibrium exciton condensation in monolayer WTe2

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“…Two-Band Model. The major source of numerical error is the finite sampling of the Brillouin zone (14), since the exciton is significantly localized in k space while the computational load prevents us from refining the mesh (Materials and Methods). However, the specific features of the exciton provide us with a workaround, since 1) the wave function is spanned essentially by those e and h states that are close to the edges of the lowest conduction and highest valence band, respectively ( Fig.…”

Section: Resultsmentioning

confidence: 99%

“…2 below): Whereas in the superconductor this phase degeneracy is protected by the conservation of electronic charge, in the EI it is contingent on the preservation of excitons (7,11) and hence lifted by those terms in the Hamiltonian that annihilate or create e-h pairs. This is the case of e-phonon (13) and spinorbit (14) interactions, which pin ϕ while hybridizing conduction and valence bands (remarkably, the combination of spin-orbit coupling and other factors may lead to a topological insulator whose character is inherited by the excitonic state) (14). Other mechanisms that act as sources/sinks for excitons include interband hybridization and Coulomb interaction terms allowed by symmetry (11), disorder (15), and environmental fluctuations of the electrostatic potential (8).…”

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Evidence of ideal excitonic insulator in bulk MoS ₂ under pressure

Ataei

Varsano

Molinari

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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Spontaneous condensation of excitons is a long-sought phenomenon analogous to the condensation of Cooper pairs in a superconductor. It is expected to occur in a semiconductor at thermodynamic equilibrium if the binding energy of the excitons—electron (e) and hole (h) pairs interacting by Coulomb force—overcomes the band gap, giving rise to a new phase: the “excitonic insulator” (EI). Transition metal dichalcogenides are excellent candidates for the EI realization because of reduced Coulomb screening, and indeed a structural phase transition was observed in few-layer systems. However, previous work could not disentangle to which extent the origin of the transition was in the formation of bound excitons or in the softening of a phonon. Here we focus on bulk MoS2 and demonstrate theoretically that at high pressure it is prone to the condensation of genuine excitons of finite momentum, whereas the phonon dispersion remains regular. Starting from first-principles many-body perturbation theory, we also predict that the self-consistent electronic charge density of the EI sustains an out-of-plane permanent electric dipole moment with an antiferroelectric texture in the layer plane: At the onset of the EI phase, those optical phonons that share the exciton momentum provide a unique Raman fingerprint for the EI formation. Finally, we identify such fingerprint in a Raman feature that was previously observed experimentally, thus providing direct spectroscopic confirmation of an ideal excitonic insulator phase in bulk MoS2 above 30 GPa.

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“…In previous years, TMDs have attracted considerable research interest for their applications as solid lubricants, [ 20 ] catalytic materials, [ 21 ] and high‐performance transistors, [ 3 ] whereas, nowadays, layered TMDs have become a focus of research primarily as strong photoluminescent materials [ 4,22 ] that could host nontrivial topological phases. [ 12,23–34 ]…”

Section: Figurementioning

confidence: 99%

Electronic Band Topology of Monoclinic MoS₂ Monolayer: Study Based on Elementary Band Representations for Layer Groups

Milošević

Popović

Nikolić

et al. 2020

Physica Rapid Research Ltrs

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Layered structures of group-VI transition-metal dichalcogenides (TMDs) MX 2 (M ¼ Mo, W; X ¼ Te, Se, S) [1,2] are of particular importance in both fundamental research and novel device design, because these compounds manifest a variety of quantum phenomena and combine technologically relevant and complementary physical properties, thus promising applications in optoelectronics, valleytronics, spintronics, energy storage, and energy harvesting. [1,3-7] The most studied compound among these group-VI TMDs, molybdenum disulfide or MoS 2 , exists as several polytypes. Even a single three-atoms-thick MX 2 sheet occurs in many different forms: semiconducting hexagonal 1H, metallic octahedral 1T, semimetallic monoclinic 1T 0 , and slightly distorted polymorphic forms of the latter (1T 00 and 1T 000[7]). Whereas the 1H phase is stable, the 1T phase is very unstable and undergoes Peierls transition to the metastable 1T 0 phase, which, together with 1T 00 and 1T 000 , embedded mainly in the 1H phase, [8] can be obtained via chemical exfoliation. Phase-controlled large-scale growth of μm-sized layered group-VI TMDs and synthesis of 1T 0-MoS 2 crystals of high purity have also been reported recently, [9] whereas from a theoretical perspective, a potassiumassisted chemical vapor deposition method for the phase-selective growth of 1T 0-MoS 2 monolayers and 1T 0 /2H heterophase bilayers has been proposed. [10] Nevertheless, despite these past efforts, 1T 0-MX 2 monolayers remain difficult to obtain experimentally, and therefore, measurements are usually performed on multilayers [11] and then, with the help of theoretical considerations and numerical calculations, extrapolated to the monolayer level. Meanwhile, structural phase transitions between different polytypes can be realized via diverse methods: alkali-metal intercalation, strain engineering, electron-beam and high-energy laser irradiation, argon plasma treatment, controlled chemical vapor deposition growth, [12-19] etc. In previous years, TMDs have attracted considerable research interest for their applications as solid lubricants, [20] catalytic materials, [21] and high-performance transistors, [3] whereas, nowadays, layered TMDs have become a focus of research primarily as strong photoluminescent materials [4,22] that could host nontrivial topological phases. [12,23-34] On the basis of the calculated Z 2 topological index, which characterizes time-reversal-invariant systems, [35] layered 1T 0 TMDs have been predicted to exhibit the quantum-spin Hall (QSH) effect, [36] and thus, construction of a field-effect transistor that would be based on the reversible topological phase transition [33] has been proposed. [23] In contrast, 1T 0 molybdenum ditelluride (MoTe 2) has quite recently been theoretically characterized as a Z 4-nontrivial higher order topological insulator. [26] Experimental verification of the QSH effect in 2D crystals of atomic-scale thickness is a challenging task, aimed at observation of phenomena that are considered characteristic for the

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A monolayer transition-metal dichalcogenide as a topological excitonic insulator

Cited by 91 publications

References 47 publications

Evidence for equilibrium exciton condensation in monolayer WTe2

Evidence for equilibrium exciton condensation in monolayer WTe2

Evidence of ideal excitonic insulator in bulk MoS ₂ under pressure

Electronic Band Topology of Monoclinic MoS₂ Monolayer: Study Based on Elementary Band Representations for Layer Groups

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A monolayer transition-metal dichalcogenide as a topological excitonic insulator

Cited by 91 publications

References 47 publications

Evidence for equilibrium exciton condensation in monolayer WTe2

Evidence for equilibrium exciton condensation in monolayer WTe2

Evidence of ideal excitonic insulator in bulk MoS 2 under pressure

Electronic Band Topology of Monoclinic MoS2 Monolayer: Study Based on Elementary Band Representations for Layer Groups

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Evidence of ideal excitonic insulator in bulk MoS ₂ under pressure

Electronic Band Topology of Monoclinic MoS₂ Monolayer: Study Based on Elementary Band Representations for Layer Groups