Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides

Glazov, M. M.; Amand, T.; Marie, X.; Lagarde, Delphine; Bouet, L.; Urbaszek, B.

doi:10.1103/physrevb.89.201302

Cited by 289 publications

(345 citation statements)

References 35 publications

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“…Polarization-resolved PL measurements yielded a valley-contrasting circular dichroism of less than 20% for both X 0 and X − resonances in all the flakes that were measured. As we argue below, the electron-hole exchange-induced mixing of the two valleys is possibly responsible for reducing the degree of circular dichroism 21,23 . Figure 2a shows the behaviour of X 0 at various B up to 8.4 T in the Faraday geometry (B z).…”

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confidence: 99%

Valley Zeeman effect in elementary optical excitations of monolayer WSe2

et al. 2015

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A monolayer of a transition metal dichalcogenide such as WSe 2 is a two-dimensional direct-bandgap valley-semiconductor 1,2 having an e ective honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly polarized light fields 3-5 , suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom 6-8 . Here we report such experiments that demonstrate the valley Zeeman e ect-strongly anisotropic lifting of the degeneracy of the valley pseudospin degree of freedom using an external magnetic field. The valley-splitting measured using the exciton transition deviates appreciably from values calculated using a three-band tight-binding model 9 for an independent electron-hole pair at ±K valleys. We show, on the other hand, that a theoretical model taking into account the strongly bound nature of the exciton yields an excellent agreement with the experimentally observed splitting. In contrast to the exciton, the trion transition exhibits an unexpectedly large valley Zeeman e ect that cannot be understood within the same framework, hinting at a di erent contribution to the trion magnetic moment. Our results raise the possibility of controlling the valley degree of freedom using magnetic fields in monolayer transition metal dichalcogenides or observing topological states of photons strongly coupled to elementary optical excitations in a microcavity 10 .Charge carriers in two-dimensional (2D) layered materials with a honeycomb lattice, such as graphene and transition metal dichalcogenides (TMDs), have a twofold valley degree of freedom labelled by ±K-points of the Brillouin zone, which are related to each other by time-reversal symmetry 7 . In TMDs, the low-energy physics takes place in the vicinity of ±K-points of the conduction and valence bands with Bloch states that are formed primarily from d z 2 and d x 2 −y 2 , d xy orbitals of the transition metal, respectively 9 . The magnetic moment of charged particles in a monolayer TMD arises from two distinct contributions: the intracellular component stems from the hybridization of the d x 2 −y 2 and d xy orbitals as d x 2 −y 2 ± id xy , which provide the Bloch electrons at ±K in the valence band an azimuthal angular momentum along z of l z = ±2h (Fig. 1a). The second-intercellular-contribution originates from the phase winding of the Bloch functions at ±K-points 11-14 . This latter contribution to orbital magnetic moment is different for conduction and valence bands owing to breakdown of electronhole symmetry. Both contributions yield magnetic-field-induced splitting with an opposite sign in the two valleys.In a 2D material such as a monolayer TMD, the current circulation from the orbitals can only be within the plane; as a consequence, the corresponding orbital magnetic moment can only point out-of-plane. A magnetic field (B) along z distinguishes the sense of circulation in 2D, causing opposite energy shifts (− µ· B) in ±K val...

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Valley Zeeman effect in elementary optical excitations of monolayer WSe2

et al. 2015

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“…As we explain below, the moiré pattern produces a periodic potential, mixing momentum states separated by moiré reciprocal lattice vectors and producing satellite optical absorption peaks that are revealing. The exciton energy-momentum dispersion can be measured by tracking the dependence of satellite peak energies on twist angle.The valley pseudospin of an exciton is intrinsically coupled to its center-of-mass motion by the electronhole exchange interaction [27][28][29][30]. This effective spinorbit coupling endows the exciton with a 2π momentumspace Berry phase [31].…”

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“…The valley pseudospin of an exciton is intrinsically coupled to its center-of-mass motion by the electronhole exchange interaction [27][28][29][30]. This effective spinorbit coupling endows the exciton with a 2π momentumspace Berry phase [31].…”

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Topological Exciton Bands in Moiré Heterojunctions

2017

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Moiré patterns are common in van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valley Zeeman field.Stacking two-dimensional (2D) materials into van der Waals heterostructures opens up new strategies for materials property engineering. One increasingly important example is the possibility of using the relative orientation (twist) angle between two 2D crystals to tune electronic properties. For small twist angles and latticeconstant mismatches, heterostructures exhibit long period moiré patterns that can yield dramatic changes. Moiré pattern formed in graphene-based heterostructures has been extensively studied, and many interesting phenomena have been observed, for example gap opening at graphene's Dirac point [1,2], generation of secondary Dirac points [3,4] and Hofstadter-butterfly spectra in a strong magnetic field [1,5,6].In this Letter, we study the influence of moiré patterns on collective excitations, focusing on the important case of excitons in the transition metal dichalcogenide (TMD) 2D semiconductors [7,8] like MoS 2 and WS 2 . Exciton features dominate the optical response of these materials because electron-hole pairs are strongly bound by the Coulomb interaction [9][10][11][12]. An exciton inherits a pseudospin-1/2 valley degree of freedom from its constituent electron and hole, and the exciton valley pseudospin can be optically addressed [13][14][15][16], providing access to the valley Hall effect [17] and the valley selective optical Stark effect [18,19].As in the case of graphene/hexagonal-boron-nitride and graphene/graphene bilayers, a moiré pattern can be established in TMD bilayers by using two different materials with a small lattice mismatch, by applying a small twist, or by combining both effects. TMD heterostructures have been realized [20][21][22] experimentally and can host interesting effects, for example the observation of valley polarized interlayer excitons with long lifetimes [23], the theoretical prediction of multiple degenerate interlayer excitons [24], and the possibility of achieving spatially indirect exciton condensation [25,26]. Our focus here is instead on the intralayer excitons that are more strongly coupled to light. As we explain below, the moiré pattern produces a periodic potential, mixing momentum states separated by moiré reciprocal lattice vectors and producing satellite optical absorption peaks that are revealing. The exciton energy-momentum dispersion can be measured by tracking the dependence of satellite peak energies on twist angle.The valley pseudospin...

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“…Spin exchange interactions are believed to be the major valley/spin depolarization channel in monolayer TMDs that causes the short valley/spin lifetime of excitons. [22,[34][35][36] To date, the direct measurement of free carriers is lacking. In this report, we use time-resolved Kerr rotation spectroscopy to unambiguously identify the valley/spin lifetime of free carriers in monolayer WSe 2 .…”

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Long valley relaxation time of free carriers in monolayer WSe2

Yan

Yang

et al. 2017

Phys. Rev. B

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Monolayer transition metal dichalcogenids (TMDs) feature valley degree of freedom, giant spinorbit coupling and spin-valley locking. These exotic natures stimulate efforts of exploring the potential applications in conceptual spintronics, valleytronics and quantum computing. Among all the exotic directions, a long lifetime of spin and/or valley polarization is critical. The present valley dynamics studies concentrate on the band edge excitons which predominates the optical response due to the enhanced Coulomb interaction in two dimensions. The valley lifetime of free carriers remains in ambiguity. In this work, we use time-resolved Kerr rotation spectroscopy to probe the valley dynamics of excitons and free carriers in monolayer tungsten diselinide. The valley lifetime of free carriers is found around 2 ns at 70 K, about 3 orders of magnitude longer than the excitons of about 2 ps. The extended valley lifetime of free carriers evidences that exchange interaction dominates the valley relaxation in optical excitation. The pump-probe spectroscopy also reveals the exciton binding energy of 0.60 eV in monolayer WSe2.

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Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides

Cited by 289 publications

References 35 publications

Valley Zeeman effect in elementary optical excitations of monolayer WSe2

Valley Zeeman effect in elementary optical excitations of monolayer WSe2

Topological Exciton Bands in Moiré Heterojunctions

Long valley relaxation time of free carriers in monolayer WSe2

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