Valley Zeeman Splitting and Valley Polarization of Neutral and

Jones , A. M.; Yu , H.; Ghimire , N. J.; Wu , S.; Aivazian , G.; Ross , J. S.; Zhao , B.; ...... Park , J. C.; Yun , S. J.; Kim , H.; Park , J.; Chae ...
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Valley Zeeman Splitting and Valley Polarization of Neutral and Charged Excitons in Monolayer MoTe2 at High Magnetic Fields Ashish Arora,*,† Robert Schmidt,† Robert Schneider,† Maciej R. Molas,§ Ivan Breslavetz,§ Marek Potemski,§ and Rudolf Bratschitsch*,† †

Institute of Physics and Center for Nanotechnology, University of Münster, Wilhelm-Klemm-Strasse 10, 48149 Münster, Germany Laboratoire National des Champs Magnétiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 25 rue des Martyrs, 38042 Grenoble, France

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S Supporting Information *

ABSTRACT: Semiconducting transition metal dichalcogenides (TMDCs) give rise to interesting new phenomena in external magnetic fields, such as valley Zeeman splitting and magnetic-fieldinduced valley polarization. These effects have been reported for monolayers (MLs) of the transition metal diselenides MoSe2 and WSe2 and, more recently, for disulfides MoS2 and WS2. Here, we present helicity-resolved magneto-photoluminescence and magnetoreflectance contrast measurements for MLs of the telluride member of the semiconducting TMDCs, 2H-MoTe2, in magnetic fields up to 29 T in Faraday geometry. Well-resolved valley Zeeman splittings for the neutral A and B excitons (X0A and X0B) and the charged exciton X± are observed with effective g-factors of −4.6 ± 0.2, − 3.8 ± 0.6, and −4.5 ± 0.3, respectively. The magnetic field induced valley polarization of X0A and X± reaches 78% and 36%, respectively, at a magnetic field of 29 T. KEYWORDS: Monolayer MoTe2, valley Zeeman splitting, valley polarization, transition metal dichalcogenides, excitons and trions, magneto optics

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charged excitons,24,28−34 relative effective masses of electrons and holes,28 and a high degree of Berry curvature associated with the charged exciton states.29 It also leads to a preferential accumulation of charge carriers in one of the valleys in the presence of intervalley scattering, which results in photon emission predominantly in one circular polarization state (valley polarization effect).13−16 These phenomena have been demonstrated previously for the neutral (X0A) and charged (X±) excitons in TMDC selenides (MoSe2, WSe2).24,28−33 More recently, the valley Zeeman effect has been found for both the X0A and B excitons (X0B) in MoSe2,35 and the sulfides (MoS2 and WS2)34,35 of the semiconducting TMDC family. The telluride member MoTe2 extends the spectral range of semiconducting TMDCs from the visible to the infrared region. Interestingly, molybdenum ditelluride exists in three phases with strongly different physical properties: the hexagonal 2H phase shows semiconducting behavior,9,10,36−39 the distorted octahedral 1T′ phase is metallic,37−39 and the orthorhombic Td phase has been predicted to be a Weyl semimetal.40 In addition, the band gap of 2H-MoTe2 is similar to that of bulk silicon and therefore promising for its use in 2D electronics.41,42 However, MoTe2

tomically thin layers of transition metal dichalcogenide (TMDC) semiconductors such as MoS2, WS2, MoSe2, WSe2, and MoTe2 have received considerable attention due to their potential for new electro-optic devices based on valleytronics.1−4 Their band structure shows a crossover from indirect to direct band gap, when the thickness is reduced from few-layer to a monolayer (ML).5−10 In addition, the absence of inversion symmetry and a large spin−orbit splitting in the MLs (150−500 meV for the valence band and up to ∼40 meV in the conduction band of different TMDCs)11,12 results in distinct states with different angular momenta in the K− and K+ valleys. The two valleys are energetically degenerate and can be selectively addressed by using circularly polarized light. The lowest energy interband transitions in the K− and K+ valleys couple to σ− and σ+ polarized light, respectively. As a consequence, monolayers of TMDCs have shown interesting physical phenomena, such as valley polarization13−16 and valley coherence.17 These materials are also promising for optoelectronic devices, such as LEDs,18−20 lasers,21,22 and single-photon emitters.23−27 Although the two valleys K− and K+ are degenerate in energy, they couple differently to an externally applied magnetic field due to the different total magnetic quantum numbers (mj) in the conduction and valence bands. As a consequence, the valley degeneracy is lifted. This “valley Zeeman effect” provides important information about the valley-resolved band structure in these materials, such as effective g-factors of neutral and © XXXX American Chemical Society

Received: February 21, 2016 Revised: April 20, 2016

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DOI: 10.1021/acs.nanolett.6b00748 Nano Lett. XXXX, XXX, XXX−XXX

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In absence of the magnetic field, well separated X0A and X± emission features are identified at 1.191 ± 0.001 eV and 1.167 ± 0.001 eV, as shown in Figure 1a for a ML on Si/SiO2 at

has not been investigated so far using magneto-optical techniques. For a comprehensive theoretical understanding of the valley Zeeman splittings, k·p perturbation theory-based calculations are needed, which must consider the effects of interband interactions for the bands lying close in energy to model the gfactor of a particular band. Although such calculations have been very successful for conventional semiconductors such as GaAs and their nanostructures,43 they have not been reported for TMDCs so far. k·p calculations of TMDCs have been published, but magnetic field effects have not been discussed.12 Interestingly, a simple tight binding model has been successful in predicting approximate values for the measured g-factors of neutral and charged excitons in TMDCs.28−34 According to this model, the excitonic valley Zeeman splitting primarily arises due to the dx2 − y2 ± idxy hybridized atomic orbitals at the top of the valence bands at the K± valleys, which have a magnetic moment of ±2 μB, where μB is Bohr’s magneton.28−34 This corresponds to a valley Zeeman splitting of Eσ+ − Eσ− = −4 μBB and a g-factor of −4. Here, Eσ+ and Eσ− are the excitonic transition energies for the σ+ and σ− polarized optical components. In all of the four TMDC MLs studied so far (MoS2, WS2, MoSe2, WSe2), the measured g-factors of the neutral and charged excitons do not deviate significantly from this value, demonstrating the applicability of this model.24,28−35 Here, we investigate ML 2H-MoTe2 using magneto-optical techniques. We perform microphotoluminescence (μPL) and microreflectance contrast (μRC) spectroscopy on MLs of 2HMoTe2 under high magnetic fields up to 29 T in Faraday geometry. We clearly observe lifting of the valley degeneracy and find valley polarization due to the magnetic field. From our measurements, we derive the effective g-factors for the neutral X0A and X0B and charged excitons X±. In addition, we find a high magnetic-field-induced valley polarization for neutral and charged excitons in ML MoTe2. MLs of 2H-MoTe2 are mechanically exfoliated onto Si/SiO2 (80 nm) and sapphire substrates44 and identified by optical contrast,10 atomic force microscopy (AFM), and Raman spectroscopy (Figure S1 of the Supporting Information).9,10,36,45 The ML flakes are first investigated by μPL and μRC measurements in the absence of magnetic field. μPL is performed using continuous-wave laser excitation at 514 nm at temperatures from T = 4 to 220 K (Figure S2 of the Supporting Information). Magneto-optical experiments (B ≠ 0) are performed with an optical-fiber-based low-temperature insert placed in a resistive magnet (29 T, 50 mm bore diameter). The samples are mounted on x−y−z piezo-nanopositioners. The excitation wavelength for the magneto-μPL is 780 nm (tunable continuous-wave Ti:sapphire laser, 0.5 mW focused in a diameter of 10 μm full width at half-maximum (fwhm)), whereas for the magneto-μRC measurements broadband light from a tungsten halogen filament is used. The diameter of the optical fibers used for excitation and detection are 50 μm. The depolarized excitation light is focused on the sample with an aspheric lens of focal length 3.1 mm (NA = 0.68). A combination of a quarter wave plate and a polarizer are used for detecting the circular polarization with an InGaAs array integrated with a monochromator. The combined spectral resolution of the setup is 0.5 meV. The measurements are performed with a fixed circular polarization, whereas reversing the direction of magnetic field yields the information corresponding to the other polarization component due to time-reversal symmetry.46

Figure 1. (a) Microphotoluminescence (μPL) (blue circles) and microreflectance contrast (μRC) (green circles) spectra of monolayer (ML) MoTe2, measured at a temperature of T = 4.2 K. Solid lines represent the modeled spectra. In μPL, the neutral X0A and the charged X± excitons are clearly observed. In μRC, the X0A and X0B excitons are found, where the PL intensity in the region involving X0B has been multiplied by a factor of 5 for clarity. (b,c) Schematic drawing of the optical selection rules between the conduction and valence bands in the K− and K+ valleys of MoX2 (X = S, Se, Te) monolayers for circularly polarized σ+ (blue) and σ− (orange) light in the absence of a magnetic field (B = 0) and with magnetic field (B > 0), following the spin conventions in refs 12 and 14. Spin−orbit split conduction and valence bands are drawn with a splitting of Δc and Δv, respectively. For clarity, the dipole-allowed transitions in both valleys are shown for the X0A exciton only. With B > 0 applied perpendicular to the plane of the sample, the shift of the valence and conduction bands in the K− and K+ valleys (solid curves, only X0A exciton) is depicted with respect to their positions at B = 0 (dashed curves), along with the individual contributions from the spin, orbital, and valley magnetic moments following the notations of refs 4, 28−31, and 50.

cryogenic temperatures. The lines exhibit narrow widths of 8.5 meV (fwhm), compared to typical line widths of other TMDC MLs (10−15 meV), suggesting a good quality of the material studied. The binding energy of the charged exciton is found to be 24 ± 1 meV, which is in agreement with previous reports.10,47 No measurable photoluminescence emission is observed at temperatures higher than 200 K, in accordance with previous work.10 μRC measurements for ML on Si/SiO2 show X0A at 1.192 ± 0.001 eV, whereas for a ML on sapphire we measure X0A at 1.195 ± 0.001 eV and a broad X0B feature (fwhm: 47 meV) at 1.464 ± 0.004 eV (Figure 1a). These values correspond to a spin−orbit splitting of 269 ± 5 meV in ML MoTe2, which is comparable to 250 ± 10 meV, recently reported by Ruppert et al.9 X± is too weak to be identified in the μRC measurements because of a low oscillator strength, possibly due to low unintentional doping. The valley-resolved electronic band structure at the K− and K+ points of the Brillouin zone in ML MoX2 (X = S, Se, Te) at B = 0 is depicted B

DOI: 10.1021/acs.nanolett.6b00748 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 2. (a) Helicity-resolved microreflectance contrast spectra of excitons in monolayer MoTe2 as a function of magnetic field, with the flakes exfoliated on (a) Si/SiO2 substrate (X0A exciton) or (b,c) sapphire substrate (X0A and X0B exciton). The solid black lines represent the modeled spectra. (d) Zeeman-split transition energies and (e) valley Zeeman splittings for the X0A (circles, Si/SiO2 substrate), X0A (squares, sapphire substrate), and X0B exciton (triangles, sapphire substrate).

responsible for the Zeeman effect are the spin (ms), atomic orbital (ml), and the valley magnetic moment (mk), which is related to the Berry curvature that causes the valley Hall effect.51 When considering only the Zeeman shift of a transition under an applied magnetic field, one finds that the spin contributions cancel out because they contribute in the same direction for the CB and the VB. However, a major contribution is due to the different ml of the states, which predominantly form the top of the VB (dx2 − y2 ± idxy hybridized orbitals with mvl = 2) and the bottom of the CB (dz2 with mcl = 0).28−34 The atomic orbital contribution to the valley Zeeman splitting is 2(mcl − mvl )μBB = −4 μBB for an excitonic transition. The contributions from the valley magnetic moment to the

in Figure 1b along with the valley-dependent optical selection rules. The conduction and the valence bands (CB and VB) consist of a pair of spin−orbit split bands each, with the corresponding splitting denoted by Δc and Δv, respectively. The lowest energy transitions in the K− and K+ valleys are degenerate in energy and involve σ− and σ+ polarized light in emission and absorption. The ordering of the spin−orbit split CBs in Figure 1b has been drawn according to theoretical calculations, which predict that the ground state exciton transition in a MoX2 ML is optically bright and optically dark in WX2 MLs.11,12 In addition, recent experimental works also favor this scenario.48,49 Upon application of a magnetic field perpendicular to the ML plane, the pair of states connected by time reversal symmetry shift in opposite direction in energy, which lifts their degeneracy (Figure 1c). For example, the lowest energy CBs in K− (spin up, blue line) and in K+ (spin down, orange line) form such a pair and, similarly, the highest energy VBs in K− (spin up, blue line) and in K+ (spin down, orange line). We have followed the spin conventions as proposed in previous works.12,14 The excitonic transition corresponding to a given circular polarization involves charge carriers in the CB and VB with the same spin.12,14 We note that with an applied magnetic field the excitonic transitions in the two valleys are at different energies (if the CB and VB undergo different splittings) with an equivalent valley Zeeman splitting of ΔEX = −2(ΔECB − ΔEVB) = −gXμBB, where ΔECB and ΔEVB represent the shift of CB and VB, respectively. μB is the Bohr’s magneton (0.05788 meV/T) and gX is the exciton’s g-factor. In Figure 1c, we present the various factors that contribute to the Zeeman effect in the CB and VB, as discussed previously.4,28−31,50 For clarity, only the bands participating in the A exciton transition are depicted. The three major contributing factors to the total magnetic moment

Zeeman shifts of CB and VB are ±

( mm* )μB in the K 0

±

valleys,

where m* is the effective mass of the charge carriers in the respective band. If the effective masses of carriers in the CB and VB are equal, this contribution will cancel out, being equal and opposite. As a consequence, the effective g-factor for the (neutral) excitonic transition would be −4. The charged exciton is a composite of a charged particle (electron or a hole) bound to a photogenerated electron−hole pair. The photoluminescence emission from a charged exciton involves a transition in which the initial state before recombination is a three-particle state, whereas the final state after recombination is a single electron in the CB or a single hole in the VB. Since the g-factor of a quasi-particle is determined by the difference between the magnetic momenta of initial and final state, the gfactor of the charged excitons is expected to be equal to the one of the neutral excitons in the simplistic approximation because the extra electron or a hole is expected to contribute equally to the magnetic moment of the initial and the final states.29,30 C

DOI: 10.1021/acs.nanolett.6b00748 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters Figure 2 a shows the σ+ (orange) and σ− (blue) components of the measured μRC spectra for a MoTe2 ML placed onto Si/ SiO2 substrate as a function of magnetic field. The reflectance contrast spectrum is defined as C(λ) = [R(λ) − R0(λ)]/[R(λ) + R0(λ)], where R(λ) and R0(λ) are the wavelength-dependent reflectance spectra of the MoTe2 monolayer on the substrate and the bare substrate, respectively. The X0A resonance shows a clear Zeeman splitting, which increases with rising magnetic field. At the same time, the magnetic field has a negligible effect on the line shape of the resonance. Identical measurements are performed on a MoTe2 monolayer on sapphire substrate (Figure 2b,c), where not only the X0A resonance but also the X0B resonance is clearly visible. The μRC spectral line shapes strongly differ for the two substrates due to interference effects in multiple layers of materials with different refractive index.52,53 We model the spectra with the transfer matrix method.52 The excitonic contribution to the dielectric response is described by a Lorentzian oscillator-like model:53,54 ϵ(E) = (nb + ik b)2 + ∑j

Figure 3. (a) Helicity-resolved microphotoluminescence spectra of the neutral X0A and the charged X± excitons (dots) in monolayer MoTe2 on Si/SiO2 substrate, as a function of magnetic field. The solid black lines represent the modeled spectra. The valley Zeeman splittings of the neutral and charged excitons are clearly resolved, and a significant magnetic-field-induced valley polarization is observed. (b) Zeemansplit transition energies, (c) valley Zeeman splitting, and (d) degree of circular polarization PC = (Iσ+ − Iσ−)/(Iσ+ + Iσ−), measured for X0A and X± transitions as a function of magnetic field.

Aj E0j 2 − E2 − iγjE

(1)

where nb + ikb represents the background complex refractive index of MoTe2 in the absence of excitonic effects. It is assumed to be equal to bulk material55 because it does not appreciably change when the layer thickness is reduced from bulk to a monolayer in TMDCs.56 The refractive indices for Si, SiO2, and sapphire are obtained from ref 57. E0j is the transition energy, Aj is the oscillator strength parameter, and γj is the fwhm line width of the jth exciton. The extracted transition energies for the σ+ and σ− polarizations (Eσ+ and Eσ−) in the three cases are shown in Figure 2d as a function of magnetic field. The corresponding Zeeman splittings (Eσ+ − Eσ−) are plotted in Figure 2e, and the g-factors for the A and B excitons from linear fits to the data are extracted to be gXA0 = −4.8 ± 0.2 for the ML on Si/SiO2, whereas gXA0 = −4.7 ± 0.4 and gXB0 = −3.8 ± 0.6 for the ML on sapphire substrate. The gXB0 excitonic feature for a ML on the Si/SiO2 substrate is not analyzed due to large uncertainties involved in its spectral fitting. Helicity-resolved μPL spectra for the MoTe2 ML on Si/SiO2 are shown in Figure 3a as a function of magnetic field. Both the X0A and X± transitions show a clear Zeeman splitting. The two lines are fit with a pair of Gaussians, and the extracted X0A and X± transition energies and the Zeeman splittings are shown in Figure 3b,c, respectively. The g-factors obtained from linear fits to the data in Figure 3c are gXA0 = −4.3 ± 0.3 and gX± = −4.5 ± 0.3, which are equal within experimental error. From the μPL and μRC measurements, an average value of the g-factor for the neutral A exciton is obtained as gXA0 = −4.6 ± 0.2. Interestingly, in our μPL spectra, the lower energy transition of the Zeeman split line (σ+) for both neutral and charged exciton gains in intensity, whereas the higher energy transition (σ−) loses with increasing magnetic field (Figure 3a). This observation in ML MoTe2 is in contrast to a report of Wang et al.33 for ML WSe2, where the PL intensity of the neutral exciton is independent of magnetic field, whereas the higher energy transition of the charged exciton gains in intensity. For ML MoSe2, they found that the low energy transitions for both neutral and charged excitons gain in intensity,33 which is the same behavior as for our ML MoTe2. However, in another report30 on ML MoSe2 the neutral excitons showed the opposite trend. Most probably, these discrepancies for different and even the same materials are associated with different

degrees of intervalley scattering in the samples, which give rise to a preferential occupation of the lower energy neutral (or charged) exciton states of the Zeeman split levels.33 The degree of circular polarization of the X0A and X± lines, defined as PC = (Iσ+ − Iσ−)/(Iσ+ + Iσ−) is shown in Figure 3d as a function of magnetic field. Here, Iσ+ and Iσ− are intensities of the corresponding circularly polarized components of the transition. The oscillatory features are due to Faraday rotation of the small linear polarization component (