# Valley phenomena in the candidate phase change material WSe2(1-x)Te2x

### Subjects

A Publisher Correction to this article was published on 18 March 2020

This article has been updated

## Abstract

Alloyed transition metal dichalcogenides provide an opportunity for coupling band engineering with valleytronic phenomena in an atomically-thin platform. However, valley properties in alloys remain largely unexplored. We investigate the valley degree of freedom in monolayer alloys of the phase change candidate material WSe2(1-x)Te2x. Low temperature Raman measurements track the alloy-induced transition from the semiconducting 1H phase of WSe2 to the semimetallic 1Td phase of WTe2. We correlate these observations with density functional theory calculations and identify new Raman modes from W-Te vibrations in the 1H-phase alloy. Photoluminescence measurements show ultra-low energy emission features that highlight alloy disorder arising from the large W-Te bond lengths. Interestingly, valley polarization and coherence in alloys survive at high Te compositions and are more robust against temperature than in WSe2. These findings illustrate the persistence of valley properties in alloys with highly dissimilar parent compounds and suggest band engineering can be utilized for valleytronic devices.

## Introduction

The valley contrasting properties of monolayer semiconducting transition metal dichalcogenides (TMDs) provide the possibility of manipulating information using the valley pseudospin1,2,3 in direct analogy to spintronics4. Devices that employ this schema for computation, commonly referred to as valleytronics, benefit from optical or electrical manipulation of the valley index, spin–valley locking, low power consumption, and the absence of Joule heating2. These advantages have stimulated vigorous investigations into the properties of two-dimensional (2D) semiconducting TMDs with an emphasis on exploring the optical interband selection rules that connect photon polarization to valley index1,2,3.

The first studies of monolayer TMDs focused solely on the photoluminescence (PL) from molybdenum disulfide (MoS2)5,6; however, attention shifted to valley-dependent studies7,8. Soon after, monolayer tungsten diselenide (WSe2) was found to be a superior TMD for valleytronics, exhibiting both exciton valley polarization and valley coherence9,10,11,12,13,14,15. Valley polarization describes the probability of an exciton created in a valley to remain there until recombination, while valley coherence quantifies the probability of an exciton to remain in a superposition state of K and K′ valleys before recombining. At low temperature, the neutral exciton (X0) in bare WSe2 monolayers exhibits a valley polarization ranging from 40% to 70% depending on the laser energy9,11,16. The depolarization of valley excitons is believed to be governed by a combination of intervalley electron–hole exchange interactions8,17, phonon-assisted intervalley scattering7,18, and Coulomb screening of the exchange interaction19,20. In addition, WSe2 holds the record for the largest degree of X0 valley coherence in bare monolayers (≈40% at cryogenic temperatures)9.

Alloying can increase the technological potential of valleytronic TMDs by combining valley contrasting properties with band engineering21. Furthermore, alloys of structurally distinct TMDs may also enable phase change memory technologies22,23,24 by reducing the energy barrier between semiconducting and semimetallic states25. Few studies, however, have explored valley phenomena in alloys despite the heavy interest in this field. The first exploration of valley properties in alloys focused on Mo1−xWxSe2 at 5 K and found that there was a transition from the intrinsic valley polarization of MoSe2 to WSe2 as the transition metal content was varied26. Experiments on a WS0.6Se1.4 alloy demonstrated a valley polarization of ≈31% at 14 K, which was much lower than that of both WS2 and WSe227. A recent study of WSxTe2−x found that the room temperature valley polarization increased from 3% in WS2 to 37% in an unspecified alloy composition28. The limited information regarding valley polarization in alloyed TMDs is a serious oversight as future valleytronic technologies will likely rely heavily on band engineering.

In this study, we examine the low-temperature optical properties of monolayer WSe2(1−x)Te2x, where the endpoints are the valleytronic semiconductor 1H-WSe2 and the topological semimetal 1Td-WTe2. Prior studies of this alloy system were performed at 300 K and focused on unpolarized optical measurements29 as well as electronic transport characterization30. Our study focuses on the impact of alloying on the valley excitons of WSe2(1−x)Te2x monolayers encapsulated in hexagonal boron nitride (hBN). We ensure good interfacial contact in the heterostructure by cleaning with the nano-squeegee method31, which substantially improves the valley polarization. Raman measurements at 5 K show that increasing Te composition leads to the shifting and splitting of vibrational modes as well as the appearance of new modes unique to alloys. Polarization-resolved Raman measurements coupled with density functional theory (DFT) calculations of the theoretical 1H-WTe2 phase allow us to assign these alloy-only features as resulting from W-Te vibrations in the 1H WSe2(1−x)Te2x structure. Temperature-dependent, polarization-resolved PL measurements of the 1H-phase alloys demonstrate band gap tunability alongside the presence of new ultra-low energy emission features. We suggest that these features are from deep mid-gap states that originate from the large difference in the W-Se and W-Te bond lengths. Despite the presence of structural disorder in the lattice, valley polarization is found to survive the alloying process for x ≤ 0.14 while valley coherence is present for alloys x ≤ 0.37, and interestingly, we demonstrate that alloys have the ability to sustain these valley properties at higher temperatures than pure WSe2. These findings illustrate the persistence of valley phenomena in significantly disordered alloys and point the way toward optimization of TMDs for novel phase change memories that naturally integrate with valleytronic devices.

## Results

### WSe2(1−x)Te2x structure and vibrational modes

Interpretation of our experimental data is guided by DFT modeling of the WSe2(1−x)Te2x phase diagram. The crystal structure of the endpoint compounds 1H-WSe2 (x = 0) and 1Td-WTe2 (x = 1) are shown in Fig. 1a, b. Regarding crystal structure notation, we refer to Td monolayers as being in the 1Td phase. Previously, Td and 1T’ notations have been used interchangeably for Td monolayers since the only difference between these structures in the bulk was believed to be a slight shift of layers relative to one another. Since the Td structure contains three layers in its unit cell while the 1T’ structure contains one layer, it was assumed that monolayers isolated from a bulk Td crystal were in the 1T’ phase. We make the 1Td notation distinction in light of a recent report which has indicated, unlike the 1T’ phase, that inversion symmetry is broken in the monolayer Td lattice32. We find from our DFT calculations, in agreement with previous studies29,30, that the 1H phase is stable with a Te concentration of x ≤ 0.4, which we illustrate in Fig. 1c. For x ≥ 0.5, 1Td becomes the lowest energy phase. As a result, we expect valleytronic optical properties for the 1H alloys corresponding to x ≤ 0.4 and semimetallic behaviors for the 1Td alloys x ≥ 0.5. These predictions are consistent with our Raman and PL measurements described in detail below.

Prior to optical measurements, monolayers are encapsulated in an hBN heterostructure, as shown in Fig. 1d, to protect from the degradative effects due to exposure to the atmosphere and to provide a uniform dielectric environment33. We explore the effects of alloying on crystal structure through low-temperature Raman spectroscopy of hBN-encapsulated monolayer WSe2(1−x)Te2x, as shown in Fig. 2a. This Raman data is fit with multiple Lorentzian peaks to extract mode frequencies, which are plotted in Fig. 2b with alloy composition x. Examples of Lorentzian fits to Raman data for select alloys can be seen in Supplementary Fig. 1.

It is instructive to first examine the properties of the endpoints WSe2 (x = 0) and WTe2 (x = 1) that appear in blue in Fig. 2a. WSe2, which naturally crystallizes in the 1H phase, is in the D3h point group and exhibits modes with $$A_1^\prime$$ and $$E^\prime$$ symmetries. In agreement with prior observations34,35, we identify eight Raman peaks in WSe2 at 132, 223, 240, 250, 264, 351, 378, and 401 cm−1. These modes and their symmetries are summarized in Table 1. The dominant feature in the WSe2 Raman spectra at 250 cm−1 (labeled peak 4 in Fig. 2a, b) is an $$A_1^\prime$$ symmetry mode where the transition metal is fixed and the chalcogens vibrate perpendicular to the basal plane36,37. In monolayer WSe2, this mode overlaps with an $$E^\prime$$ symmetry mode where the chalcogen and transition metal layers both vibrate in plane but out of phase36,37. These findings agree with prior calculations34,36,37 as well as our own DFT modeling of the WSe2 phonon band structure that predicts the 0 K frequency of the dominant $$A_1^\prime$$ mode at 239 cm−1 and the $$E^\prime$$ mode at 236 cm−1 (Fig. 2c). Additional monolayer WSe2 modes are enhanced at 5 K, which are usually assigned as disorder-activated finite momentum phonons, combination modes, or difference modes34,35,38. We find that previous assignments of these features to Raman difference modes conflict with our low-temperature data. Difference modes originate from a two-phonon process where one phonon is absorbed (anti-Stokes process) and another is created (Stokes process). Since this requires the presence of a phonon before photoexcitation, its occurrence is expected to follow a Boltzmann-like temperature dependence that disappears at cryogenic temperatures39. The presence of these so-called difference modes in our measurements at 5 K calls this assignment into question. Thus it is more likely that these features are combination modes for which there are many possible assignments (Table 1); however, there is presently no explanation for the mode at 132 cm−1.

We now discuss the Raman spectrum of WTe2, which is presented in Fig. 2a. Our attempts to exfoliate large-area monolayers of WTe2 were met with limited success, which may be due to the rapid oxidation rate of this material40. In contrast, we found it straightforward to achieve large-area bilayer WTe2, which is known to be less susceptible to oxidation40. The Raman spectra of bilayer and monolayer WTe2 are nearly identical41, which lets us safely use bilayer WTe2 to discriminate between 1Td- and 1H-WSe2(1−x)Te2x. Bilayer WTe2 (Td phase) belongs to the C2v point group, and so only A1 and A2 symmetry modes can be observed42. Five peaks in the 70–425 cm−1 range are present at 87, 107, 166, 218, and 327 cm−1 and are labeled with letters in Fig. 2a, b. Assignment of the mode symmetries is based on prior studies of WTe241,43 and is included in Table 1. The feature at 327 cm−1, labeled peak e, has not been previously observed, and we assign it as either a second-order overtone of the 166 cm−1 A1 mode (peak c) or a combination of the 107 cm−1 A2 and 218 cm−1 A1 modes (peaks b and d, respectively).

Low-temperature Raman measurements of the alloys (black curves of Fig. 2a) reveal fascinating new details regarding the vibrational modes that were not observed in a previous study of WSe2(1−x)Te2x alloys29 owing to thermal broadening at 300 K (see Supplementary Fig. 2 for comparison of 5 and 300 K spectra). Alloys with x ≤ 0.37 are in the 1H phase, which is further supported by the presence of PL in these samples to be discussed later, and exhibit complex mode structures in the ≈230–275 cm−1 range. Polarization-resolved Raman measurements (Supplementary Fig. 3) reveal that the dominant WSe2 $$A_1^\prime$$ mode at 250 cm−1 splits into two peaks at 244 and 253 cm−1 for x = 0.04 (see red points in Fig. 2b). This differs from studies of WS2(1−x)Se2x where this primary out-of-plane WSe2 feature typically only shifts with alloying44,45. The splitting of out-of-plane vibrational modes with alloying, however, has been seen in MoSxSe2−x monolayers46,47 and has been carefully documented in few-layer MoSxSe2−x48. Jadczak et al. attributed the splitting of this feature in alloys to the polarization of the alloy unit cell due to the substitution of heavier chalcogens that introduce different force constants in the lattice48. Thus, owing to the splitting of the primary $$A_1^\prime$$ mode, we find that the $$E^\prime$$ mode is distinguishable from the $$A_1^\prime$$ mode in alloy monolayers and only slightly shifts to lower frequencies with increasing x.

Several other WSe2-like vibrational modes show sensitivity to alloying for 1H-phase compositions x ≤ 0.37. Second-order finite momentum peaks 6, 7, and 8 of Fig. 2a, b shift to lower frequencies and broaden with increasing alloy composition. This alloy data may clarify disagreements in the literature on whether $$A_1^\prime$$ or $$E^\prime$$ phonons are the dominant contributor to these higher-order modes34,35. The band predictions of 1H-WSe2 in Fig. 2c show both branches of the $$E^\prime$$ mode that originate at 236 cm−1 shift to lower frequencies away from the Γ point. This behavior is opposite to that of the $$A_1^\prime$$ mode, which originates at 239 cm−1 and shifts to higher frequencies away from the Γ point. Since peaks 6, 7, and 8 broaden asymmetrically on the lower frequency side of their centers as x is increased, this may indicate that the $$E^\prime$$ mode, rather than the $$A_1^\prime$$ mode, contributes to these higher-order processes. The shifting and broadening of the WSe2 modes for compositions x ≤ 0.37 indicate that alloying introduces significant disorder into the lattice but globally maintains the 1H phase.

A particularly interesting alloy-induced feature resolved in 1H samples is the Raman peak labeled D1 at 191 cm−1 in x = 0.04 (red points in Fig. 2b). This feature splits into the two peaks labeled D2 and D3 at 190 and 200 cm−1, respectively, as x is increased. Polarization-resolved Raman measurements (Supplementary Fig. 3) indicate that these features have $$A_1^\prime$$ symmetry and DFT calculations of the 1H-WSe2 phonon band structure (Fig. 2c) show no $$A_1^\prime$$ phonon modes present in this range. We therefore calculate the phonon band structure of metastable 1H-WTe2 phase in Fig. 2d, which predicts an $$A_1^\prime$$ Γ-point mode at 172 cm−1. This mode is the closest to the observed results and so we assign the D1 peak to an $$A_1^\prime$$ mode arising from W-Te vibrations in the 1H WSe2(1−x)Te2x alloys. We attribute its splitting to increasing force constant variations introduced into the lattice with noticeable Te content as discussed previously for the primary $$A_1^\prime$$ mode of WSe248. Raman measurements reveal several other new peaks in the 1H alloys, which we label D4, D5, D6, and D7 in Fig. 2b. These polarization-independent features (see Supplementary Fig. 3) most likely arise from either finite momentum WSe2-like phonons or WSe2 combination modes. We exclude difference modes based on the use of low-temperature spectroscopy as discussed previously. Possible assignments are $$E^\prime \left( M \right)$$ for D6 and $$E^\prime + E^\prime \left( M \right)$$ for D7, while D4 and D5 remain unassigned but may originate from combinations of 1H-WSe2 and 1H-WTe2 modes. As WSe2(1−x)Te2x transitions to the 1Td phase with alloying, the Raman spectra for x ≥ 0.79 show the two primary A1 vibrational modes of pure WTe2, labeled peaks c and d in Fig. 2a, b. These features are shifted and broadened due to alloy disorder in agreement with other WTe2 alloys49. The phonon band structure of 1Td-WTe2 is shown in Fig. 2e for comparison with that of 1H-WTe2 in Fig. 2d.

### Excitonic properties

In Fig. 3a–e, we present temperature-dependent PL spectra for representative 1H-phase alloys. Each spectrum has been normalized by the maximum intensity and was excited with right circularly polarized light (σ+) at 1.96 eV. The collected PL is passed through a waveplate/analyzer combination to select σ+ emission. At 300 K, the PL spectra show contributions from both the neutral exciton (X0) and the trion (XT)12. Increasing the Te concentration causes both features to redshift due to the lower band gap of 1H-WTe250. As temperature decreases from 300 to 5 K, X0 and XT sharpen, blueshift, and weaken in intensity. The latter behavior is due to the sign of the conduction band spin–orbit coupling, which makes the lowest exciton state dark51. The sign of the spin–orbit coupling is the same for all W-based TMDs51 and so we expect no change in the optical activity of the lowest exciton state with Te substitution. The presence of broad features at lower energies compared to X0 and XT originate from a combination of higher-order excitonic complexes52 and localized exciton states from lattice defects, strain, and residual impurities introduced during fabrication9,12,53.

We explore band gap tunability of 1H-WSe2(1−x)Te2x by extracting X0 energy as a function of temperature, which is plotted in Fig. 4a. This data is fit with a semi-empirical formula for temperature-dependent optical band gaps given by54

$$E_{\mathrm{g}}\left( T \right) = E_0 - S\left\langle {\hslash \omega } \right\rangle \left[ {{\mathrm{coth}}\left( {\frac{{\left\langle {\hslash \omega } \right\rangle }}{{2kT}}} \right) - 1} \right]$$
(1)

where E0 is the gap at absolute zero, S is a dimensionless electron–phonon coupling parameter, $$\hslash \omega$$ is an average phonon energy, and k is the Boltzmann constant. This formula models the reduction in band gap with increasing temperature due to a combination of increasing lattice constants and exciton–phonon coupling54. Fits of Eq. (1) to our data are presented as solid lines in Fig. 4a and the compositional dependence of E0, S, and $$\hbar \omega$$ from these fits are plotted in Fig. 4b–d. Figure 4b shows that E0 (i.e., X0 energy) varies in 1H-WSe2(1−x)Te2x from ≈1.735 eV in WSe2 to ≈1.519 eV in the x = 0.37 alloy. These experimental results agree extremely well with the optical band gaps of the alloys computed using DFT with the HSE06 exchange-correlation functional55,56, which predict a gap of 1.75 eV in 1H-phase WSe2 that decreases to 1.53 eV at a Te concentration of x = 0.375 (blue triangles of Fig. 4b). At higher x, the system transforms to the 1Td phase (Supplementary Fig. 4), which is a semimetal. For a comparison of DFT results for the optical band gaps of all WSe2(1−x)Te2x monolayers calculated using both the HSE06 and Perdew–Burke–Ernzerhof (PBE) functionals and the density of states determined using the HSE06 functional, see Supplementary Fig. 4. Since the alloys are in the 1H phase only up to x = 0.37 and 1H-WTe2 does not exist in nature, we are unable to reliably determine the bowing parameter for E021. Therefore, we instead fit E0 from x = 0 to 1 with a linear function as shown by the red line in Fig. 4b. From a linear extrapolation to x = 1, we determine the 0 K optical band gap of 1H-WTe2 to be 1.15 eV. Lastly, extracted values for S range from 1.93 to 2.24 and for $$\hbar \omega$$ between 4 and 16 meV (32.3–129 cm−1) and are plotted versus x in Fig. 4c, d.

Elaborating on the 5 K PL spectra of Fig. 3, we find that XT appears ≈30 meV below X0 in our data and shifts in lockstep with the neutral exciton so that there is only weak dependence of the X0–XT binding energy on x (Supplementary Fig. 5). Spatial PL mapping of an x = 0.33 alloy sample at 5 K indicates little variation of the intensities, energies, and line widths of X0 and XT. These maps are discussed in detail in Supplementary Note 1 and Supplementary Fig. 6. In addition, we find evidence for excitonic transitions and exciton–phonon complexes at energies above X0 known to originate from coupling between hBN and WSe2 in van der Waals heterostructures57,58. A detailed discussion of these features is presented in Supplementary Note 2 and Supplementary Fig. 7. In 5 and 300 K reflectance measurements presented in Supplementary Fig. 8, both the A and B excitons are clearly visible and the valence band spin–orbit coupling is found to increase with Te incorporation.

Localized excitons are common in W-based TMDs owing to the long lifetime of the dark exciton ground states. We identify such features in all alloys and the parent compound WSe2, beginning with an emission band ≈100 meV below X0 hereafter referred to as L1. For all x > 0.04, L1 is accompanied by a second localized emission feature (L2) approximately ≈300 meV below X0 (Fig. 3c–e). This feature has never been observed in TMDs, alloyed or otherwise. L1 and L2 maintain a similar energy separation with respect to X0 at all nonzero x but do exhibit variations in their temperature-dependent behaviors.

The new defect band L2 must originate from a disorder unique to Te-rich alloys and may be connected to the preference of WTe2 to crystallize in a 1Td structure. Scanning tunneling electron microscopy measurements and molecular dynamics (MD) simulations of a similar alloy system, WS2−xTex59, indicate that Te substitution at levels approaching 15% can substantially modify the structure of a 1H-phase alloy. The bond lengths and lattice constants of 1H-WSe2 with 1H-WTe2 are predicted to differ by ≈7–8%59, which also leads to a mismatch between the metal–chalcogen bond angles. MD simulations presented by Tang et al.59 illustrate that these internal strains can lead to the displacement of Te atoms from the expected chalcogen site for concentrations as low as 8%. These shifts lead to the compression and stretching of neighboring hexagonal rings and in turn result in the displacement of the native chalcogen and even the W atoms. For the WS2–WTe2 alloys, continuing to increase the Te doping to 15%, 20%, and finally 25% increased the displacements of W, S, and Te atoms and ultimately drove the W atoms closer together in a prelude to the 1H–1Td transition59. These Te concentrations compare favorably with the values at which we observe the presence of the L2 feature (Fig. 3). The presence of such substantial atomic displacements and internal strains seems to be unique to TMD alloys that are mixtures between different structural phases. We therefore suggest that the internal strains driven by Te incorporation in 1H-phase alloys create a new band of defect states (i.e., the L2 feature) lower than those typically expected from chalcogen or transition metal vacancies (i.e., the L1 feature)53.

### Valley phenomena

Next, we explore valley contrasting in 1H-WSe2(1−x)Te2x alloys at 5 K using 1.96 eV excitation with σ+ polarization. The schematic band structure in Fig. 5a illustrates the spin–valley polarized selection rules in WSe2, where transitions between the valence band and the second highest conduction band are σ+ (σ−) polarized at the K (K′) point. Any emission in the opposite polarization channel is a sign of intervalley scattering. Valley polarization is determined by measuring co- and cross-polarized PL spectra in the circular basis as shown in Fig. 5b. The degree of valley polarization ρVP for σ+ excitation is defined as $$\rho _{VP} = \left( {I_{\sigma + } - I_{\sigma - }} \right)\! / \! \left( {I_{\sigma + } + I_{\sigma - }} \right)$$, where $$I_{\sigma + }\;\left( {I_{\sigma - }} \right)$$ is the intensity of the collected light with σ+ (σ−) orientation. Valley coherence measurements are similar except measurements are carried out in a linear basis with co-polarized $$\left( \parallel \right)$$ and cross-polarized $$\left( \bot \right)$$ configurations as shown in Fig. 5c. The degree of valley coherence ρVC is calculated similarly as $$\rho _{{\mathrm{VC}}} = ( {I_\parallel - I_ \bot } )/( {I_\parallel + I_ \bot } )$$, where $$I_\parallel$$ $$\left( {I_ \bot } \right)$$ is the intensity of the collected light that is $$\parallel$$ $$\left( \bot \right)$$ to the incident light.

Alloy-dependent values of ρVP for X0 (black squares) and XT (red circles) at 5 K are plotted in Fig. 5d. We find that ρVP ≈ 49% for X0 in WSe2, which agrees with previously reported values9. Achieving this value required cleaning our heterostructures post-assembly using the nano-squeegeeing technique31. This process improved the WSe2 ρVP of X0 by a factor of ≈1.7, thus increasing the signal from 29% to 49%, whereas it appeared to have very little effect on ρVC. This result illustrates the impact of contaminants on valley properties and a comparison of squeegeed and non-squeegeed alloys can be found in Supplementary Fig. 9.

As Te is substituted into the lattice, ρVP first remains unchanged at x = 0.04 and then decreases to 32% at x = 0.14 (Fig. 5d). For x > 0.14, no valley polarization is observed. XT exhibits a similar trend with x: ρVP ≈ 67% for XT in WSe2 and is zero for x > 0.14. To the best of our knowledge, there is no systematic theory for understanding valley depolarization from alloy disorder. However, we do observe an interesting correlation between ρVP and the integrated intensity ratio of XT/X0, as shown in Supplementary Fig. 10. The ρVP XT/X0 integrated intensity ratio generally decreases with Te incorporation from ≈2.4 in WSe2 to ≈0.25 in x = 0.37. While there is an initial increase in the ρVP XT/X0 intensity ratio from ≈2.4 in WSe2 to ≈3.8 in the x = 0.04 sample, this is most likely the result of a superior cleaned interface via the nano-squeegee method rather than an intrinsic material property. The decrease in the ρVP XT/X0 intensity ratio as x is increased suggests a connection between ρVP and an apparent reduction in doping with increasing Te substitution. Valley coherence is only present for neutral excitons9 and we plot ρVC versus x at 5 K in Fig. 5e. ρVC ≈ 20% in WSe2, which is slightly lower than the literature value9, and decreases to ≈13% when x = 0.04 after which point it remains essentially constant until the 1H-1Td phase transition. We note that valley coherence remains finite even when valley polarization goes to zero at large x.

Temperature-dependent measurements of ρVP and ρVC for X0 in Fig. 6 show interesting behaviors that suggest disorder can in some cases improve valley polarization and valley coherence. In all cases for the 1H-phase alloys, we find a decrease of both quantities with increasing temperature. However, alloys exhibit a different temperature dependence when compared to WSe2 (x = 0). Beginning with ρVP in Fig. 6a, we observe a sharp decrease with increasing temperature that is consistent with prior examinations of WSe2 monolayers12,60. Surprisingly, we find that valley polarization remains large for the x = 0.04 alloy and can exceed that of WSe2, reaching a maximum enhancement factor of 3.5× at 100 K. While valley polarization is overall lower for the x = 0.14 alloy, it also exceeds that of WSe2 at 100 K and has the same temperature dependence as the x = 0.04 case. We note that ρVP of XT also shows similar temperature and alloy dependence, which can be seen in Supplementary Fig. 11. This observation indicates that, counter to intuition, alloys can exhibit valley polarization that meets or exceeds that of WSe2, especially at higher temperatures.

Currently, there is no systematic understanding of the impact of alloy disorder on valley polarization. The prevailing theories of valley polarization revolve around a balance between the mean exciton lifetime τx and the valley relaxation lifetime τv, which are parametrized by the relationship $$\rho _{{\mathrm{VP}}} = \frac{{\rho _0}}{{1 + 2\left( {\gamma _{\mathrm{v}}/\gamma _{\mathrm{x}}} \right)}}$$, where $$\gamma _{\mathrm{v}} = \left( {2\tau _{\mathrm{v}}} \right)^{ - 1}$$ is the intervalley scattering rate and $$\gamma _{\mathrm{x}} = \left( {\tau _{\mathrm{x}}} \right)^{ - 1}$$ is the exciton recombination rate8,19. Temperature dependence enters this equation via the scattering and recombination rates, and the valley depolarization rate for excitons is determined by a combination of electron–hole exchange interactions8,17, intervalley phonon scattering7,18, and Coulomb screening61 of the exchange interaction. Miyauchi et al.19 more deeply explore the temperature dependence of τv and find that valley depolarization at low temperatures is driven by long-range electron–hole exchange interactions, but as temperatures are increased, intervalley phonon scattering dominates. A subsequent experimental study demonstrated that the valley polarization can be enhanced over a range of temperatures by electrostatic gating, which adds additional carriers to the material that screen the electron–hole exchange interaction20. Therefore, we suggest that carrier doping may be a contributing factor to the enhancement of ρVP in alloys at elevated temperatures, which is supported by the larger XT/X0 integrated intensity ratio for x = 0.04 compared to WSe2 (Supplementary Fig. 10). However, we cannot conclude that doping is the only factor since the XT/X0 integrated intensity ratio of the x = 0.14 alloy is less than that of WSe2 but its valley polarization is larger at 100 K. Another possible explanation for the sustained valley polarization at higher temperatures may be a reduction in τx due to disorder62. We have attempted to fit our data using functional forms provided by Miyauchi et al.19 but cannot obtain unique fitting parameters since both τx and τv are complicated functions of temperature, bright-dark exciton splitting, phonon scattering rates, and exciton relaxation times.

The valley decoherence rate differs from the valley depolarization rate by its additional sensitivity to pure dephasing $$( {\gamma _{{\mathrm{dep}}}} )$$. This results in a different expression $$\rho _{{\mathrm{VC}}} = \frac{{\rho _0}}{{1 + 2\left( {\gamma _{\mathrm{v}} + \gamma _{{\mathrm{dep}}}} \right)/\gamma _{\mathrm{x}}}}$$63,64. Unique temperature dependencies for ρVP and ρVC are therefore expected and observed in Fig. 6a and Fig. 6b, respectively. We again find that for alloys the valley coherence is larger than in WSe2 at higher temperatures. The impact of pure dephasing on valley coherence makes it more sensitive to scattering events than valley polarization. According to Hao et al.11, changes in exciton momentum due to scattering from defects yields an in-plane magnetic field that leads to depolarization and decoherence. As the frequency of impurity scattering is increased, however, the time-averaged effective magnetic field experienced by excitons due to the electron–hole exchange interaction17 is reduced, which can act to enhance valley properties. Further studies on WSe2(1−x)Te2x using temperature-dependent and time-resolved spectroscopies such as those conducted by Miyauchi et al.19 and Hao et al.11 are required to determine the respective contributions of the above decoherence and depolarization mechanisms.

## Discussion

We have used low-temperature Raman and temperature-dependent, polarization-resolved PL spectroscopy to characterize different crystal phases spanned by monolayer WSe2(1−x)Te2x alloys and explore how incorporation of Te into the WSe2 lattice affects valleytronic and semiconducting properties. DFT calculations of the phonon dispersion curves for 1H-WSe2 and 1Td-WTe2 alongside low-temperature Raman measurements allowed us to assign the vibrational modes of the WSe2 and WTe2 endpoint compounds. The shifting and splitting of these vibrational modes were tracked with composition x, and we found the appearance of alloy-only features resulting from W-Te vibrations in the 1H alloys that we confirm through the combination of polarization-resolved Raman measurements and DFT calculations. Temperature-dependent PL measurements were used to demonstrate band gap tunability, identify the alloy dependence of exciton and trion states, and observe a new defect-related emission feature. DFT calculations of the optical band gap in the alloys agree very well with low-temperature PL measurements when using the HSE06 functional. Polarization-resolved PL measurements show that alloys still exhibit valley polarization and coherence and that these valley properties can be superior to those of WSe2 at higher temperatures. Reflectance measurements were also used to measure the A and B excitons in select alloys, indicating that the spin–orbit splitting of the valence band can be increased with the addition of Te. This study illustrates the resilience of valley phenomena in alloys and the prospect of their application in a novel class of phase change memory technologies that also take advantage of spintronic and valleytronic information processing.

## Methods

### Crystal growth and structural characterization

WSe2(1−x)Te2x alloys (x = 0…1) were grown by the chemical vapor transport method. Appropriate amounts of W (99.9%), Se (99.99%), and Te (99.9%) powders were loaded in quartz ampoules together with ≈90 mg (≈4 mg/cm3 of the ampoule’s volume) of TeCl4 which served as a transport agent. The ampoules were then sealed under vacuum and slowly heated in a single-zone furnace until the temperature at the source and the growth zones reached 980 and 830 °C, respectively. After 4 days of growth, the ampoules were ice-water quenched. Crystal phases of the alloys were determined by examining powder X-ray diffraction patterns using the MDI-JADE 6.5 software package. We found that alloys with x ≤ 0.4 crystallized in the 2H phase and those with x ≥ 0.8 were in the Td phase. Results are consistent with a previous report of WSe2(1−x)Te2x29. Chemical compositions were determined by the energy-dispersive X-ray spectroscopy (EDS) using a JEOL JSM-7100F field-emission scanning electron microscope equipped with an Oxford Instruments X-Max 80 EDS detector.

### Sample preparation

For optical studies, WSe2(1−x)Te2x bulk crystals were mechanically exfoliated and monolayers were identified by optical contrast. Monolayers were then fully encapsulated in an hBN heterostructure (top and bottom layers) using the viscoelastic dry-stamping method on a SiO2/Si substrate (90 nm oxide thickness) to protect them from the degradative effects due to exposure to the atmosphere and to provide a uniform dielectric environment33. We note that, before encapsulation, monolayers were exposed to the atmosphere for <1 h. To guarantee clean hBN/TMD contact, the nano-squeegee method was used with a scan line density of ≥10 nm/line and a scan speed of ≤30 µm/s as suggested by Rosenberger et al.31 to physically push contaminants out from in between heterostructure interfaces. Results of this procedure can be seen in the atomic force microscopic image of Supplementary Fig. 6. Here the contaminants removed from the interfaces are gathered along both sides of the nano-squeegeed region (dark vertical lines, ≈50 nm in height above sample).

### Optical studies

Raman and PL measurements were performed on home-built confocal microscopes, both in backscattering geometries, that were integrated with a single close-cycle cryostat (Montana Instruments Corporation, Bozeman, MT). A 532 nm laser was used for Raman measurements since it has been shown that this excitation source can excite first- and second-order features34, whereas a 633 nm laser was used for PL measurements since it has been shown to yield a much higher degree of valley polarization than excitation with a green laser16. Both set-ups focus the excitation source through a 0.42 NA long working distance objective with ×50 magnification. For Raman measurements, the laser spot was ≈2.4 µm, and the laser power density was fixed at 66 µW/µm2, while for PL measurements, the laser spot was determined to be ≈2.2 µm, and the laser power density was fixed at 21 µW/µm2. Collected light in both cases was directed to a 500 nm focal length spectrometer with a liquid nitrogen-cooled CCD (Princeton Instruments, Trenton, NJ). The spectrometer and camera were calibrated using a Hg-Ar atomic line source. For spectral analysis, Raman peaks were fit with Lorentzian profiles, whereas PL peaks were fit with Gaussians.

### DFT calculations

DFT calculations were performed using the Vienna ab initio Simulation Package65,66,67. Projector augmented wave pseudopotentials68 and the PBE exchange-correlation functional55 were utilized. Spin–orbit coupling was included in all calculations except for the phonon band structure, which is a standard procedure69. It has been recently reported that there are slight differences between the 1T’ and 1Td phases in monolayer TMDs32, with WTe2 likely forming in the 1Td phase. However, in this work we performed all calculations with the WTe2 monolayer in the 1T’ structure. Owing to very small differences between the 1T’ and 1Td phases, this assumption is appropriate. Full relaxations of the lattice parameters and ionic positions were performed on monolayer WSe2 and WTe2 in the 1H and 1T’ phases using a 32 × 32 × 1 and 32 × 16 × 1 Γ-centered k-mesh, respectively, and a 500 eV plane-wave cutoff. The phonon band structures of these compounds were computed using density functional perturbation theory70. Various chalcogen-alloyed compositions of the form WSe2(1−x)Te2x were created by expanding these unit cells and substituting the appropriate amount of Te with Se (or vice versa). Full relaxations were again performed in each case, with the k-mesh scaled appropriately to the size of the unit cell. In the case when multiple substitutional anions were needed to achieve a given composition, all combinations of the position of the alloying atoms relative to each other were tested, with the lowest energy configuration considered the ground state (Supplementary Fig. 12). The density of states was computed using the aforementioned PBE functional, as well as the HSE06 functional56, with 25% Hartree–Fock exact exchange included.

### Disclaimer

Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

P.M.V. and S.M.O. acknowledge support from the National Science Foundation (NSF) under Grant No. DMR-1748650, the George Mason University Quantum Materials Center, and the George Mason University Presidential Scholars Program. J.Y. was supported by funds from Binghamton University. Computational resources were provided by the Department of Defense High Performance Computing Modernization Program. S.K. acknowledges support from the US Department of Commerce, NIST under financial assistance award 70NANB18H155. T.L.R. was supported by the Office of Naval Research.

## Author information

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### Contributions

P.M.V. and S.M.O. conceived and designed the experiments and wrote the manuscript with input from all coauthors. S.M.O. prepared van der Waals heterostructures and carried out all experiments. A.V.D. and S.K. grew the bulk crystals used in this work. J.Y. and T.L.R. performed the density functional theory calculations.

### Corresponding author

Correspondence to Patrick M. Vora.

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### Cite this article

Oliver, S.M., Young, J., Krylyuk, S. et al. Valley phenomena in the candidate phase change material WSe2(1-x)Te2x. Commun Phys 3, 10 (2020). https://doi.org/10.1038/s42005-019-0277-7

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## Further reading

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