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Highly anisotropic in-plane excitons in atomically thin and bulk-like 1T-ReSe Ashish Arora, Jonathan Noky, Matthias Drüppel, Bhakti Jariwala, Thorsten Deilmann, Robert Schneider, Robert Schmidt, Osvaldo Del Pozo Zamudio, Torsten Stiehm, Arnab Bhattacharya, Peter Krüger, Steffen Michaelis de Vasconcellos, Michael Rohlfing, and Rudolf Bratschitsch Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b00765 • Publication Date (Web): 17 Apr 2017 Downloaded from http://pubs.acs.org on April 18, 2017

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Highly anisotropic in-plane excitons in atomically thin and bulk-like 1′-ReSe2 Ashish Arora,†,* Jonathan Noky,‡ Matthias Drüppel,‡ Bhakti Jariwala,§ Thorsten Deilmann,‡,¶ Robert Schneider,† Robert Schmidt,† Osvaldo Del Pozo-Zamudio,† Torsten Stiehm,† Arnab Bhattacharya,§ Peter Krüger,‡ Steffen Michaelis de Vasconcellos,† Michael Rohlfing,‡ and Rudolf Bratschitsch†,* †

Institute of Physics and Center for Nanotechnology, University of Münster, Wilhelm-Klemm-

Strasse 10, 48149 Münster, Germany ‡

Institute of Solid State Theory, University of Münster, D-48149 Münster, Germany

§

Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental

Research, Homi Bhabha Road, Colaba, Mumbai 400005, India ¶

Center for Atomic-Scale Materials Design (CAMD), Department of Physics, Technical

University of Denmark, DK-2800 Kongens Lyngby, Denmark KEYWORDS: ReSe2, transition metal dichalcogenides, polarization, excitons, anisotropy, GW BSE

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ABSTRACT: Atomically thin materials such as graphene or MoS2 are of high in-plane symmetry. Crystals with reduced symmetry hold the promise for novel opto-electronic devices based on their anisotropy in current flow or light polarization. Here, we present polarizationresolved optical transmission and photoluminescence spectroscopy of excitons in 1′-ReSe2. On reducing the crystal thickness from bulk to a monolayer, we observe a strong blue shift of the optical band gap from 1.37 to 1.50 eV. The excitons are strongly polarized with dipole vectors along different crystal directions, which persist from bulk down to monolayer thickness. The experimental results are well reproduced by ab initio calculations based on the GW-BSE approach within LDA+GdW approximation. The excitons have high binding energies of 860 meV for the monolayer and 120 meV for bulk. They are strongly confined within a single layer, even for the bulk crystal. In addition, we find in our calculations a direct band gap in 1T'ReSe2 regardless of crystal thickness, indicating weak interlayer coupling effects on the band gap characteristics. Our results pave the way for polarization-sensitive applications, such as optical logic circuits operating in the infrared spectral region.

Keywords: ReSe2, polarized excitons, layered semiconductor, van der Waals material, GW-BSE, band structure


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Recent optical investigations of atomically thin semiconducting transition metal dichalcogenides (TMDCs) have demonstrated exciting new physical phenomena on the atomic scale and novel device-based applications.1,2 For example, TMDCs of the form WX2 and MoX2 (X = S or Se) exhibit an indirect-to-direct band gap crossover when reducing their thickness from bulk to a monolayer (1L).3–6 However, their hexagonal crystal structure results in an isotropic in-plane response to the polarization of incident light, rendering them optically uniaxial. Recently, newly emerging members of the layered semiconducting TMDCs of the type ReX2 (X = S or Se) and black phosphorous have gained attention due to their weak interlayer coupling and in-plane anisotropy.7–21 For example, the band structure of ReS2 and ReSe2 has been shown to depend only weakly on the crystal thickness.7,14,18 Both of these materials preferably crystallize in a distorted 1T (1′) phase with triclinic symmetry.22–24 The unit cell of 1′-ReSe2 is represented in Fig. 1(a). The Se atoms have a distorted octahedral coordination around the Re atoms. It results in the formation of Re-Re chains of “diamond-shaped” clusters along the a-axis (Fig. 1(b) (e)).22

The triclinic symmetry of their crystal lattice renders them optically biaxial, hence

resulting in an inherent anisotropic in-plane polarization response.22,25 Consequently, these materials are promising candidates for optical logic gates and optical computation, where linearly polarized light is used as a low/high bit value.26 Optical studies of ReS2 and ReSe2 demonstrating these effects have been scarce. Anisotropic Raman-active modes have been reported for thin layers of ReS2 and ReSe2.10,12,15,17,20 Linear polarization-resolved optical spectroscopy has been performed, demonstrating the anisotropic absorption edge of bulk ReS2 and ReSe2.20,25,27–30 However, the in-plane polarization anisotropy of excitons has been studied only for ReS2 crystals of 1L,8,16 and 3L8 thickness.

Zhao et al.14 have presented room-

temperature photoluminescence spectra of ReSe2 for thicknesses ranging from the bulk down to


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1L and found a blue shift of the photoluminescence with reduced thickness. However, due to the large line widths and high temperature, the close-lying excitonic transitions could not be resolved. They also performed polarization-resolved PL for 6L and 10L crystals. However, the mixing of many excitonic features into a single resonance made the analysis of the spectra exceedingly difficult. Concerning the electronic band structure, there are numerous reports on 1L and bulk ReS2 and ReSe2 at the density functional theory (DFT) level.7,11–14,17,19,20,31 In contrast, there is only one recent work, which has used the GW-BSE approach to compute the optical spectra and in-plane polarization properties of band edge excitons in a monolayer of ReS2 and ReSe2.21 Here, we present polarization-resolved micro-photoluminescence (PL) and microtransmission (Tr) spectroscopy of 1′-ReSe2 with thicknesses ranging from bulk down to a monolayer. We are able to resolve multiple close-lying excitonic transitions and find them strongly polarized in-plane along different crystal orientations. We perform GW-BSE-based ab initio calculations for bulk material and the monolayer to compute the polarization-resolved absorption spectra due to the various excitons, which compare well with our experiments. Our calculations indicate that ReSe2 is a direct band gap material, irrespective of the layer thickness. Single crystals of 1′-ReSe2 are obtained from two sources. They are grown directly by a modified Bridgman method from the constituent Re and Se elements. Details of the growth process are reported elsewhere.23 X-Ray diffraction and electron microscopy confirms a distorted triclinic 1′ crystal structure.23,24 Alternatively, ReSe2 crystals are bought from 2D Semiconductors Inc. (California, USA). Crystals from both sources yielded similar results. Monolayer, few-layer, and bulk-like crystals are mechanically exfoliated on a 500 μm thick polished c-cut sapphire substrate, and are identified by optical microscopy and atomic force microscopy (AFM) height profiles (Fig. 1(f) - (h)). The monolayer height measured from 1L to


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2L flakes (or alternatively 2L to 3L) in Fig.1 (f) is 0.7 ± 0.05 nm. By mechanical exfoliation, the ReSe2 crystal cleaves with edges along the a and b axes. The a axis is indicated by a red line in the optical images. Figures 2(a) and 2(b) show the measured (unpolarized) [1 − Tr] (Tr′ henceforth) and PL spectra for a 60 nm thick bulk-like and a 1L crystal, respectively (see supporting information for experimental details). The Tr′ spectrum captures the salient features of the absorption spectrum, if reflectance effects are neglected (see supporting information). In the Tr′ spectrum of the bulk-like flake in Fig. 2(a), 4 excitonic transitions in the range 1.372 eV - 1.404 eV can be identified. We label them as X1 to X4. While X2 and X4 are the two prominent features, X1 and X3 appear as respective shoulders at their low energy side. These features are more clearly distinguishable in polarization-resolved measurements, which we discuss later. The PL spectrum of the bulk-like flake in Fig. 2(a) also consists of two prominent lines X2 and X4, with X1 as a shoulder to X2. X3 could not be resolved in PL. The transition energies of the X1, X2, and X4 lines in PL are red-shifted (Stokes shift) by 3 meV with respect to their Tr′ counterparts. This small Stokes shift and the narrow full-width at half-maximum (FWHM) linewidths (5 − 9 meV) indicate an excellent quality of our sample.23 For the 1L case in Fig 2(b), the Tr′ and PL signatures of the excitons are much weaker and broader (25 − 55 meV) with a larger Stokes shift of 20 meV. Similar to the bulk-like flake, two prominent features (X1,2 and X3,4, which represent a superposition of broadened X1 and X2; and X3 and X4, respectively) are identified in the 1L Tr′ spectrum. Our GW-BSE calculations for freestanding ReSe2 crystals (Fig. 2(c)) show a set of four close-lying optically bright excitonic transitions for both the 1L and bulk case, starting at 1.58 eV (around the Γ point of Brillouin zone in Fig. 3(a)) and 1.37 eV (around the Ζ point of Brillouin zone in Fig. 3(b)), respectively, in excellent agreement with our


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measurements. For both 1L and bulk, the direct transitions take place from the valence band maximum (VBM) to the conduction band minimum (CBM). Both the VBM and the CBM are twofold degenerate, with each degenerate pair consisting of bands with opposite spins. This results in four possible interband transitions (X1 to X4) with different combinations of spins. In the BSE Hamiltonian, we find different exchange energy contributions for these different spin combinations, i.e. the exchange interaction splits the four excitations. We find a very good agreement between experimentally and theoretically obtained excitonic energies for the bulk crystal. For the 1L case, a deviation of a few tens of meV between experiment and theory arises, since the calculations are performed for freestanding 1L crystals without the sapphire substrate. In Fig. 2(b), a broad line X5 around 1.68 eV is found in the Tr′ spectrum of the 1L flake. Theoretically, we observe a set of four transitions around 1.75 eV for the 1L flake (Fig. 2(c)). We associate the overlap of these close-lying transitions with the experimentally measured X5 line. Fig. 3(c) and Fig. 3(d) show the LDA (dashed lines) and the quasiparticle (solid lines) band structure of 1L and bulk ReSe2, respectively, within the LDA+GdW approximation. Because of inversion and time reversal symmetry, each band is twofold degenerate. We find indirect LDA gaps of 0.92 eV for the bulk and 1.22 eV for 1L, which are in good agreement with previously reported values of 0.98 eV12 and 1.22 eV,21 respectively. However, in the LDA+GdW approximation, both 1L and bulk ReSe2 show direct band gaps with values of 2.44 eV and 1.49 eV, respectively. The weak interlayer coupling preserves the thickness-dependent direct band gap character. The measured integrated PL intensity for the bulk-like crystal is about 400 times larger than that of the monolayer (see Figs. 2(a) and 2(b)). A reduction in PL intensity with decreasing layer thickness has also been observed for ReS2[7] and in room temperature PL


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measurements of ReSe2.14 In contrast, in other TMDCs such as MoS2,3,4,6 a steep rise in the PL intensity is observed if the flake thickness is reduced from bulk to a monolayer. In these materials, relatively strong interactions between the chalcogen atoms of the neighboring layers result in the direct-to-indirect band gap crossover with increasing crystal thickness. Unpolarized Tr′ spectra of ReSe2 flakes with decreasing thickness from bulk to 1L are presented in Fig. 2(d). The X2 and X4 exciton transitions can be observed for crystals of all thicknesses. X1 is discernible in all flakes except 1L, X3 is only resolved for bulk, and X5 for the 1L and 2L case. The extracted excitonic transition energies obtained by Gaussian fits of the Tr′ spectra (see supporting information) are plotted in Fig. 2(e), where the solid lines are a guide to the eye. We find blue shifts of 120 meV and 140 meV, respectively for the X2 and X4 lines, if the layer thickness is reduced from bulk to the monolayer. From GW-BSE calculations, we observe that the excitons exhibit such blue shifts as well, which lie between 210 meV and 240 meV. This result is qualitatively consistent with our measurements. Recently, blue shifts of 140 meV, 170 meV, and 300 meV were observed for the first three excitonic transitions in ReS2.8 These large shifts are in strong contrast to other TMDCs, where the shifts for the ground state A excitons are much smaller: 50 meV for WSe2,35 58 meV for MoSe2,36 65 meV for MoTe2,34 and of similar order for WS2.5 Based on GW-BSE calculations, Molina-Sánchez et al.37 reasoned in the case of MoS2 that an increasing band gap with decreasing flake thickness compensates the effect of an increasing excitonic binding energy, resulting in a weak dependence of exciton transition energy on the layer thickness. The measured polarized PL (normalized) and Tr′ spectra of the 60 nm thick bulk-like ReSe2 crystal are presented in Fig. 4(a) - (b). The polarizer angle is varied between 5∘ and 355∘ with


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respect to the Re chain axis (a-axis) in steps of 10∘ . The spectra are vertically shifted for clarity with respect to the 5∘ measurement. In both PL and Tr′, the relative intensity of the excitonic transition lines changes drastically with the polarization angle, implying that these excitons are strongly polarized along different directions of the crystal. The effect is most prominent for the strongest features X2 and X4. The weaker features X1 and X3 (X3 only in Tr′) become clearly visible for polarizations, where the neighboring stronger lines (X2 and X4, respectively) are suppressed. For example, X1 appears in the 5∘ Tr′ spectrum, whereas X3 becomes visible in the 295∘ Tr spectrum. The integrated PL intensities and the relative oscillator strengths of the excitons (see supporting information) are plotted as a function of polarization angle in Figs. 4(c) and (d), respectively. The data for the

!"

transition is fitted using the function #$ (&) =

#),$ cos - (& − &$ ) + #/,$ sin- (& − &$ ), where #) and #/ are the x and y components of the PL intensity/oscillator strength, and &$ is the orientation of the excitonic transition with respect to the a axis. In the Tr′ polarization patterns (Fig. 4(d)), we are able to clearly distinguish the orientations for all four excitons. They exhibit almost perfectly polarized dipole patterns (#/ ∼ 0). In the emission (PL) patterns (Fig. 4(c)), mixing of the unresolved X3 transition with other lines results in a finite #/ , leading to slightly tilted polarization patterns. However, the orientation &$ of the excitonic transitions with respect to the a axis derived from both cases do not deviate significantly from each other, indicating identical emission and absorption characteristics of the excitons. The calculated polarization-dependent oscillator strengths of the excitonic features are depicted in Fig. 4(f). Similar to the experiments, the four excitons exhibit strongly polarized dipole patterns. The calculated patterns for X1, X2, and X4 compare reasonably well with the experiment in Fig. 4(d) with deviations smaller than 20∘ . Only X3 behaves strongly different in experiment and theory. In addition, the calculated relative oscillator strength of X4 significantly


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exceeds the experimental value. Both of these deviations may be related to the fact that in the GW-BSE approach the excitonic wave functions are much more difficult to converge than their energies. Therefore, the calculation of the oscillator strength and the polarized dipole pattern of excitons can have large errors. Nevertheless, our calculations capture many salient features of the experimental results on a qualitative level. Fig. 4(e) represents the side-view (upper panel) and the top-view (lower panel) of the excitonic spatial distribution for X1 in the ReSe2 crystal (see supporting information for details). The spatial distributions for X2, X3, and X4 are similar to X1. Interestingly, even for the bulk case, the exciton is mainly confined to a single layer (68%). This is a signature of weak interlayer interactions in TMDCs,37 and Re-based materials in particular. Therefore, two-dimensional physics is largely applicable for the bulk case. The root-mean-square (RMS) radius of the exciton 3〈5 - 〉 is obtained as 9.6 Å (see supporting information), whereas the excitonic binding energy is calculated to be 120 meV. The polarization-resolved Tr′ spectra for the 1L to 3L thick ReSe2 crystals are represented in Fig. 5(a) - (c) in steps of 20∘ . For the monolayer, we can analyze the polarization response of X1,2, X3,4, and X5. For the 2L and 3L, the two prominent X2 and X4 lines are investigated. The derived excitonic oscillator strengths for the three cases are plotted in Figs. 5(d), (f), and (g), respectively. In Fig. 5(e), we present the calculated polarization patterns for the first four excitons in the monolayer. X1, X2 and X3 show highly polarized dipole character, whereas X4 is only weakly polarized in the plane. A direct comparison with the experimental results in Fig. 5(d) is difficult due to overlapping neighboring exciton transitions. However, qualitatively, both experiment and theory point towards an overall directional character of excitonic polarization along the a axis. The calculated RMS radius of all the excitons is 7.5 Å (see Fig. S3 of supporting information for the spatial distribution), and the binding energy is 860 meV. It is of


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the same order as for the monolayer TMDCs such as MoS2.37,38 The calculated polarization patterns for the four higher-lying excitonic features observed around 1.75 eV are presented in Fig. S5 of the supporting information. Since these features merge to form a broad maximum X5 in the experimental spectra, it is not possible to make a comparison with theory. For the 2L and 3L thick crystals, the polarization directions of the X2 and X4 excitons are similar to those of the bulk material. Again, this observation demonstrates the weak effect of increasing thickness on the excitons in ReSe2. In conclusion, we have investigated the polarization-resolved excitonic band structure of atomically thin to bulk-like 1′-ReSe2 crystals using micro-photoluminescence and microtransmission spectroscopy measurements combined with GW-BSE based ab initio calculations. We find strongly polarized excitonic transitions, where the polarization characteristics persist from bulk down to monolayer crystals. From our calculations we find that 1′-ReSe2 is a direct band gap material irrespective of the crystal thickness. Also in bulk material, the excitons are strongly confined to a single layer and have a high binding energy of 120 meV. The excitonic anisotropy of the newly emerging TMDC ReSe2 paves the way for controlling optical fields at atomic scales and for potential applications in polarization-sensitive detection and optical computation/logic circuits. ASSOCIATED CONTENT

Supporting Information. The following file is available free of charge. Details of experimental and theoretical methods; five figures showing the convergence of the calculations; spatial distribution of the monolayer excitons; measured reflectance spectra of bulk


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ReSe2, and calculated and measured polarization patterns of the X5 feature in Fig. 2(a). (PDF file) Corresponding Authors *[email protected] (RB), *[email protected] (AA) Fax: +49 251 83-36414 Funding Sources Ashish Arora acknowledges the financial support from the Alexander von Humboldt foundation. Acknowledgements The authors thank Philipp Eickholt and Markus Donath for fruitful discussions. The computing times granted by the John von Neumann Institute for Computing (NIC) and the JURECA supercomputing facility at Jülich Supercomputing Centre (JSC) are also acknowledged. Notes The authors declare no competing financial interests.


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Figure 1. (a) Schematic representation of the 1′-ReSe2 unit cell and the coordination of the constituent Re (blue) and Se (golden) atoms, along with the marked a, b, and c axes. (b) Oblique view depicting the relative arrangement of atoms in the adjacent layers of the bulk crystal. (c) Top view (along the c-axis), (d) side view along the a axis, and (e) side view along the b axis of the crystal in (b), showing Re chains along the a axis. (f) - (h) Optical microscopy (transmission) images of the flakes with corresponding height profiles obtained by atomic force microscopy. Red lines mark the a axis (i.e. the Re chain direction) in the optical images. Dashed black lines outline the thin layers.


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Figure 2. (a) Unpolarized [1-Transmission] (or Tr′, blue) and micro-photoluminescence (PL) spectra (gray) for a 60 nm thick bulk-like ReSe2 flake at a temperature of T = 10 K. The resonances X1 to X4 in the Tr′ spectrum are marked by arrows. The weak X3 is more clearly identifiable in polarization-resolved spectra (Fig. 4(b)). (b) Unpolarized Tr′ (pink) and PL (gray) spectra for a 1L ReSe2 flake at a temperature of T = 10 K. The resonances X1,2, X3,4, and X5 in the Tr′ spectrum are marked by arrows. (c) Calculated absorption spectra for 1L (pink) and bulk (blue) ReSe2. (d) Measured Tr spectra of ReSe2 crystals with thicknesses ranging from 1L to the bulk-like limit at a temperature of T = 10 K, with X1 to X5 marked with vertical arrows following the color schemes in (a) and (b). The spectra are vertically shifted by the offsets indicated on left side of the plots (in %) with respect to the 1L spectrum. X3 can only be resolved for the bulk-like crystal, whereas X5 is observed only for 1L and 2L samples. (e) Transition energies of the excitons as a function of layer thickness extracted from Fig. 2(d).


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Dotted lines are guides to the eye. Theoretically obtained excitonic energies for 1L and bulk crystals are also marked using horizontal bars.


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Figure 3. Brillouin zone and high symmetry points of (a) 1L, and (b) bulk ReSe2. The green lines represent the directions along which the band structure is calculated in (c) and (d). Band structure at LDA (dashed lines) and GdW (solid lines) levels for (a) monolayer, showing a direct GdW quasiparticle gap of 2.44 eV at the Γ point of the Brillouin zone (BZ), and for (d) bulk with a direct GdW quasiparticle gap of 1.49 eV at the Z point of the BZ. Each band is twofold degenerate because of inversion and time reversal symmetry.


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Figure 4. (a) Measured normalized PL spectra, and (b) Tr′ spectra for the same 60 nm thick bulk-like crystal as a function of polarization angle (with respect to the a axis), measured in steps of 10∘ at a temperature of T = 10 K. The spectra are vertically shifted for clarity. The photoluminescence intensity and the absorption cross section of the excitonic transitions strongly change with polarization angle. (c) Extracted photoluminescence intensity, and (d) relative oscillator strength of the excitons as a function of the polarization angle. Dots represent the experimental data. Solid lines are modeled curves, as mentioned in the text. &$ indicates the orientation of the

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excitonic transition with respect to the a axis. (e) Side view and top view of


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the calculated spatial excitonic distribution of X1 in the bulk ReSe2 crystal. The lattice vectors are shown as in Fig. 1. The excitonic distributions for X2, X3, and X4 are identical to the one of X1. (f) Calculated excitonic oscillator strengths for the four energetically lowest excitonic transitions as represented in Fig. 2(b).


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Figure 5. Measured Tr′ spectra of (a) 1L, (b) 2L and (c) 3L crystals as a function of polarization angle (with respect to the a axis), measured in steps of 20∘ at a temperature of T = 10 K. The spectra are vertically shifted for clarity. In (a), three main features X1,2, X3,4, and X5 are identified. In (b) and (c), the X2 and X4 transitions are investigated for their polarization dependence. (d) Experimentally determined and (e) theoretically calculated relative oscillator strengths of the excitons for the monolayer (1L) depending on polarization. The experimentally determined relative oscillator strength of the excitons as a function of the polarization angle is shown for (f) 2L, and (g) 3L thick flakes. In (d), (f), and (g), dots represent the experimental data and solid lines are the modeled curves, as mentioned in the text. &$ indicates the orientation of the

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excitonic transition with respect to the a axis.


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