Article | Open | Published:

Exciton binding energy and hydrogenic Rydberg series in layered ReS2

Abstract

Unlike monolayers of transition metal dichalcogenides such as MoS2, which possess high in-plane symmetry, layered ReS2 exhibits reduced in-plane crystal symmetry with a distorted 1 T structure. This unique symmetry leads to anisotropic optical properties, very promising for light polarization devices. Here, we report on low temperature polarization-resolved emission and absorption measurements of excitons in ReS2 from bulk to monolayer. In photoluminescence and reflectivity contrast spectra we distinguish two strongly polarized excitons X1 and X2 with dipole vectors along different crystal directions, which persist from bulk down to monolayer. Basing on the PL and RC spectra of bulk crystals we determine the energy of the ground and first four excited states of both excitons, which follow the usual hydrogenic Rydberg series of energy levels of 3D excitonic states (En = Ry*/n2). From the numerical fit we estimate that the energy gap is direct and equal to 1671.7 meV and binding energy of X1 and X2 is equal to 117.5 and 86.6 meV, respectively. In magneto-PL spectra of bulk ReS2 up to B = 10 T, the energy shift of all the states is below 2 meV. On reducing the crystal thickness from bulk to monolayer the ground state experience a strong blue shift.

Introduction

Layered semiconducting transition metal dichalcogenides (TMDCs) have attracted great and current interest, fueled by underlying physics and anticipated applications in optoelectronic and spintronics1,2,3,4,5,6,7,8,9,10,11,12,13. Similarly to graphene, in monolayers of group VI TMDCs, such as MoS2, MoSe2, WS2, and WSe2 the bottom of the conduction band and the top of the valence band are located at the K points of the 2D hexagonal Brillouin zone. On the other hand, contrary to graphene, the lack of inversion symmetry and a strong spin-orbit coupling in single layers of group VI TMDCs results in a valley-contrasting strong spin splitting of the valence and conduction bands which enable excitation of carriers with various combination of valley and spin indices using circularly polarized light4,5,6,7. However, due to the high symmetry of the crystal structure, their linear optical properties, recorded in absorption and emission spectra, are isotropic in the layer plane. Then again, group VII TMDCs, such as ReS2 and ReSe2, possesses reduced crystal symmetry compared to the molybdenum and tungsten dichalcogenides which leads to anisotropic in-plane optical properties of ReS2 and ReSe214,15,16,17. Successful preparation of ReS2 and ReSe2 layers of selected thickness from bulk down to single layer, has given rise to intensive studies of their structural, electronic and optical characterization18,19,20,21,22. However, there are many aspects of their physical properties that are still under debate. Tongay et al.18 have claimed that due to in-plane distortion in ReS2 the interlayer coupling is weak and stacked layers in bulk behave as electronically and vibronically decoupled monolayers. In contrast, Aslan et al.19 in recent photoluminescence (PL) and reflectance spectroscopy experiments on bulk, few- and monolayer ReS2 have observed strong linear polarization dependence of the absorption and emission spectra and found that the transition energies of the observed excitons can be tuned with layer thickness. Another controversy is related to the nature of the energy gap of ReS2. Some authors have argued that ReS2 exhibits a transition from the indirect to direct optical band gap when thinned from bulk to monolayer20,21, similarly as in the group VI TMDCs. However in ref.18, on the base of photoluminescence and reflectivity measurements, and in recent angle-resolved photoemission spectroscopy (ARPES) experiments22, the authors have proven the contrary, i.e. that the energy gap in ReS2 is direct independently of the number of layers. Layered character of ReS2 suggests a strong enhancement of the Coulomb binding energy of excitons, bound electron-hole pairs (X = e + h) which can lead to their stability even at room temperature. A comprehensive explanation of how excitons are formed is significant both for the comprehension of the underlying physics in such layered materials and for their potential application in optoelectronic devices. Most of optical spectroscopy studies of ReS2 in bulk and monolayer form have been performed at room temperature, where absorption and emission lines are broad and overlapping, which hinders detailed analysis of individual excitonic lines.

The aim of this paper is to clarify those issues, and to provide insight into the nature of excitons observed in the optical spectra of ReS2 using the accuracy of low temperature experiments. We report on low temperature (7 K) photoluminescence, photoluminescence excitation (PLE) and reflectivity contrast (RC) measurements of ReS2 from bulk to monolayer, all of which reveal linearly polarized optical transitions of excitons X1 and X2. The comparative analysis of PL, PLE and RC spectra allows us to conclude that from bulk down to monolayer the energy gap of ReS2 is direct and increases with the decrease of the layer thickness. For bulk crystals we determine the energy of the ground and first four excited states of excitons X1 and X2 which follow the usual hydrogenic Rydberg series of energy levels of the three dimensional (3D) excitonic states (En = Ry*/n2). We establish their large exciton binding energy equal to 118 and 83 meV. We find that both excitons are related to the same energy gap equal to 1671.7 meV. In magneto-PL spectra of bulk ReS2 recorded in Voigt configuration up to B = 10 T and temperature T = 1.8 K, for both excitons, the energy shift of the ground state is not measurable, whereas the shift for excited states is below 2 meV.

Results and Discussion

Layered rhenium disulphide crystallizes in a distorted 1 T diamond-chain structure with triclinic symmetry unit cell23,24,25. Figure 1 presents the crystal structure of a single ReS2 layer, from the top and side view, along the b-axis. Each layer consists of a sheet of Re atoms located between two S atoms sheets, bound by strong ion-covalent bond between Re and S atoms22,23,24,25. The S atoms have a distorted octahedral coordination around the Re atoms which results in the formation of Re−Re chains clusters along the b-axis25. Bulk ReS2 crystals are composed of stacks of such layers bound by weak van der Waals forces.

Figure 1
figure1

Scheme of monolayer ReS2 from: (a) top view and (b) side view. The Re and S atoms are denoted in grey and yellow, respectively. The Re chain is along the b direction.

We have studied anisotropic optical properties of ReS2 in complementary polarization resolved photoluminescence, photoluminescence excitation and reflectivity contrast measurements. Figure 2 presents polarization-resolved photoluminescence spectra of the bulk ReS2 crystal. To omit polarization dependent effects the incident light was circularly polarized and incident photon energy, of 2.33 eV was much higher than the energy of all the observed PL lines. For both the σ+ and σ excitation the PL spectra exhibit the same variation as a function of polarisation, regarding both the shape and energy position of emission lines. Then, the PL spectra were analyzed in linear polarization configuration with the polarization angle of the electric field light (E) varied between 30° and 120° with respect to the Re chain axis (b-axis) in steps of 4° (for visibility only PL spectra with 8° step are displayed in Fig. 2). For clarity, the spectra are vertically shifted with respect to the 33° measurement. In the low energy sector of the PL spectra we observe two well resolved excitonic peaks which we attribute to the excitonic ground states 1 s and label as X1(1) and X2(1). Their relative PL intensity changes drastically with the polarization angle but the PL maxima of both lines are detected at the same energy independently of the polarization angle. This implies that these excitons are strongly polarized along different directions of the crystal. In the higher energy sector of the PL spectra we observe four peaks, labelled in analogy to hydrogenic series as 2 s, 3 s, 4 s and 5 s, whose intensity and energy position change as a function of the polarization angle. We tentatively assume that these lines are excited states of the Rydberg series of the excitons X1(1) and X2(1). According to theoretical predictions optical transitions between the s- like states with zero angular momentum are dipole allowed in most of semiconductors, including semiconducting TMDC26,27,28.

Figure 2
figure2

(a) Polarization-resolved photoluminescence spectra, measured at 8° intervals from 30° to 120°. (b) The integrated PL intensity of the X1(1) and X2(1) ground states emission plotted as a function of the polarization angle. The data are presented in a polar plot over a 360° range for clarity.

In order to distinguish between the two excitonic series of excited n = 2–5 states we analyse the PL spectra in two opposite polarisations where emission of the X1(1) exciton or the X2(1) exciton disappears from the spectra. We assume that in the polarization in which X1(1) emission is suppressed, the emission from its excited states X1(n) (n > 2) is also suppressed and only the hydrogenic Rydberg series of the X2(n) exciton is detected. The opposite relation is anticipated for the observation of the X1(n) hydrogenic Rydberg series. From the detailed analysis of the evolution of total PL intensity of X1(1) and X2(1) emission presented in Fig. 2b (the integrated area under the X1(1) and X2(1) peaks in the ranges from 1.525 eV to 1.562 eV and from 1.562 eV to 1.604 eV, respectively) we find that X1(1) related peak disappears at 113° polarization angle, whereas X2(1) one at 33°, which is in a good agreement with the recent report of Aslan et al.19. The PL spectra recorded at these two polarisations are presented in Fig. 3a. The 33° PL spectrum is drawn in red, whereas the 113° PL spectrum is drawn in blue. As it is clearly seen, the peaks of the X1(n) excitonic Rydberg series are shifted to lower energies in relation to peaks of the X2(n) excitonic Rydberg series. In addition, for both X1(n) and X2(n) series, we observe the decrease of both the peak intensity and the energy separation for the increasing number of states, which are characteristic features of an excitonic Rydberg series. The peak positions determined as the maxima in PL spectra are plotted in Fig. 3b,c for the excitons X1 and X2, respectively. To strengthen our interpretation we additionally perform pseudo-absorption reflectivity contrast (RC) measurements. The RC spectra recorded in the same polarization as PL spectra are presented in the upper part of Fig. 3a. In both 33° RC and 113° RC spectra we observe well resolved resonances positioned at the same energies as their counterparts in PL spectra. The observation of the same optical transitions in absorption and emission spectra allows us to conclude that the energy gap in bulk ReS2 is direct.

Figure 3
figure3

(a) Polarization-resolved PL and RC spectra of bulk ReS2 recorded in two linear polarisation with the angle between E and b equal to 33° (red line) and 113° (blue line). (b) and (c) Experimentally and theoretically obtained transition energies for the 3D exciton states as a function of the quantum number n, for the X1 and X2 excitons, respectively.

In our estimations of the binding energy of X1 and X2 excitons we assume that both excitons are related to the same energy gap Eg, as predicted in recent numerical calculations29. Echeverry and Gerber have studied the effect of the interlayer coupling on the band-gap character by means of the self-energy corrected GW method for optimized and experimental sets of structure’s data29. They show at the G0W0 level of theory, when the thickness of the ReS2 sample decreases from bulk to bilayer and to a freestanding monolayer, the band gap remains direct at the Γ point of the Brillouine zone, with its energy increasing from 1.6 to 2.0 and 2.4 eV, respectively. In this calculations the valence band maxima and conduction-band minima are double degenerated. This implies up to four excitonic interband transitions with different combinations of spin. The splitting between four excitons is due to the exchange interaction. The observation of four excitons with different optical amplitudes (two strong and two weak) were reported in the optical spectroscopy studies of ReSe2 from bulk to monolayer30. However, in our studies we observe only two excitons X1 and X2. In order to calculate the exciton binding energies of X1 and X2 excitons we compare experimental data with theoretical prediction of hydrogenic Rydberg series. We use a formula typically employed for the description of three dimensional (3D) Wannier excitons in inorganic semiconductors26:

$${{\rm{E}}}_{{\rm{b}}}^{(n)}={{\rm{E}}}_{{\rm{g}}}-{{\rm{Ry}}}^{\ast }/{{\rm{n}}}^{2}$$
(1)

where Eg is the energy gap, n is the number of exciton state, Eb(n) is the binding energy at nth excitonic state and Ry* is the effective Rydberg constant. The results of a fit are plotted in Fig. 3b,c for X1 and X2 excitons, respectively. The calculated values of the ground and all excited states are in excellent quantitative agreement with the experimental data for the X1 exciton. For the X2 exciton the calculated energy of the states 2 s and 3 s are slightly higher than those determined from the experiment. This can be due to the fact that in contrast to the theoretical calculations which predict four different excitonic series29 we observe only two.

The observation of two Rydberg series of excitons instead of four can be caused by different optical amplitudes of excitons. Indeed, in the absorption spectra of ReSe2 Arora et al.30 have detected two excitons with high optical amplitudes and two excitons with low optical amplitudes. They distinguished between all four excitons X1, X2, X3 and X4 since they are polarized along different directions of the crystal and the weaker features X1 and X3 are visible for polarizations, where the neighbouring stronger lines, X2 and X4, respectively are suppressed. In contrast Aslan et al.19 have reported of the observation of three excitons (exciton 1, exciton 2, exciton 3) in the reflection contrast spectra of ReS2 from few-layer to monolayer. However, on the basis of the comparative studies of the evolution of energies and resonance strengths of these three excitons as function of number of layers they have proposed that exciton 3 is an excited (Rydberg) excitonic state of the lower-lying excitons. This scenario is compatible with the increasing separation in energy of exciton 3 from excitons 1 and 2 with decreasing layer thickness. Simultaneously, the thinner samples should exhibit increased exciton binding energy and, hence, increased energy separation between the transitions. This interpretation is consisted with our results and analysis. Namely, we conclude that the broad line named as the exciton 3 in ref.19 is indeed related to the superposition of the excited states of the excitons X1 and X2. In contrast to ref.19, in our studies we can resolve between different transition related to the excited states of excitons X1 and X2 since we investigate bulk ReS2 crystals. Nevertheless, as in ref.19, we are not able to distinguish between the excited excitonic states in a few-layer ReS2.

The energy gap estimated from the Eq. 1 equals 1671.7 meV, which is higher than the result of 1600 meV obtained in recent theoretical calculations29. The Coulomb binding energies of excitons X1 and X2 equal to 117.5 and 86.6 meV are very high in comparison to the exciton binding energy in typical semiconductors belonging to the II-VI and III-V groups, e.g. Eb = 4.8 and 10 meV in GaAs and CdTe, respectively26. The hydrogenic Rydberg excitonic series in bulk ReS2 was previously studied by Ho et al.17 by means of polarized photoreflectance spectroscopy. However, in contrast to our experiments, they compared photoreflectance spectra with optical polarizations along and perpendicular to the b axis. They assumed that the two series of excitons are related to the splitting of the top of the valence band equal to 5 meV. As a consequence they estimated the Coulomb binding energy of the excitons X1 and X2 equal to 157 and 152 meV. Since the X1 and X2 excitons are 3D Wannier excitons, we calculate their relative Bohr radius using the well know relations for hydronic like excitons:

$${{\rm{E}}}_{{\rm{b}}}/{\rm{Ry}}={{\rm{m}}}_{{\rm{ex}}}/{{\rm{\varepsilon }}}^{2}$$
(2)

and

$${{\rm{a}}}_{{\rm{ex}}}/{{\rm{a}}}_{{\rm{H}}}={\rm{\varepsilon }}/{{\rm{m}}}_{{\rm{ex}}},$$
(3)

where: Ry = 13.6 eV and aH = 0.53 A are Rydberg constant and Bohr radius of the hydrogen atom, respectively; mex is a relative effective mass of an exciton, ε is the relative dielectric constant of ReS2 and aex is the exciton Bohr radius. We estimate the relative effective masses of X1 and X2 excitons (1/mex = 1/me + 1/mh) using the tensor of the electron effective mass obtained from the electrical transport study of multilayer ReS2 with polymer electrolyte gating31 and the tensor of the hole effective mass obtained in the study of bulk ReS2 by means of high resolution angle-resolved photoemission spectroscopy22. We obtain effective masses of the X1 and X2 excitons equal to ~0.33 and ~0.39 (in units of electron mass), respectively, From Eq. 2 we obtain two dielectric constants in directions along and perpendicular to b axis equal to ~6.2 and ~7.8 and finally from Eq. 3 we estimate the exciton Bohr radius to be equal ~1 nm for both X1 and X2 excitons.

To gain further insight into the nature of the excitons X1 and X2 we have performed additional measurements of photoluminescence excitation and magneto-photoluminescence of bulk ReS2. Figure 4 presents polarised 113° PL and 113° PLE spectra in which only the Rydberg series of the exciton X2 is detected. The PLE signal is presented in Fig. 4b as a color map. The blue color is related to low signal whereas the red color is related to high signal To facilitate the analysis of the PLE signal the PL spectra in relevant energy regions are displayed in Fig. 4a,c. The PLE signal was detected in the energy range related to the ground exciton state from 1535 to 1605 meV. The laser excitation energy was tuned across the energy of the excited states 2 s, 3 s, 4 s and 5 s from 1619 to 1676 meV. The features observed in the low energy sector of 113° PLE spectra are related to Raman active optical phonons. For comparison, Fig. 4d shows the non-resonant (2.33 eV), unpolarized Raman scattering spectra of bulk ReS2. In the 120–450 cm−1 range we can distinguish up to 18 phonon modes (marked by arrows) whose energies agree well with the previous studies of Raman spectra of ReS232. As it is seen from the comparison of PLE and PL spectra in Fig. 4b,c the energy position of all the related peaks are detected at almost the same energies which confirms our interpretation of these lines as Rydberg series of the exciton X2. The same relations are observed between 33° PL and 33° PLE spectra in which only the Rydberg series of the exciton X1 is observed.

Figure 4
figure4

The photoluminescence and photoluminescence excitation spectra of bulk ReS2 recorded at T = 1.8 K. (a) The 113° PL spectrum. The energy regions of detection and excitation of PLE signal are marked by dotted lines and arrows, respectively. (b) The 113° PLE signal plotted as a color map. Red and blue color indicate high and low intensity, respectively. (c) The 113° PL spectrum presented in the energy region of PLE signal.

The magneto-photoluminescence measurements have been conducted in the Voigt configuration with magnetic field up to 10 T with a 1 T step applied along the b axis (B||b)33. Due to the strong anisotropy of the in-plane optical properties resulting from triclinic symmetry of bulk ReS2 we have not performed experiments in Faraday configuration with magnetic field perpendicular to the plane through b axis (Bb). However, the Faraday configuration is commonly used in the magneto-spectroscopy studies of the exciton diamagnetic shifts in the high symmetry structures, for example, in the monolayer group-VI transition metal dichalcogenides12 or in the two dimensional GaAs/Ga1−xAlxAs structures34,35,36. In Fig. 5a and c the PL spectra recorded in the magnetic fields from 0 to 10 T with a 2 T step are presented for two distinctive linear polarizations (E(33°)B||b) and (E(113°)B||b) (as in Fig. 3a), respectively. The magnetic shift of all the observed lines is very small. For the ground states of the excitons X1 and X2 the shift is not measurable, whereas for the excited states it is less than 2 meV for the highest applied magnetic field B = 10 T. This observation mainly confirms the strong Coulomb binding of the both excitons. Due to the large width of emission lines (full widths at half maximum (FWHM) equal to ~15 meV and ~7 meV for the ground and excited states of X1 and X2 excitons, respectively) the Zeeman splitting is not observed and the accurate estimation of the Lande g factor and diamagnetic constant an from the formula:

$${{{\rm{\Delta }}E}^{({\rm{n}})}}_{{\rm{B}}}=\pm \,1/2\,{g{\rm{\mu }}}_{{\rm{B}}}{\rm{B}}+{{\rm{a}}}_{{\rm{n}}}\,{{\rm{B}}}^{2}$$

used for low magnetic field limit33,37 is not possible. More detailed verification of the influence of the magnetic field on the ground and excited states in ReS2 crystals would necessitate further measurements at higher magnetic field and theoretical calculations of the diamagnetic coefficient of an exciton in layered semiconductor structures.

Figure 5
figure5

(a) and (c) Magnetic field evolution of PL spectra of bulk ReS2 at T = 1.8 K in polarizations E(<33°) B||b and E(<113°) B||b, respectively. (b) and (d) Energies of different excitonic transitions extracted from PL spectra recorded in σ and π polarizations, respectively.

Finally, we perform optical spectroscopy measurements of ReS2 flakes. Figure 6a presents unpolarized PL spectra of ReS2 flakes with different number of layers. The Supplementary Fig. 1 presents optical microscope image of the studied ReS2 flakes prepared by mechanical exfoliation and deposited on target SiO2(295 nm)/Si substrate. The number of layers have been tentatively estimated by optical contrast and then the thickness of the particular areas of ReS2 structure have been determined by means of AFM measurements, presented in Supplementary Figs 2a2s). For all the studied flakes in the low energy sector of PL spectra two emission lines are detected, which by comparison to PL spectra of bulk crystals we have attributed to optical transitions of the ground states of excitons X1 and X2. However, in contrast to bulk ReS2 crystals, we are not able to resolve between the excited states of excitons X1 and X2 in the PL or RC spectra. We observe only the broad PL feature at the higher energy (marked as ExS in Fig. 6a). Moreover, as in the bulk ReS2 crystal, the excitons X1 and X2 are strongly polarized in emission and pseudo-absorption spectra. In Fig. 6b the polarized PL and RC spectra for 15 and 6 layers samples are presented (see also Supplementary Fig. 3 in Supplementary Materials). The total PL intensity of both excitons strongly increases with the number of layers, and starts to saturate for flakes thicker than 8 layers, which is seen in Fig. 6a. The similar increase of PL intensity of ReS2 with the increased number of layers have been recently reported at room temperature experiments18. This is in contrast to the behavior observed in the group VI TMDCs, such as MoS2, MoSe2, WS2 and WSe2, where the PL intensity of the monolayer increases by orders of magnitude due to the crossover from an indirect band gap in the bulk to a direct band gap in the monolayer. According to the recent theoretical calculations of Echeverry and Gerber29 in layered ReS2 the direct band gap occurs at the Γ-point of the Brillouin zone irrespective of the crystal thickness. Hence, the oscillator strength of excitonic transitions should increase simultaneously for thicker samples. Moreover, with decrease of the number of layers, from 15 L to 1 L (Fig. 6d), both X1 and X2 excitons exhibit strong blue shift, which is 114 meV and 146 meV, respectively. Also, their relative energy separation increases, as shown in Fig. 6c. These large shifts are in strong contrast to other, well known group VI TMDCs, where the shifts for the ground state A excitons are much smaller and are in the order of tens meV38,39. It is likely due to the stronger electron-hole coupling at Γ-point than at K-point, where direct band gap occurs for the monolayer MoS2, MeS2, WS2 and WSe2. In the case of group VI TMDCs, an increasing band gap with decreasing flake thickness compensates the effect of an increasing excitonic binding energy40 resulting in a weak dependence of exciton transition energy on the layer thickness. In ReS2, observed increase of the exciton transition energy caused by quantum confinement is less compensated. Moreover, this energy change is different for excitons X1 and X2 likely due to induced in-plane anisotropy.

Figure 6
figure6

(a) Unpolarized PL spectra of 1 L, 2 L, 4 L, 5 L, 6 L and 8 L ReS2 flakes. (b) Polarization-resolved PL and RC spectra of 15 L and 6 L flakes recorded in two linear polarization with the angle between E and b equal to 33° (red line) and 113° (blue line). (c) Energies of different excitonic transitions extracted from PL measurements.

Conclusion

Summarizing, we have studied at low temperature the polarization-resolved emission and absorption of excitonic states in layered ReS2, from bulk to monolayer. In photoluminescence, photoluminescence excitation and reflectivity contrast spectra we distinguish two strongly polarized excitons X1 and X2, with dipole vectors along different crystal directions, which persist from bulk down to monolayer. The detailed analysis of optical spectra allows us to conclude that in ReS2 from bulk to monolayer the energy gap is direct. We have experimentally determined the energies of the ground and first four excited excitonic states of the fundamental optical transition in bulk ReS2 for excitons X1 and X2 and found that they follow the Rydberg series of energy levels of the three dimensional excitonic states. From the numerical fit we have calculated the energy gap of bulk ReS2 equal to 1671.7 meV and the binding energy of excitons X1 and X2 equal to 117.5 and 86.6 meV, respectively. In magneto-photoluminescence spectra of bulk ReS2 performed in the fields up to 10 T we have detected a very small shift of all the observed peaks, below 2 meV, which confirm strong Coulomb binding of excitons. In optical spectra of the few and monolayer ReS2 we can distinguish only the ground states of X1 and X2 excitons which experience a strong blue shift on reducing the crystal thickness from bulk to monolayer.

Methods

The studied ReS2 crystals were grown by chemical vapour transport technique (CVT). Prior to the crystal growth, the powdered compounds of the series were prepared from the elements (Re: 99.99%; S: 99.999%) by reaction at T = 1000 °C for 10 days in evacuated quartz ampoules. The chemical transport was achieved with Br2 as a transport agent in the amount of about 5 mg/cm3. The ReS2 crystals formed thin silver-colored, graphite-like platelets up to 2 cm2 in area. The X-ray diffraction patterns confirmed the triclinic symmetry of ReS2 with all the parameters consistent with those previously reported16,23,24. Hall effect measurements reveal n-type semiconducting behavior. The flakes of ReS2 of thickness from bulk down to monolayers were prepared by mechanical exfoliation of bulk crystals. Initially, flakes are exfoliated onto a DGL film (Gel-Pak) attached to a glass plate and identified by their optical contrast and characterized by Raman scattering and PL measurements at 295 K. For further optical studies, they are deposited on the same Si/SiO2 (295 nm) target substrate. The number of layers is determined by means of Atomic Force Microscopy measurements. We have measured the thickness of a single ReS2 layer to be equal to ~0.7 nm.

The experiments were conducted using two set-ups. In experiments where magnetic field was not applied the samples were mounted on a cold-finger of non-vibrating closed cycle cryostat, where temperature can be varied from 7 to 300 K. Photoluminescence was excited by the 532 nm (2.33 meV) line of a Diode-Pumped Solid State laser. The laser beam was focused on the sample under normal incidence using a 50x high resolution, long distance microscope objective (NA = 0.65). The diameter of the excitation spot was equal to ~1.5 μm. The PL signal was collected by the same objective. The Raman scattering measurements were performed in backscattering geometry. The spectra were analyzed with a 0.5 m focal length spectrometer and a 600 lines/mm grating. A Peltier-cooled Si charge couple device was used as a detector. The reflectivity contrast measurements were conducted in the same set-up, with a filament lamp as a light source. The magneto-optical measurements were conducted in the similar optical set-up, with the use of a bath liquid helium cryostat with a superconducting magnetic coil. The experiments were done in Voigt configuration in magnetic field up to B = 10 T and temperature T = 1.8 K.

References

  1. 1.

    Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

  2. 2.

    Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Single-layer MoS2 transistors. Nat. Nanotechnol. 6, 147–150 (2011).

  3. 3.

    Kadantsev, E. S. & Hawrylak, P. Electronic structure of a single MoS2 monolayer. Solid State Commun. 152, 909–913 (2012).

  4. 4.

    Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).

  5. 5.

    Cao, T. et al. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat. Commun. 3, 885–887 (2012).

  6. 6.

    Sallen, G. et al. Robust optical emission polarization in MoS2 monolayers through selective valley excitation. Phys. Rev. B 86, 81301 (2012).

  7. 7.

    Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).

  8. 8.

    Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol. 7, 699–712 (2012).

  9. 9.

    Jadczak, J., Delgado, A., Bryja, L., Huang, Y. S. & Hawrylak, P. Robust high-temperature trion emission in monolayers of Mo(SySe1−y)2 alloys. Phys. Rev. B 95, 195427 (2017).

  10. 10.

    Van Tuan, D., Scharf, B., Žutić, I. & Dery, H. Marrying excitons and plasmons in monolayer transition-metal dichalcogenides. Phys. Rev. X 41040, 1–19 (2017).

  11. 11.

    Jadczak, J., Kutrowska-Girzycka, J., Kapuściński, P., Wójs, A. & Bryja, L. Probing of free and localized excitons and trions in atomically thin WSe2, WS2, MoSe2 and MoS2 in photoluminescence and reflectivity experiments. Nanotechnology 28, 395702 (2017).

  12. 12.

    Smoleński, T. et al. Magnetic field induced polarization enhancement in monolayers of tungsten dichalcogenides: effects of temperature. 2D Mater. 5, 15023 (2018).

  13. 13.

    Bieniek, M. et al. Band nesting, massive Dirac fermions, and valley Landé and Zeeman effects in transition metal dichalcogenides: A tight-binding model. Phys. Rev. B 97, 1–9 (2018).

  14. 14.

    Friemelt, K., Lux-Steiner, M.-C. & Bucher, E. Optical properties of the layered transition-metal-dichalcogenide ReS2: Anisotropy in the van der Waals plane. J. Appl. Phys. 74, 5266 (1993).

  15. 15.

    Fang, C. M., Wiegers, G. A. & de Groot, R. A. Electronic structures of ReS2, ReSe2 and TcS2 in the real and the hypothetical undistorted structures. J. Phys. Condens. Matter 9, 4411–4424 (1997).

  16. 16.

    Ho, C. H., Huang, Y. S., Tiong, K.-K. & Liao, P. C. Absorption-edge anisotropy in ReS2 and ReSe2 layered semiconductors. Phys. Rev. B 58, 130–135 (1998).

  17. 17.

    Ho, C. H., Yen, P. C., Huang, Y. S. & Tiong, K. K. Photoreflectance study of the excitonic transitions of rhenium disulphide layer compounds. Phys. Rev. B 66, 1–5 (2002).

  18. 18.

    Tongay, S. et al. Monolayer behaviour in bulk ReS2 due to electronic and vibrational decoupling. Nat. Commun. 5, 3252 (2014).

  19. 19.

    Burak Aslan, O., Chenet, D. A., van der Zande, A. M., Hone, J. C. & Heinz, T. F. Linearly Polarized Excitons in Single-and Few-Layer ReS2 Crystals. ACS Photonics 3, 96–101 (2015).

  20. 20.

    Gehlmann, M. et al. Direct Observation of the Band Gap Transition in Atomically Thin ReS2. Nano Lett. 17, 5187–5192 (2017).

  21. 21.

    Gutierrez-Lezama, I., Reddy, B. A., Ubrig, N. & Morpurgo, A. F. Electroluminescence from indirect band gap semiconductor ReS2. 2D Mater. 3 (2016).

  22. 22.

    Webb, J. L. et al. Electronic band structure of ReS2 by high-resolution angle-resolved photoemission spectroscopy. Phys. Rev. B 96, 115205 (2017).

  23. 23.

    Wildervanck, J. C. & Jellinek, F. The dichalcogenides of technetium and rhenium. J. Less-Common Met. 24, 73–81 (1971).

  24. 24.

    Alcock, N. & Kjekshus, A. The Crystal Structure of ReSe2. Acta Chem Scand (1965).

  25. 25.

    Lamfers, H.-J., Meetsma, A., Wiegers, G. A. & de Boer, J. L. The crystal structure of some rhenium and technetium dichalcogenides. J. Alloys Compd. 241, 34–39 (1996).

  26. 26.

    Klingshirn, C. Semiconductor optics (Springer-Verlag Berlin Heidelberg 2005).

  27. 27.

    Qiu, D. Y., Da Jornada, F. H. & Louie, S. G. Optical spectrum of MoS2: Many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 1–5 (2013).

  28. 28.

    Berghäuser, G. & Malic, E. Analytical approach to excitonic properties of MoS2. Phys. Rev. B - Condens. Matter Mater. Phys. 89, 1–6 (2014).

  29. 29.

    Echeverry, J. P. & Gerber, I. C. Theoretical investigations of the anisotropic optical properties of distorted 1 T ReS2 and ReSe2 monolayers, bilayers, and in the bulk limit. Phys. Rev. B 97, 75123 (2018).

  30. 30.

    Arora, A. et al. Highly Anisotropic in-Plane Excitons in Atomically Thin and Bulklike 1 T′-ReSe2. Nano Lett. 17, 3202–3207 (2017).

  31. 31.

    Ovchinnikov, D. et al. Disorder engineering and conductivity dome in ReS2 with electrolyte gating. Nat. Commun. 7, 1–7 (2016).

  32. 32.

    Feng, Y. et al. Raman vibrational spectra of bulk to monolayer ReS2 with lower symmetry. Phys. Rev. B 92, 1–6 (2015).

  33. 33.

    Miura, N. Physics of Semiconductors in High Magnetic Fields (Oxford University Press 2008).

  34. 34.

    Jadczak, J., Kubisa, M., Ryczko, K., Bryja, L. & Potemski, M. High magnetic field spin splitting of excitons in asymmetric GaAs quantum wells. Phys. Rev. B 86, 245401 (2012).

  35. 35.

    Bryja, L. et al. Cyclotron-resonant exciton transfer between the nearly free and strongly localized radiative states of a two-dimensional hole gas in a high magnetic field. Phys. Rev. B 85, 165308 (2012).

  36. 36.

    Jadczak, J., Bryja, L., Wójs, A. & Potemski, M. Optically induced charge conversion of coexistent free and bound excitonic complexes in two-beam magneto-photoluminescence of two-dimensional quantum structures. Phys. Rev. B 85, 195108 (2012).

  37. 37.

    Walck, S. N. & Reinecke, T. L. Exciton diamagnetic shift in semiconductor nanostructures. Phys. Rev. B 57, 9088 (1998).

  38. 38.

    Arora, A. et al. Exciton band structure in layered MoSe2: from a monolayer to the bulk limit. Nanoscale 7, 20769–20775 (2015).

  39. 39.

    Arora, A. et al. Excitonic resonances in thin films of WSe2: from monolayer to bulk material. Nanoscale 7, 10421–10429 (2015).

  40. 40.

    Molina-Sánchez, A. et al. Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS2. Phys. Rev. B 88, 045412 (2013).

Download references

Acknowledgements

This work was supported by the Polish NCN Grant No. 2013/09/B/ST3/ and the Polish-Taiwanese Joint Research OSTMED PL-TWII/5/2015.

Author information

J.J. performed the PL and RC measurements, analyzed and interpreted the data with discussion from L.B. J.J. and T.S. performed magneto-PL and PLE. measurements. J.K-G. prepared and characterized mono- and a few-layers of the ReS2 crystals. J.J. and L.B. wrote the manuscript. J.J. L.B., P.K. supervised the experiments. Y.S.H. synthesized the ReS2 single crystals by the CVT method. All authors discussed the results and commented on the manuscript.

Correspondence to J. Jadczak.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information, Exciton binding energy and hydrogenic Rydberg series in layered ReS2

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.