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Direct observation of the band gap transition in atomically thin ReS

Mathias Gehlmann, Irene Aguilera, Gustav Bihlmayer, Slavomir Nemsak, Philipp Nagler, Pika Gospodaric, Giovanni Zamborlini, Markus Eschbach, Vitaliy Feyer, Florian Kronast, Ewa Mlynczak, Tobias Korn, Lukasz Plucinski, Christian Schüller, Stefan Bluegel, and Claus M. Schneider Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b00627 • Publication Date (Web): 31 Jul 2017 Downloaded from http://pubs.acs.org on August 2, 2017

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Direct observation of the band gap transition in atomically thin ReS2 Mathias Gehlmann,† Irene Aguilera,‡ Gustav Bihlmayer,‡ Slavomír Nemšák,† Philipp Nagler,¶ Pika Gospodarič,† Giovanni Zamborlini,† Markus Eschbach,† Vitaliy Feyer,† Florian Kronast,§ Ewa Młyńczak,†,k Tobias Korn,¶ Lukasz Plucinski,∗,† Christian Schüller,¶ Stefan Blügel,‡ and Claus M. Schneider† †PGI-6, Forschungszentrum Jülich GmbH, Germany ‡PGI-1/IAS-1, Forschungszentrum Jülich GmbH and JARA, Germany ¶Institut für Experimentelle und Angewandte Physik, Universität Regensburg, Germany §Abteilung Materialien für grüne Spintronik, Helmholtz-Zentrum Berlin, Germany kFaculty of Physics and Applied Computer Science, AGH University of Science and Technology, Poland E-mail: [email protected]

Abstract

vices and van der Waals heterostructures.

ReS2 is considered as a promising candidate for novel electronic and sensor applications. The low crystal symmetry of this van der Waals compound leads to a highly anisotropic optical, vibrational, and transport behavior. However, the details of the electronic band structure of this fascinating material are still largely unexplored. We present a momentum-resolved study of the electronic structure of monolayer, bilayer, and bulk ReS2 using k-space photoemission microscopy in combination with firstprinciples calculations. We demonstrate that the valence electrons in bulk ReS2 are – contrary to assumptions in recent literature – significantly delocalized across the van der Waals gap. Furthermore, we directly observe the evolution of the valence band dispersion as a function of the number of layers, revealing the transition from an indirect band gap in bulk ReS2 to a direct gap in the bilayer and the monolayer. We also find a significantly increased effective hole mass in single-layer crystals. Our results establish bilayer ReS2 as an advantageous building block for two-dimensional de-

Keywords ReS2 , band gap transition, photoemission spectroscopy, GW structure calculations, van der Waals materials. Introduction. Transition metal dichalcogenides (TMDs) hold a tremendous potential for novel electronic and sensoric applications. 1–3 Being van der Waals (vdW) compounds they can be thinned down to atomically thin sheets in the same fashion as graphene, but since they include several semiconducting materials with band gaps within the optical range 4,5 they pose a crucial addition to the available “atomic Legos” 6 as building blocks for two-dimensional devices and vdW heterostructures. 3,7–14 For several years the majority of research in this field focused on the classical TMDs: MoS2 , MoSe2 , WS2 , and WSe2 . The bulk crystals of these materials are indirect band gap semiconductors, but undergo a transition into a direct band gap when they are thinned down to the monolayer limit. 5,15–19 The direct band gap leads to a drastically increased performance of the mono-

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cause the quantum confinement shifts the bulk VBM at the Γ point below the distinct valleys at the BZ edges, which do not exist in ReS2 in this form. The indirect character of the gap is by far less pronounced in ReS2 , which is a likely explanation why recent studies found indications for both an indirect and a direct gap. The fundamental band gaps predicted by the GW approximation are 1.85, 1.70, and 1.57 eV for the monolayer, bilayer, and bulk, respectively. In terms of the valence band structure our GW calculations are equivalent to our results from DFT. It is worth mentioning that the indirect character of the bulk band structure found in the GW calculations is a result of the many-body effects that are not incorporated in the GGA calculations. The conduction band structure in the GGA calculations is slightly different from GW and shows a direct band gap at the A-point of the bulk crystal (see supporting information for comparison). Another interesting aspect that is revealed by our results is that the thinning step from bilayer to monolayer, which enforces the complete confinement of the valence electrons within two dimensions, is accompanied by a significant decrease of the valence band dispersion in the xy-directions as well. This observation can be interpreted as an increased effective mass of the electrons close to the VBM. Recently, it was found in layer-dependent transport measurements that monolayers of ReS2 have a drastically reduced conductivity compared to bilayers or thicker crystals. 30 Apart from the larger band gap, this behavior was attributed to a significantly stronger influence of impurities and the interface. Our results rather suggest an intrinsic mechanism that suppresses the delocalization of VBM electrons within the x-y-plane. This behavior could significantly impact the electron mobility for single monolayer crystals. Recent studies using Raman spectroscopy have found indications for the existence of different polytypes in exfoliated ReS2 crystals. 22–25 Although the commercially available single crystals used in this study are grown in the distorted T1 phase 39 (see fig. 1), there is a chance that the stacking order of the bilayer sample was disturbed, e.g. by mechanical force

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during the exfoliation process. Therefore, we studied the influence of different stacking orders and structural relaxation on the band structure via DFT. The additional band structure calculations are included in the supporting information, and show that the band structure of bilayer ReS2 is not significantly altered by such effects. In particular, the direct band gap and the strong dispersion of the valence band close to the Γ point appear to be very robust properties. Conclusions. Using a combination of kspace photoemission microscopy and band structure calculations we have presented a thorough, momentum-resolved study of the electronic band structure of monolayer, bilayer, and bulk ReS2 . By showing a significant outof-plane delocalization of the valence electrons we have demonstrated that – contrary to assumptions in the recent literature – the layers of bulk ReS2 are not electronically decoupled. We identified the layer-dependent position of the VBM in our photoemission data, and in combination with our band structure calculations we concluded that only bilayer ReS2 has a direct band gap with well-dispersing band edges, although the indirect character of the gap for other crystal thicknesses is far less pronounced than in classical TMDs. Our results have shown that in monolayer ReS2 the valence electrons at the VBM suffer from a drastic increase of their effective mass, suggesting an intrinsic mechanism that could reduce the hole mobility in the in-plane directions compared to bilayers or thicker crystals. For many applications this feature in combination with the direct band gap would make ReS2 bilayers a preferred choice in comparison to monolayers or thicker crystals. Sample Preparation. The ReS2 single crystal was purchased from HQGraphene and cleaved in air with adhesive tape immediately before it was introduced into ultra-high vacuum and degassed at 250◦ C. Atomically thin ReS2 samples were produced ex situ by mechanical exfoliation from a bulk crystal. Using an all dry viscoelastic stamp method, which is described in Ref. (40), a ReS2 sample that simultaneously contained monolayer as well as bilayer areas


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was transfered onto HOPG. The thicknesses of the ultra-thin sample areas can be identified by the optical contrast in the transmission mode of an optical microscope, and were confirmed via atomic force microscopy (AFM) (see supporting information). The atomically thin samples were degassed in situ for one hour at 150◦ C. PEEM images of the samples and optical microscope images taken before and after the transfer process are shown in the supporting information. Photoemission Experiments. The photoemission experiments on the ReS2 bulk crystal were performed at the NanoESCA beamline of Elettra, Trieste, using a modified FOCUS NanoESCA. Homogeneous areas on the cleaved surface were identified using PEEM in real space mode and Hg lamp as excitation source. The lateral resolution of the k-resolved photoemission maps was limited by the beam size (10 µm × 10 µm) ruling out the influence of step edges and grain boundaries. The total energy resolution was better than 100 meV. Due to the highly focused synchrotron beam on the sample, the spectra suffered from charging effects, which were corrected in the data by an energy offset of 100 − 150 meV. The photoemission experiments on the atomically thin ReS2 samples were performed at the UE49 SPEEM endstation of BESSY II, Berlin. Using the field aperture of the PEEM the field of view in real space was limited to ≈ 5 µm. This way the monolayer and bilayer parts of the sample could be selectively measured in momentum mode. The total energy resolution was 300 meV. The orientation of the BZ was aligned by identifying the series of flat bands perpendicular to the baxis as they are visible in fig. 2 (a) and fig. 3 (d), as well as in our band structure calculations. Band structure calculations. Calculations were carried out with the DFT code Fleur 41 and the GW code spex, 42 which use the all-electron full-potential linearized augmented-plane-wave (FLAPW) formalism. The electron density was obtained with the Perdew-Burke-Ernzerhof (PBE) functional. We used the experimental lattice structure of Ref. (20). The calculations of the monolayer, bilayer, and 3-layer slab were performed with a tight-binding Hamiltonian with ab-initio

parameters obtained from the bulk GW calculation. Maximally localized Wannier functions, generated by the wannier90 library, 43 were used as a basis. Acknowledgement The authors thank the Helmholtz-Zentrum Berlin and Elettra Sincrotrone Trieste for providing synchrotron radiation. The financial support by the Helmholtz Association via the Initiative and Networking Fund and via the Virtual Institute for Topological Insulators, and by the DFG via GRK1570 is gratefully acknowledged. Supporting Information Available: Computational details of the band structure calculations. Comparison of the DFT and GW band structure calculations for bulk ReS2 . Optical microscope images of the exfoliated sample. AFM measurements of the exfoliated sample. Additional band structure calculations including structural relaxation and different stacking orders of bilayer crystals. This material is available free of charge via the Internet at http://pubs.acs.org/.

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