Ab-initio calculations for electronic and optical properties of Er W defects in tungsten disulfide M. A. Khan 1, a) and Michael N. Leuenberger 2, b) 1) Department of Applied Physics, Federal Urdu University of Arts, Science and Technology, Islamabad, Pakistan 2) NanoScience Technology Center, Department of Physics, and College of Optics and Photonics, University of Central Florida, Orlando, FL 32826, USA (Dated: 4 May 2021) Ab-initio calculations for the electronic and optical properties of single-layer (SL) tungsten disulfide (WS 2 ) in the presence of substitutional Erbium defects (Er W ) are presented, where the W atom is replaced by an Er atom. Defects usually play an important role in tailoring electronic and optical properties of semiconductors. We show that neutral Er defects lead to localized defect states (LDS) in the band structure due to the f- orbital states of Er, which in turn give rise to sharp transitions in in-plane and out-of-plane optical absorption spectra, α ‖ and α ⊥ . We identify the optical transitions at 3 µm, 1.5 µm, 1.2 µm, 920 nm, 780 nm, 660 nm, and 550 nm to originate from Er W defect states. In order to provide a clear description of the optical absorption spectra, we use group theory to derive the optical selection rules between LDS for both α ‖ and α ⊥ . I. INTRODUCTION Single-layer (SL) transition metal dichalcogenides (TMDs) have attracted a lot of attention due to their intriguing electronic and optical properties, with a wide range of promising applications. 1,2 SL TMDs are direct band gap semiconductors, 3,4 which can be used to pro- duce smaller and more energy efficient devices, such as transistors and integrated circuits. Moreover, the band gap lies in the visible region which makes them highly responsive when exposed to visible light, a property with potential applications in optical detection. It is well- known that the exfoliation or growth processes can in- troduce defects and impurities in SL materials which can significantly alter their electronic, optical and magnetic properties. 5–7 Khan et al. 8,9 recently developed theoretical models based on density functional theory (DFT), tight-binding model, and 2D Dirac equation for the description of the electronic and optical properties of vacancy defects in TMDs, which are naturally occurring during different growth processes, such as mechanical exfoliation (ME), chemical vapor deposition (CVD), and physical vapor de- position (PVD). A central result of their papers is that group theory can be used to derive strict selection rules for the optical transitions, which are in excellent agree- ment with the susceptibility calculated by means of the Kubo-Greenwood formula using the Kohn-Sham orbitals. Recently, Bai et al. have developed experimental methods to create Er-doped MoS 2 thin films using CVD growth 10 and wafer-scale layered Yb/Er co-doped WSe 2 using pulsed laser deposition (PLD). 11 One of the main motivations of doping TMDs with rare-earth ions (REIs) is that REIs inside an insulator or semiconductor crys- tal exhibit the unique property of having electrons in the a) Electronic mail: mahtabahmad.khan@fuuast.edu.pk b) Electronic mail: michael.leuenberger@ucf.edu unfilled 4f shell that is strongly isolated from crystal by the surrounding d shell. This property leads generally to high quantum yields, atom-like narrow bandwidths for optical transitions, long lifetimes, long decoherence times, high photostability, and large Stokes shifts. A prime example is Er-doped semiconductors and optical fibers that emit 1.5 µm light with ultra-narrow band- width and are therefore crucial for optoelectronic devices and optical telecommunication. Interestingly, Bai et al. show upconversion from 980 nm to 800 nm and simul- taneous downconversion from 980 nm to 1550 nm using Er:MoS 2 atomic layers. In the case of Yb/Er:WSe 2 they observed downconversion from 980 nm to 1540 nm. Some of the peaks in the theoretically calculated optical spec- trum (see Fig. 6) are in good agreement with the available experimental data, in particular with the optical transi- tion at 1.5 µm. 10–12 Pristine TMDs are invariant with respect to the re- flection σ h about the Mo or W plane of atoms (z =0 plane). Therefore, electron states can be classified into two catagories: even and odd or symmetric and antisym- metric with respect to the z = 0 plane. Khan et al. found that the even and odd bands in TMDs have two different band gaps E g‖ and E g⊥ , respectively. 8,9 E g⊥ has been usually neglected for pristine TMDs because of its substantially larger value and weak optical response as compared with E g‖ . Earlier studies 8,9,13 show that the presence of VDs gives rise to LDS in addition to the normal extended states present in conduction or valence bands in SL MoS 2 . These LDS appear within the band gap region and they can also be present deep inside the valence band depending on the type of VD. Optical tran- sitions between LDS across Fermi level appear as reso- nance peaks, both in α ‖ and α ⊥ , which shows that odd states are necessary for understanding the properties of VDs in SL MoS 2 . 8,9 The same symmetry considerations apply to Er:MX 2 when Er substitutes the M atom. The goal of this paper is to demonstrate the existence of localized Er states inside the bandgap of WS 2 , the arXiv:2105.00498v1 [cond-mat.mes-hall] 2 May 2021