Orbital-hybridization-created optical excitations in Li 8 Ge 4 O 12 Vo Khuong Dien, 1 Hai Duong Pham, 1 Ngoc Thanh Thuy Tran, 2 Nguyen Thi Han, 1 Thi My Duyen Huynh, 1 Thi Dieu Hien Nguyen, 1, * and Ming Fa-Lin 1, 2, † 1 Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan 2 Hierarchical Green Energy Materials, Hi-research Center, National Cheng Kung University, Tainan, 70101, Taiwan Li8Ge4O12, a ternary electrolyte compound of Li + -based battery, presents the unusual essential properties. The main features are thoroughly explored from the first-principles calculations. The concise pictures, the critical orbital hybridizations in Li-O and Ge-O bonds, are clearly examined through the optimal M oir ´ e superlattice, the atom-dominated electronic energy spectrum, the spatial charge densities, the atom- and orbital-decomposed van Hove singularities, and the strong optical responses. The unusual optical transitions cover the red-shift optical gap, 14 frequency-dependent absorption structures and the most prominent plasmon mode in terms of the dielectric functions, energy loss functions, reflectance spectra, and absorption coefficients. Optical excitations, depending on the directions of electric polarization, are strongly affected by the excitonic effects. The close combinations of electronic and optical properties can identify a significant orbital hybridization for each available excitation channel. The developed theoretical framework will be very useful in fully understanding the diverse phenomena of cathode/electrolyte/anode materials in ion-based batteries. I. INTRODUCTION Lithium-ion batteries (LIBs) dominate in commercial purposes due to their high-performance energy resources, e.g. high power, energy densities, and high reliability, as well as other certain fundamental merits including af- fordable price, long cycle life, and friendly environment [1–3]. The recent experimental progress shows many applications of LIBs such as electric vehicles (EV) and hybrid EV and mobile devices, which require the op- timum in producing efficient energy. A Li-ion battery principally consists of a cathode (positive electrode), an anode (negative electrode), and an ionically conductive Li + -containing electrolyte, in which the third component is closely related to the unusual transport of the posi- tive lithium ions (Li + ) between two electrodes[1–3]. De- pending on the combined alternative materials of three components, Li-ion batteries could provide various per- formance, e.g, the specific energy density in the values of 100 to 250 W.h/Kg [4, 5], the volumetric energy den- sity from 250 to 680 Wh/L [6], the specific power density in the range of 300 to 1500 W/kg [7, 8], and the faster charging time (80 % of charge of states in 15 mins) [9]. The critical mechanisms of LIBs are characterized by the specific charging and discharging process which is based on the exchange of Li + -ions. During the charging pro- cess, Li + -ions commonly move from the cathode material and transport externally to intercalate into the anode through the electrolyte. When discharging, the electrons flow from the anode to the cathode through an outer cir- cuit creating an electric current, mainly converted chem- ical energy into electrical energy. Most importantly, the electrolyte plays an important role during the charging- discharging process, however, recently electrolyte used * Corresponding author: nguyenhien1901@gmail.com † Corresponding author: mflin@mail.ncku.edu.tw in Li-ion batteries is not compatible with latterly devel- oped high-voltage positive electrodes, which are one of the most effective ways of increasing the energy density. Nowadays, solid electrolytes are now rapidly emerging as promising alternatives given their wider electrochemical window of stability [10]. As potential electrolyte candi- dates, Li-Ge-O compounds exhibit the large ionic con- ductivity (1.5×10 -5 Ω.cm -1 for Li 2 GeO 3 ), in which elec- tronic conductivity is negligible with a high ionic trans- ference number [10]. Furthermore, Li 2 GeO 3 shows wide cycling stability with a reserved charge capacity of 725 mAhg -1 after 300 cycles at 50 mAg -1 [11]. As for the battery safety, Li 2 GeO 3 is suitable for the selection of solid electrolytes according to the reasonable decreasing in interface resistance. Recently, a lot of high-resolution experimental mea- surements on essential physical properties of an- odes/cathodes/electrolytes in the Li + -based batteries, e.g, optimized geometry structures, band structures, op- tical properties and transport. The X-Ray diffraction and the low-energy electron diffraction (LEED; [12]) are available in investigating the 3D lattice symmetries, es- pecially Li-X-O related systems. The angle-resolved pho- toemission spectroscopy (ARPES;[13]) is a powerful ex- perimental technique directly measuring the single parti- cle spectral function, depending on wave vectors and fre- quency. For example, ARPES could measure the Dirac cone structure of AA/AB bilayer graphene, the band en- ergy dispersion along the synthetic dimension, band gap, and so on. There are many methods developed for mea- suring optical properties, for example, the complex per- mittivity, which is based on the constraints in specific frequencies, materials, applications could be measured by transmission/reflection line method [14], open-ended coaxial probe method [14], free space method [14], reso- nant method [14]. Other optical properties, such as en- ergy loss functions, reflectance, absorptance, refractivity, excitation could be found through spectroscopy measure- arXiv:2009.02160v1 [physics.app-ph] 4 Sep 2020