Single-Layer Tl 2 O: A Metal-Shrouded 2D Semiconductor with High Electronic Mobility
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1 Supporting information for Single-Layer Tl 2 O: A Metal-Shrouded 2D Semiconductor with High Electronic Mobility Yandong Ma, Agnieszka Kuc, and Thomas Heine*, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig, Germany *Corresponding author: thomas.heine@uni-leipzig.de Computational methods Canonical ensemble with Nosé thermostat and a 3 3 supercell are chosen for ab initio molecular dynamics (MD) simulations. Snapshots at 5 ps for each elevated temperatures (300 K and 500 K) are plotted in Figures S2 and S3 in SI. Neither structure disruption nor structure reconstruction was found to occur in SL Tl2O. Geometry optimizations of molecular dynamics snapshots for SL Tl2O result in its corresponding original structure. We therefore conclude that SL Tl2O is thermally stable. Phonon spectra are calculated using the density functional perturbation theory as implemented in Quantum Espresso code. 1 Carrier mobility of SL Tl2O is calculated by: eħ 3 C μ = k B Tm m d (E i l ) 2 where C is the elastic modulus of the longitudinal strain, El is the deformation functional constant of the VBM (CBM) for hole (electron), and m * is the carrier effective mass in the transport direction. C is obtained from (E E 0 ) S 0 = 1 C (Δl) 2. Here E, E0, S0, l0 and l is, respectively, the total energy for the 2 l 0 compressed or dilated SL Tl2O, the total energy at equilibrium, the equilibrium lattice area, the equilibrium lattice constant in the transport direction, and the deformation of l0. Average effective mass md is calculated by m d = m x m y, and x and y directions are indicated in Figure 1b in the main text. El is given by E i l = ΔV il 0. Here Vi is the energy change of i th band under compression Δl or dilatation. Temperature T = 300 K is used here. S1
2 Figure S1. Crystal structure of few-layer Tl2O. Black O, orange Tl. Figure S2. Changes of the total energy (a) and temperature (b) with the trajectory time, obtained from MD simulations of SL Tl2O at 300 K. (c) Snapshot of SL Tl2O at the end of MD simulation at 300 K, with the dashed line marking the supercell used in the simulation. Black O, orange Tl. Figure S3. Changes of the total energy (a) and temperature (b) with the trajectory time, obtained from MD simulation of SL Tl2O at 500 K. (c) Snapshot of SL Tl2O at the end of MD simulation at 500 K, with the dashed line marking the supercell used in the simulation. Black O, orange Tl. S2
3 Figure S4. (a) Atom and orbital projected density of states of SL Tl2O shown together with the (b) highest occupied and lowers unoccupied crystal orbitals. The HOCO is dominated by O p orbitals, while LUCO is composed almost entirely by Tl p orbitals, supporting ionic character of the bonds. Figure S5. Partial charge density indicated in yellow for (a) conduction band minimum and (b) valence band maximum. Figure S6. Band structure of SL Ga2O (a) and In2O (b) with SOC calculated using HSE06 functional. S3
4 Figure S7. Phonon spectra of SL Ga2O (a) and In2O (b). Figure S8. Crystal orbital Hamilton population (COHP) analysis for SL Tl2O with the orbital projections on the Tl O bonds. LCOHP stand for the total -COHP at the respective atom projections. S4
5 Figure S9. (a) Crystal structure of the interface between SL Tl2O and Tl metal. Black O, orange Tl. (b) Projected density of states of Tl p orbital (atom marked as a black circle) from the interface (black lines) and an isolated SL Tl2O (red lines). Here, the isolated SL Tl2O is taken from the interface without any further optimization. The vertical dashed lines represent the Fermi levels for both systems. The isolated SL Tl2O is a semiconductor. After forming the interface with Tl metal, the Fermi level is shifted up (black lines), indicating that the electrons are injected into the SL Tl2O from the Tl metal. The system becomes metallic. Table S1. Carrier effective masses and mobilities, as well as, related terms along x and y transport directions in SL Tl2O. m x* /m 0 m y* /m 0 C x (Jm -2 ) C y (Jm -2 ) E lx (ev) E ly (ev) µ x (cm 2 V -1 s -1 ) µ y (cm 2 V -1 s -1 ) electron hole S5
6 Figure 10. Band structures of (a) SL, (b) bilayer (2L), (c) trilayer (3L), (d) four-layer (4L), (e) five-layer (5L) and (f) bulk Tl2O. Fermi level is shifted to VBM. S6
7 Figure S11. Band dispersions of the band edges near the M point of (a) monolayer, (b) bilayer, (c) trilayer, (d) four-layer, (e) five-layer, and (f) bulk Tl2O with SOC calculated using HSE06. S7
8 Figure S12. Band structures of SL Tl2O under strain of (a) -3%, (b) -2%, (c) -1%, (d) 1%, (e) 2% and (f) 3% with SOC calculated using HSE06. PBE results: Table S2. Effective messes and carrier mobilities as well as the related terms along the x and y transport directions (cf. Figure 1b in the main text) in SL Tl2O with SOC calculated by using PBE. m x* /m 0 m y* /m 0 C x (J m -2 ) C y (J m -2 ) E lx (ev) E ly (ev) µ x (cm 2 V -1 s -1 ) µ y (cm 2 V -1 s -1 ) electron hole Figure S13. Band structures of SL Tl2O with SOC calculated using PBE. S8
9 Figure S14. Band structures of (a) bilayer, (b) trilayer, (c) four-layer, (d) five-layer and (e) bulk Tl2O with SOC calculated using PBE. S9
10 Figure S15. Band structures of SL Tl2O under strain of (a) -3%, (b) -2%, (c) -1%, (d) 1%, (e) 2% and (f) 3% with SOC calculated using PBE. References 1. Giannozzi, P. ; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; Dal Corso, A.; Fabris, S.; Fratesi, G.; de Gironcoli, S.; Gebauer, R.; Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos, L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.; Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.; Smogunov, A.; Umari, P.; Wentzcovitch, R. M. J. Phys.: Condens. Matter. 2009, 21, S10
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