Optical properties of single-layer, double-layer, and bulk MoS2
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1 Optical properties of single-layer, double-layer, and bulk MoS Alejandro Molina-Sánchez, Ludger Wirtz, Davide Sangalli, Andrea Marini, Kerstin Hummer
2 Single-layer semiconductors From graphene to a new family of materials EF Graphene No bandgap ~6 ev Hexagonal boron nitride Molybdenum disulfide ~,9 ev
3 Single-layer semiconductors From graphene to a new family of materials The bandgap and the high mobility makes MoS a suitable alternative to graphene or carbon nanotubes. EF Graphene No bandgap ~6 ev Hexagonal boron nitride Molybdenum disulfide ~,9 ev Appealing for transistors, tunable photo-thermoelectric effect, field-effect transistors Spin-orbit coupling and class of symmetry lead to the spin and valley Hall effects of electrons and holes Broad variety: MoSe, WS, MoSe See review Nature Nanotechnology 7, 699 (0) A. Castellanos, Nano Lett., Phys. Rev. Lett. 08, 9680 (0)
4 Transition metal dichalcogenides Single-layer semiconductors Crystal symmetry determines the electronic structure and optical properties Single-layer (D3h) Double-layer and bulk (D6h) No inversion symmetry Inversion symmetry CB SO inter. splits the valence bands VB A B Interlayer inter. and SO splits the VB
5 Transition metal dichalcogenides Single-layer semiconductors Crystal symmetry determines the electronic structure and optical properties Single-layer (D3h) Double-layer and bulk (D6h) No inversion symmetry Inversion symmetry CB SO inter. splits the valence bands A B Interlayer inter. and SO splits the VB VB Control of the light polarization helicity by tunning the excitation energy (valley physics). VB splitting is exhibited in the PL and absorption by a two peaks structure Phys. Rev. Lett. 05, (00) Nature Nanotechnology 7, 494 (0)
6 Transition metal dichalcogenides Single-layer semiconductors Crystal symmetry determines the electronic structure and optical properties Single-layer (D3h) Double-layer and bulk (D6h) No inversion symmetry Inversion symmetry CB SO inter. splits the valence bands A B Interlayer inter. and SO splits the VB VB Control of the light polarization helicity by tunning the excitation energy (valley physics). We have studied the electronic structure and the optical properties of MoS, and the dependence on the number of layers on the excitonic effects VB splitting is exhibited in the PL and absorption by a two peaks structure Phys. Rev. Lett. 05, (00) Nature Nanotechnology 7, 494 (0)
7 MoS. Band Structure. LDA and GW method GW LDA Correction of LDA bandgap underestimation by means of the GW method (spin-orbit interaction is included). LDA calculations made with ABINIT
8 MoS. Band Structure. LDA and GW method GW LDA Correction of LDA bandgap underestimation by means of the GW method (spin-orbit interaction is included). Electronic correllation is very sensitive to variations in dielectric screening. The addition of more layers changes the dielectric screening, the symmetry and the interlayer interaction. Phys. Rev. B 84, 5543 (0). LDA calculations made with ABINIT
9 MoS. Band Structure. LDA and GW method GW LDA Correction of LDA bandgap underestimation by means of the GW method (spin-orbit interaction is included). Electronic correllation is very sensitive to variations in dielectric screening. The addition of more layers changes the dielectric screening, the symmetry and the interlayer interaction. Phys. Rev. B 84, 5543 (0). The GW correction is mainly a rigid shift of the conduction band. The correction is smaller when the number of layers incresases (screening of the electron correllation). Bandgap extremely sensitive to lattice optimization The addition of more layers pushes up the valence band at Γ, making double-layer and bulk MoS indirect SCs. Excitonic effect on the optical properties... LDA calculations made with ABINIT
10 MoS. Excitonic Effects. Bethe-Salpeter Equation e Coulomb e-h interaction forms the exciton h W XB XA Hexc(n,n ),(n,n ) = (En En )δ(n,n )δ(n,n ) Energy difference 4 Bethe-Salpeter + i(fn fn )Ξ(n,n ),(n,n ) Kernel ΞKK = ivkk + iwkk Unscreended short ranged exchange interaction 3 4 K (c, v, k) Screened coulomb interaction
11 MoS. Excitonic Effects. Bethe-Salpeter Equation e Coulomb e-h interaction forms the exciton h W XB XA Hexc(n,n ),(n,n ) = (En En )δ(n,n )δ(n,n ) Energy difference 4 Bethe-Salpeter + i(fn fn )Ξ(n,n ),(n,n ) Kernel ΞKK = ivkk + iwkk Unscreended short ranged exchange interaction 3 4 K (c, v, k) Screened coulomb interaction Key issue in reliable results: convergence in number of conduction and valence band states and k-points!
12 MoS. Excitonic Effects. Bethe-Salpeter Equation e Coulomb e-h interaction forms the exciton h W XB XA Hexc(n,n ),(n,n ) = (En En )δ(n,n )δ(n,n ) Energy difference 4 Bethe-Salpeter + i(fn fn )Ξ(n,n ),(n,n ) Kernel ΞKK = ivkk + iwkk Unscreended short ranged exchange interaction 3 4 K (c, v, k) Screened coulomb interaction Key issue in reliable results: convergence in number of conduction and valence band states and k-points! Lack of convergence in k-points normally overestimate the exciton binding energy. The k-sampling is directly related to the numbers of unit cells employed to map the exciton wave functions. Low k-sampling gives also artifacts in the optical absorption.
13 MoS. Excitonic Effects. Bethe-Salpeter Equation e XB XA W h The exciton binding energy decreases with the number of layers. Consequence of larger dielectric screening. This compensates partially the GW correction.
14 MoS. Excitonic Effects. Bethe-Salpeter Equation e XB XA W h The exciton binding energy decreases with the number of layers. Consequence of larger dielectric screening. This compensates partially the GW correction. For single-layers (around 3 ev) the absorption gains in efficiency (strongly bound exciton). The theoretical spectra captures nicely the peaks separation for all the cases. XA XB
15 MoS. Excitonic Effects. Bethe-Salpeter Equation The intensity of the optical absorption is related with the localization of the excitons. (c)
16 MoS. Excitonic Effects. Bethe-Salpeter Equation The intensity of the optical absorption is related with the localization of the excitons. (c) For bulk, the exciton is confined in only one layer, due to the large interlayer distance. We can appreciate the shape of the d-orbitals in the excitonic wavefunction
17 Conclusions and ongoing work The bandgap (direct or indirect) depends critically on the number of layers and lattice optimization. Importance of convergence for reliable results. Excitonic effects are stronger in enviroments with small dielectric constant (single-layers). Further studies will deal with strained layers and the influence on the optical response (tunability of the bandgap).
18 Acknowledgements Kerstin Hummer, University of Vienna. Davide Sangalli and Andrea Marini, Istituto di Struttura della Materia (ISM), Consiglio Nazionale delle Ricerche (CNR), Rome Italy.
19 Acknowledgements Kerstin Hummer, University of Vienna. Thank you for your attention! Davide Sangalli and Andrea Marini, Istituto di Struttura della Materia (ISM), Consiglio Nazionale delle Ricerche (CNR), Rome Italy.
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