Electronic and optical properties of phosphorene quantum dots under electric and magnetic fields Longlong Li Department of Physics (CMT Group), University of Antwerp, Belgium Institute of Solid State Physics, Chinese Academy of Sciences, China Hefei 2 3 4 Contents Introduction Model and Theory Main Results Conclusions 5 Overview of Family of 2D Materials Up to now, more than 140 2D materials are explored. P. Miro, M. Audiffred and T. Heine, Chem. Soc. Rev. 43, 6537 (2014) The number is still growing and new 2D materials are expected to arise. The most known are graphene, h-BN, TMD, silicene, germanene, etc. These 2D materials have their own unique properties and hold prospects for practical applications. Recently, a new 2D material, named phosphorene, has drawn a lot of attention. 6 ABC of Phosphorene: Bulk and Nano 7 Allotropes of Phosphorus 8 From Black Phosphorus to Phosphorene Research on BP dates back to 1914: P. M. Bridgman, JACS 36, 1344 (1914) 100 years Phosphorene research starts in 2014: Liu et al., ACS Nano 8, 4033 (2014) 2D Materials Family Superstars Graphene: 2004 Phosphorene: 2014 9 Lattice Structure of Phosphorene a single layer of BP puckered honeycomb lattice covalent bonds of P atoms 3 four atoms in a unit cell (a) 3D view (b) Top view (c) Side view Red: P atoms in lower layer Blue: P atoms in upper layer , : unit cell lengths 10 Band Structure (From DFT Calculations) Direct band gap of 2 eV at point Band anisotropy along∼ andΓ axes Anisotropic effective masses:ΓX ΓY = 0.17 ; = 1.12 ΓX ΓY = 0.15 0 ; = 6.35 0 ΓX ΓY ℎ 0 ℎ 0 2D Mater. 1, 025001 (2014) Nat. Commun. 5, 4475 (2014) 11 Comparison with other 2D Materials (Selected) Material Structure Bandgap Mobility Graphene Flat 0 > 10 cm2/V/s [1] Mono TMD Trilayer 1.3 1.9 eV [2] 2005 cm2/V/s [2] 1.5 10 2 Phosphorene Puckered ∼ eV [3] ∼ cm /V/s [4] 3 ∼ ∼ In addition, phosphorene is an anisotropic 2D material, showing optical and transport anisotropy [3], which is not typical for most 2D materials. [1] A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007) [2] Q. H. Wang et al., Nat. Nanotech. 7, 699 (2012) [3] J. Qiao et al., Nat. Commun. 5, 4475 (2014) [4] L. Li et al., Nat. Nanotech. 9, 372 (2014) 12 Investigation of Phosphorene: Current Status For Bulk Strain-engineered band structure: PRL 112, 176801 (2014) Superior mechanical flexibility: APL 104, 251915 (2014) Strong excitonic effect: Nat.Nano 10, 517 (2015) Nonlinear optical response: Opt. Express 23, 11183 (2015) Magneto-optical transport: PRB 92, 045420 (2015) Integer quantum Hall effect: Nat. Nano 11, 593 (2016) Anisotropic spin-orbit coupling: PRB 94, 155423 (2016) For Nanoribbons Effects of edge, size, strain, and external fields: . EPL 108, 47005 (2014); JAP 116, 144301 (2014) . PRB 89, 245407 (2014); NJP 16, 115004 (2014) . PRB 92, 035436 (2015); PRB 91, 085409 (2015) 13 Quantum Dots in 2D BP: Experimental Fabrication D: Lateral size H: Thickness D 4.9 ± 1.6 nm H 4 ± 2 layers ∼ ∼ X. Zhang et al., Angew. Chem. Int. Ed. 54, 3653 (2015). Z. Sun et al., Angew. Chem. 127, 11688 (2015). 14 Theoretical Aspects on 2D BP Quantum Dots Mid-gap edge states (TB) Anomalous size dependence of optical emission gap (DFT) 2D Mater. 2, 045012 (2015). J. Phys. Chem. Lett. 7, 370 (2016). 15 Our Research Subject & Motivation Research Subject: Investigating electronic and optical properties of phosphorene quantum dots in the presence of electric and magnetic fields. Research Motivation: Why phosphorene: Finite direct band gap Anisotropic material Why quantum dots: Strong quantum confinement Significant edge effects Why electric and magnetic fields: Efficient tuning of the properties 16 Model System & Theoretical Approch 17 Model System Rectangular phosphorene quantum dot Armchair ( -direction) and zigzag ( -direction) edges In-plane electric field and perpendicular magnetic field : Side length along armchair direction Why rectangular shape: : Side length along zigzag direction Easy to realize by experiment : Perpendicular magnetic field Why AC and ZZ edges: : Electric field along armchair direction Proven to be chemically stable : Electric field along zigzag direction 18 Tight-binding Hamiltonian (1) Without electric and magnetic fields: = + TB GW + , + � � , : creation and destruction operators +: on-site energy at site : hopping energy between sites and (2) In the presence of electric and magnetic fields: PRB 89, 201408: , = , , = ( , ) = 1.220 eV = 3.665 eV 1 − → −exp ⋅i 2 = 0.205 eV 2 3 = 0.105 eV : magnetic→ vector potential� ⋅ − ℎ 4 = 0.055 eV In the Landau gauge, = (0, , 0) − 5 − 19 Electronic States, DOS and Optical Absorption Electronic States: = Pybinding package* Density퐻 of퐻 States:⟹ = ( ) Pybinding package* Optical Absorption:∑ − ⟹ = Your own codes ℏ =∑ ℏ ⟹ ( + ) 2 ℏ= − ⋅ − ℏ * D. Moldovan and F. M. Peeters, Pybinding v0.8.x: a python package ⟨ ⟩ for tight-binding calculations (doi: 10.5281/zenodo.56818). 20 Main Results: Electronic and Optical Spectra 21 Well-defined Edge States = 5.3 nm = 4.1 nm = = 0 (a) Energy levels (b) DOS (c) Wave functions 22 Energy Spectrum: Electric- and Magnetic-field Dependence = : flux : armchair dir Φ 23 Optical Absorption: Electric- and Magnetic-field Effects bb: bulk-to-bulk ee: edge-to-edge eb: edge-to-bulk 24 Robust Edge Absorption with Magnetic Field Edge-to-edge Absorption 25 Polarization Sensitive Absorption = 0 = 0.03 V/nm 26 Conclusions The edge states are found within the bulk band gap of phosphorene quantum dot The electric and magnetic fields have very different influences on the bulk and edge states There are two (three) types of optical transitions observed in the presence of a magnetic (an electric) field. The edge-to-edge absorption is robust with magnetic field The bulk-to-bulk, edge-to-bulk, and edge-to-edge absorptions are all polarization sensitive. 27 Publications @ CMT Group, UA [1] L. L. Li, D. Moldovan, W. Xu, and F. M. Peeters, Electronic and optical properties of phosphorene quantum dots, Nanotechnology 28, 085702 (2016). [2] L. L. Li, M. Zarenia, W. Xu, H. M. Dong, and F. M. Peeters, Exciton states in a circular graphene quantum dot, Phys. Rev. B 95, 045409 (2017). [3] L. L. Li, D. Moldovan, P. Vasilopoulos, and F. M. Peeters, Aharonov-Bohm oscillations in phosphorene quantum rings, Accepted by Phys. Rev. B. Future Plans and Considerations: Materials Systems: Phosphorene, Graphene or Other 2D Materials Physical Properties: Electronic, Optical and Transport Properties 28 Thank you for your attention Thank you for your attention .