Valley Zeeman Effect of free and bound excitons in WSe2
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1 Valley Zeeman Effect of free and bound excitons in WSe2 Ajit Srivastava Quantum Photonics Group ETH Zurich, Switzerland
2 TMD Research Motivation Optical control of spins & pseudo-spins 2D optical excitations Strong light-matter interactions Valley Spin Light Layer Valley Optoelectronics Valley physics Optical signatures of Berry curvature Strongly bound Excitons Charged excitons - Trions Enhanced light-matter coupling due to 2D limit Polaritons 2
3 Zeeman effect of valleys Valley degeneracy lifting by B-field TMD Research Highlights Novel contribution to magnetic moment Srivastava et. al., Nature Phys. 11, (2015). Single quantum emitters in WSe2 Sharp, localized emission Single photon sources Valley degree robust Srivastava et. al., Nature Nanotech. 10, (2015). 3
4 TMD team Meinrad Sidler Prof. Atac Imamoglu Dr. Adrien V. Allain Prof. Andras Kis Dominik S. Lembke 4
5 Valleys in Band-Structure Inequivalent points in Brillouin zone Valley Low energy physics 2 valleys Liu et. al., Phys. Rev. B 88, (2013) 5
6 Band Structure at K-points (Valleys) Degenerate Valleys time-reversal Conduction ~ 4-40 mev ~ ev 2 valley flavors Spin-valley locked Spin-orbit ( > 100 mev) Valence 6
7 Valley Polarization Angular momentum conservation - Circularly polarized transition Valleys - polarized Optical addressability of valleys Valley polarization like spin polarization Valley mixing requires spin flip and short-range impurities Mak et. al., Nat. Nanotech. 7, 494 (2012) 7
8 Valley Coherence Linear polarization gives coherent superposition of valleys Valley coherence ~ Spin coherence Valley qubit ~ Spin qubit Coherence time > Lifetime Valley - quantum degree of freedom like spin - pseudospin Jones et. al., Nat. Nanotech. 8, 896 (2013) 8
9 Analogy to Spin Q. How do valleys respond to magnetic field? Can valley degeneracy be lifted by B-field? Zeeman-like effect for pseudo-spin? Key step for valleytronics schemes 9
10 Photoluminescence (PL) Spectra of WSe 2 h e e h e Impurity Band 10
11 B-field dependent PL of Exciton 11
12 B-field dependent (Voigt) laser No observable splitting with in-plane B-field 12
13 Summary of Exciton B-field Data Split peaks are circularly polarized with opposite helicity Helicity Valleys Valleys split Linearly increase in splitting with B Valley magnetic moment opposite in the two valleys (time-reversal) Spin splitting not detected in optics Not spin Zeeman! must be out-of-plane (2D limit) Valley Zeeman Effect 13
14 Magnitude of splitting? Contribution I: Intracellular orbital moment Contribution II: Intercellular orbital moment Berry curvature related Excitonic effect? Srivastava et al. Nature Phys. 11, (2015). 14
15 Similar results by Cornell, U. Washington and Columbia group MacNeill et. al., Phys. Rev. Lett. 114, (2015). Aivazian et. al., Nature Phys. 11, (2015). Yi et. al., Phys. Rev. Lett. 113, (2014). 15
16 Photoluminescence (PL) Spectra of WSe 2 h e e h e Impurity Band 16
17 Quantum Emitters in TMDs 100 times narrower linewidth than free exciton! 17
18 Photon correlations Antibunching Photon source must be quantum emitter 0D or Quantum Dot! Valley Zeeman effect of free and bound excitons in WSe2 18
19 QD B-dependence Faraday vs. Voigt Valley Zeeman effect of free and bound excitons in WSe2 19
20 Splitting vs. B-field Fit function Srivastava et al. Nature Nanotech. 10, 491 (2015) Valley Zeeman effect of free and bound excitons in WSe2 20
21 Similar results by Grenoble, USTC and Rochester group Koperski et. al., Nature Nanotech. 10, , He et. al., Nature Nanotech. 10, (2015). Chakraborty et. al., Nature Nanotech. 10, (2015) Valley Zeeman Effect of Free and Localized Excitons in WSe2 21
22 Berry Curvature & Exciton Fine Spectra 2D Hydrogen atom 2D Exciton (in a solid) 2s 2px 2py 2s 2p+ 2p- Zeeman effect in k-space 1s 1s *F. Wu et. al., Phys. Rev. B. 91, (2015) A. Srivastava & A. Imamoglu, arxiv: v1. 22
23 Conclusions Valley analog of Zeeman effect - Valley degeneracy lifted - Key demonstration for Valleytronics schemes - Novel contribution to orbital magnetic moment Observation of optically active quantum dots in WSe2 - Single photon emitters with long lifetime - Sensor applications - Robust valley degree of freedom - Quantum information schemes Valley Zeeman effect of free and bound excitons in WSe2 23
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