Dirac matter: Magneto-optical studies

Transcription

1 Dirac matter: Magneto-optical studies Marek Potemski Laboratoire National des Champs Magnétiques Intenses Grenoble High Magnetic Field Laboratory CNRS/UGA/UPS/INSA/EMFL MOMB nd International Conference on High Magnetic Fields in Semiconductor Physics, HMF, 4-9 July, 016, Sapporo, Japan

2 Outline: - Graphene; electron-phonon and electron-electron interactions - Atomically-thin TMDs: valley polarization; bright and darkish monolayers - Bi Se 3 : topological insulator with simple (Dirac-like) bulk states - Cd 3 As : 3D Dirac or massless Kane fermions, or both? Acknowledgements + research groups from Grenoble (LPPMC, INEEL) Warsaw Manchester Wurzburg Geneva New York Montpellier Novosibirsk Toshiba

3 Graphene: D massless Dirac electrons E( k) = ± v k E n = ± v e B n E E + n = 3 + n = + n =1 k x, k y n = 0 B n =1 B = 0 B > 0 n = n = 3 But in a crystal : phonons, v = c/300, dielectric screening effects of interactions? electron-phonon and electron electron interactions

4 Probing electronic (inter Landau level) excitations by magneto-raman scattering hν + σ /σ hν ' + σ /σ E Dominant transitions n = B B E exc = hν ' hν 1 weakly allowed 3 n = 1, Experiment: Grenoble, PRL, (011) Theory: O. Kashuba & V.I. Falko PRB, (009); M. Mucha-Kruczynski et al., PRB, (010)

5 Electronic Raman scattering: Inter Landau level transitions Graphene and its Bernal stacks Strasbourg, Grenoble, Nano Lett. (011)

6 Electron-phonon interaction : resonant effects L -3,3 L -3, (-,3) L -, L -,1 (-1,) L -1,1 "D " band E g phonon L 0,1 (-1,0) Grenoble, D Materials, (016)

7 Electron-phonon interaction : resonant effects L -3,3 L -3, (-,3) L -, L -,1 (-1,) L -1,1 ђω Γ family ђω K family L 0,1 (-1,0) E ph = E 1,3 Grenoble, D Materials, (016)

8 Strength of electron-electron interactions E C QED: (v = c) graphene (v = c/300, ε) 1 1 c / E kin = α = << 1 α eff = α 137 ε v ε Electrons in graphene = strongly interacting system E( k) = ± v k ε v = v ( E) v 0 ε αc E ln 4ε W αc ε + = diel diel v 0 J. Gonzalez, F. Guinea, M. Vozmediano, Mod. Phys. Lett. (1993) J. Hofmann, E. Barnes, S Das Sarma, PRL (014) M. Görbig, Rev. Mod. Phys. (011) 3 D. C. Elias, R.V. Gorbachev,, F. Guinea, A.K. Geim Nature Phys. (011) B < v > v 0 + ε diel C E ~ B ε + β n diel 3

9 [Bychkov, Eliashberg, Iordanskii, JETP Lett., 1981] K. Shizuya, PRB, 010 "excitonic effect" v n = v 0 αc ( Σ 4ε ln l l B 0 B ) + αc 4ε diel C n 1/ε diel ε ε diel + 3! 1/ε suspended graphene ε diel = 1 v 0 W = = ( v 0 / l m / s Σ B ) = ev graphene in hbn ε diel = 5 graphene on graphite eff ε diel 10 Grenoble,, PRL, (015)

10 Beyond graphene; other than graphite layered compounds e.g., Transition Metal Dichalcogenides (TMDs) semiconductors properties of atomically thin layers?

11 emiconducting Transition Metal Dichalcogenides: WSe MoSe, MoS, WS, MoTe Mono layers (three X-M-X atomic sheets) H-stacked layers (most stable) a c very first view: graphene with broken sublattice symmetry - gap - valley dependent selection rules for circularly polarized light Optical pumping? Exc (σ + ) I em (σ + ) 1L σ+ σ - I em (σ - ) K + K -

12 Valley polarization by optical pumping: - effective in MoS, WSe, WS e.g., in WSe: E exc =1.953eV T=4K B = 0T Significantly increased by application of small magnetic fields?! E exc =1.953eV T=4K B = 0.1T Warsaw, Grenoble, PRX (016)

13 Valley polarization by optical pumping: - ineffective in MoSe, MoTe??? MoTe monolayer ineffective orientation or fast decay of valley polarization? MoSe monolayer PL (arb. units) E exc = 1.7eV T =10 K exc σ + det σ + det σ Energy (mev) Warsaw, Grenoble, unpublished extremely fast decay of valley polarization [ and extremely fast (radiative?) decay ] Grenoble, arxiv: (016)

14 Beyond gapped graphene: - d-orbitals - spin orbit splitting - strong excitonic effects (., effective intervalley scattering for bright excitons) M.M. Glazov, PRB, (014) Δ so,c d 0 d>1ml ~ 30meV A B σ+ σ - A B Δ so,v d d>1ml ~300meV K + K - Q Г

15 Distinct alignment of spin-orbit subbands in the conduction band Grenoble, Nanoscale (015), G. Wang et al. arxiv (015), Hanan Dery, Yang Song, Phys. Rev. B (015) X-X. Zhang et al, PRL (015) MoSe, (MoTe ) ) WSe, (WS ) Δ so,c ~ 30meV A B σ+ σ - A B A B σ+ σ - A B Δ so,v ~300meV K + K - K + K - optically active, "bright" optically "darkish " fast intervalley scattering slower intervalley scattering

16 Bright MoSe : magneto-photoluminescence 30T σ + σ g A ~ 4. PL intensity (arb. units) 5T 0T 15T 10T 5T Magnetic field (T) g X- ~ 4. 0T Emission energy (mev) X - - X (A) Emission energy (mev) Not much of excitements

17 PL inensity (arb. units) Darkish WSe : magneto-photoluminescence 30T 5T 0T 15T 10T 5T 0T σ + σ A7 A6 A5 A4 A3 A X-A XA Emission energy (mev) Complex spectra, origin of the emission lines? different and often huge g-factors Magnetic field (T) Emission energy (mev) Energy (mev) X A g ~ 4 A A3 A4 g ~ 1 A6 g ~ 6 g ~ 4 (?) A7 σ + σ 0.5(σ + +σ ) g ~ 1 A5 Grenoble, unpublished g ~ Magnetic field (T)

18 Electronic bands in 3D topological insulators (Bi Se 3 family) Topological insulators = narrow gap semiconductors with conducting Dirac-type surface states Bi Se 3, Bi Te 3, Sb Te 3, Bi x Sb 1-x,. Effective Dirac Hamiltonian at the Γ point: H. Zhang et al., Nature Phys. 5, 438 (009) C.-X. Liu et al., Phys. Rev. B 8, 0451 (010) Electronic bands (electron and hole branches):

19 Landau level spectrum: cyclotron energy = spin-splitting Dirac Hamiltonian (4x4): Massive Dirac particles ) ( ) ( ) ( ) ( D D D m p c m pc c m p E + ± + ± = c m pc D << c m D, = = = = E c m E m m m C D g D h e ω

20 Cyclotron resonance: Thin layer of Bi Se 3 : Infrared magneto-transmission Bi Se 3 on InP(B) substrate (Wurzburg) thickness 70 nm, n~ cm- Interband inter-landau level excitations: m e 0.14m 0 Conduction and valence band parabolic Negligible electron hole asymmetry m r 0.07m 0 E n (σ+) = E n (σ-) E g = 00 mev Grenoble, PRL (015)

21 Electronic bands in bulk Bi Se 3 (Γ point) Experiment (magneto-optics): Conduction and valence band parabolic High electron-hole symmetry Conduction band Theory: H. Zhang et al., Nature Phys. 5, 438 (009) C.-X. Liu et al., Phys. Rev. B 8, 0451 (010) Valence band E( k) ± ( m D v D + k 4m D ) m e = m h = m D = 0.14m 0 (exp) E g = m Dv D = 00 mev (exp)

22 Electronic bands in bulk Bi Se 3 ( Γ point ) Electron mass Energy gap, particles masses and g factors in Bi Se 3 determined by only two parameters Landau level spectrum: Hole mass Grenoble,, PRL (015) cyclotron energy = spin-splitting g m m 0 e = gh = = D 5 (7.5 by EPR)

23 Band structure of Bi Se 3 as deduced from ARPES Parabolic conduction band Indirect band gap ( mev) Camelback valence band In conflict with magneto-optics! M. Bianchi et al., Nature Comm. 1, 18 (010) ARPES data for bulk states difficult to interpret?

24 Dirac semimetal Cd 3 As = stable 3D analogue of graphene? ARPES: Z. K. Liu et al., Nature Mater. 13, 677 (014) S. Jeon et al., Nature Mater. 13, 851 (014) S. Borisenko et al., Phys. Rev. Lett. 113, (014) M. Neupane et al., Nature Comm. 5, 3786 (014)

25 Dirac semimetal Cd 3 As = stable 3D analogue of graphene? ARPES: but relevant controversies : I. Rosenman, J. Phys. Chem. Solids 30, 1385 (1969) M. J. Aubin, et al., Phys. Rev. B 3, 360 (1981) H. Schleijpen et al., Int. J. Infrared Milli. 5, 171 (1984) S. Jeon et al., Nature Mater. 13, 851 (014)

26 Cd 3 As : optical response at B = 0 Absorption of light in solids (e.g., Fermi s golden rule): joint density of states σ 1 ( ω) ω For conical bands in 3D: Absorption coefficient linear in photon frequency! e.g., T. Timusk et al., Phys. Rev. B 87, 3511 (013) see also: Grenoble, Nature Phys. (014)

27 Geneva, Grenoble,, ArXiv (016) Cd 3 As : high-field magneto-reflectivity Cyclotron resonance (CR) in the quantum limit Magneto-optical response linear in = typical signature of massless particles

28 Geneva, Grenoble,, ArXiv (016) Cd 3 As : high-field magneto-reflectivity Cyclotron resonance (CR) in the quantum limit Magneto-optical response linear in = typical signature of massless particles.massless yes, but not 3D Dirac

29 Dirac electrons Landau level spectrum

30 Another linear in 3D system: Massless Kane electrons in gapless HgCdTe Magneto-absorbance σ ( ω) ω 1 E n B Grenoble,, Nature Phys. (014)

31 Electronic bands in Cd 3 As Two kind of conical bands in Cd 3 As : Γ point: Two symmetry-protected Dirac cones at the scale of crystal field splitting (δ < 50 mev) A single cone of massless Kane electrons, no symmetry protection (energy scale ~1 ev ) J. Bodnar,, Proc. III Conf. Narrow-Gap Semiconductors, Warsaw, (Elsevier, 1977), p. 311 Geneva, Grenoble,, ArXiv (016)

32 3D massless Dirac and Kane electrons Landau level spectrum

33 Conclusions: magneto-optics maters as a relevant experimental tool to: - uncover the electronic bands of "new" materials - study the effects of interactions MOMB