Magneto-plasmonic effects in epitaxial graphene Alexey Kuzmenko University of Geneva Graphene Nanophotonics Benasque, 4 March 13
Collaborators I. Crassee, N. Ubrig, I. Nedoliuk, J. Levallois, D. van der Marel University of Geneva M. Ostler, F. Fromm, M. Kaiser, Th. Seyller Univ. of Erlangen Univ. Chemnitz J. Chen, F. Huth, R. Hillenbrand CIC nanogune, San Sebastian M. Orlita, M. Potemski CNRS, Grenoble
Different types of epitaxial graphene (EG) Si-face monolayer on buffer layer Highly doped Growth at ~ 15 o C in Ar C-face twisted multilayer undoped K. Emtsev, Nature Materials, 8, 3 (9) Highly doped H Quasi-freestanding monolayer (hydrogenated dangling bonds) C. Riedl et al. PRL 13, 4684 (9) Highly doped C. Berger et al. J. Phys. Chem. B 18, 1991 (4) Defect free-regions of several micron size
Single layer graphene on Si-face of SiC Ultrafast graphene transistors cm Mobility µ 3 V s QHE resistance standard Current gain Terrace steps IBM group: Wu et al. Nano Letters (1) A. Tzalenchuk et al. Nature Nano. (1)
Infrared/THz magneto-optical setup Split-coil SC magnet FTIR spectrometer hω hω from to 1 mev.5 ev B from -7 to +7 T Linear polarization Far-field / large spot Finally we extract: + σ ( ω) = σ ( ω) ± iσ ( ω) ± xx xy Absorption Optical conductivity σ xx (ω) Optical Hall Faraday conductivity rotation ) σ xy (ω
Optical conductivity of one monolayer (theory) Interband hω B = Drude ε F Re σ Re σ σ xx σ xy 4..1..3.4.5-4 - Drude ε F T, n-type Simulation Interband σ = e 4h 4..1..3.4.5 hω (ev) T. Ando JPSJ, 71, 1318 ()
Interband hω Optical conductivity of one monolayer (theory) B = Drude ε F LL transitions E n = ± v B F ehnb CR Re σ Re σ σ xx σ xy 4..1..3.4.5-4 - Drude CR ε F T, n-type 1 T, n-type Simulation Interband LL transitions σ = e 4h 4..1..3.4.5 hω (ev) T. Ando JPSJ, 71, 1318 ()
Interband hω Optical conductivity of one monolayer (theory) B = Drude ε F LL transitions E n = ± v B F ehnb CR Re σ Re σ σ xx σ xy 4..1..3.4.5-4 - Drude CR ε F T, n-type 1 T, n-type 1 T, p-type Simulation Interband LL transitions σ = e 4h LL transitions ε F CR In reality: all layers add to the signal doping changes across layers stacking and grains may invalidate simple theory 4..1..3.4.5 hω (ev) T. Ando JPSJ, 71, 1318 ()
What magneto-optics can tell about graphene? hω SiC B r Thickness / homogeneity Doping level Doping type (p or n) Doping homogeneity Mobility Fermi velocity Cyclotron mass Electron-hole asymmetry Stacking Grains boundaries Sees all layers No contacts/resist No UHV needed Done routinely useful for routine characterization
Extracting physical parameters Quasi-free standing monolayer ε F.35 ev n 8 1 1 cm m CR.55 m e v F µ = 1.5 1 5 cm 6 m/s /(V s) Absorption.3..1. THz 4 6 8 1 1 5 K Drude peak T 1 T T 3 T 4 T 5 T 6 T 7 T 1 3 4 5 Energy [mev] Absorption.3..1. 3 K ε F Interband threshold.4.6.8 1. Energy [ev] E ε F [ev] ARPES p-doped as grown ebv ωc = ε momentum F F I. Crassee et al. Nature Physics 7, 48 (11)
Electrons or holes? Quasi-free standing monolayer Monolayer on buffer layer θ F (rad).8.6.4.. -. -.4 p-doped 1 T 3 T 5 T 7 T θ F (rad).4.. -. -.4 -.6 n-doped 5 K 5 K 1T 3T 5T 7T Faraday rotation is sensitive to the doping type 1 3 4 5 6 Photon Energy [mev] 1 3 4 5 6 Photon Energy [mev] I. Crassee et al. Nature Physics 7, 48 (11) N. Ubrig et al., in preparation
THz 4 6 8 1 1 Drude peak QFS monolayer.3 T Absorption..1. 1 3 4 5 Energy [mev] I. Crassee et al. Nano Lett. 1, 47 (1)
Drude peak is not a Drude peak! THz 4 6 8 1 1 Quasi-freestanding monolayer.3 T Absorption..1. 1 3 4 5 Energy [mev] Plasmon excitation Caused by steps (and wrinkles) Edge resistance should be big I. Crassee et al. Nano Lett. 1, 47 (1)
AFM-near field optical plasmon imaging AFM topography IR laser (1 m) metallic AFM tip.7 nm near-field 5 nm graphene plasmon SiC plasmon λ / Near field signal SiC terraces and graphene wrinkles are strong plasmon scatterrers 5 nm Details: talk of R. Hillenbrand on Tuesday See also: J. Chen et al, Nature 487, 77 (1); Fei et al, ibid, p. 8.
Absorption.3..1 THz 4 6 8 1 1 ω Magnetoplasmons in graphene ω + T 1 T T 3 T 4 T 5 T 6 T 7 T. 1 3 4 5 Energy [mev] Energy [mev] 15 1 QFS monolayer 5 1 ω 4 6 8 B [T] 4 µm ω + GaAs 4 3 THz active in active in Plasmon splits in two magnetoplasmons Bulk and edge modes similar to classical works on DEGs Allen, Stormer and Hwang, Phys. Rev. B 8, 4875 (1983) I. Crassee et al. Nano Lett. 1, 47 (1)
σ Effective medium approximation ne i ω ± ω + iγ ω / ω ± ( ω) = m ω ± = ω + ± c 4 S. Mikhailov, PRB 54, 1335 (1996) ω c ω c 6 7 T 4 Re σ xx /σ 4 5 T 3 T 1 T Re σ xy /σ T 1 3 4 5 Energy (mev) 1 3 4 5 Energy (mev) EMA works surprisingly well! I. Crassee et al. Nano Lett. 1, 47 (1)
Magnetoplasmons in graphene epitaxial graphene 1 m I. Crassee et al. Nano Lett. 1, 47 (1) CVD graphene disks Also magnetoplasmons observed in the QHE regime I. Petkovic et al. PRL 11, 1681 (13) H. Yan et al. Nano Lett. 1, 3766 (1)
Multilayer epitaxial graphene on C-side of SiC twisted multilayer (1-15 layers) 3 Drude electrons Drude holes 3 low doping high doping 4.T 3.5T 3.T Re σ + /σ.5t.t Re σ - /σ 3 1-1 - -3 1 approximately charge-neutral B electron-hole asymmetry stacking effects hω c 1.5T 1.T.75T.5T 1-1.5T -1-1 4 6 8 4 6 8 (mev) (mev) ε 1 = v F ehb hω c 1 I. Crassee et al. Phys. Rev. B 84, 3513 (11)
Optical LL transition intensities σ/σ twisted multilayer (15- layers) 4 3 1 1-1 3.5T D 1 (mev) 3 1 1-1 D σ ( ω) = d( h ) σ 1 ω 6 7 8 hω [mev] 1 3 4 B (T) I. Crassee et al. Phys. Rev. B 84, 3513 (11)
Optical LL transition intensities σ/σ twisted multilayer (15- layers) 4 3 1 1-1 3.5T D 1 (mev) 3 1 1-1 theory (1 layer) D σ ( ω) = d( h ) σ 1 ω 6 7 8 hω [mev] 1 3 4 B (T) theory for Dirac fermions NO B 1/ dependence 1 layer: D1 = ε 1 N layers: D N 1 = ε1 Intensity catastrophically lower than expected!!! I. Crassee et al. Phys. Rev. B 84, 3513 (11)
Re σ σ xy 6 4 Optical LL transition intensities T T -1 1 Peak too small! 1-1 - twisted multilayer (15- layers) 4 6 hω [mev] only 1- layers (out of 15-) contribute to Landau peaks A stacking effect? Most layers overdamped? I. Crassee et al. Phys. Rev. B 84, 3513 (11)
Re σ σ xy 6 4 Optical LL transition intensities T T -1 1 Peak too small! twisted multilayer (15- layers) 4 6 hω [mev] Too little Landau peaks only 1- layers (out of 15-) contribute to Landau peaks A stacking effect? Most layers overdamped? I. Crassee et al. Phys. Rev. B 84, 3513 (11)
Graphene for magneto-optical applications Absorption.3..1 THz 4 6 8 1 1 T 1 T T 3 T 4 T 5 T 6 T 7 T Faraday rotation (rad).1.5. THz 4 6 8 1 1. 1 3 4 5 Energy (mev) -.5 1 3 4 5 Energy (mev) Absorption coefficient* 7 % nm Verdet constant* degrees 15 T nm *provided that layers can be stacked without affecting their properties QFS monolayer Potentially tunable by gate! Ultrafast control! I. Crassee et al. Nature Physics 7, 48 (11); Nano Lett. 1, 47 (1)
Faraday rotation affected by magneto-plasmons.4 THz 5 1 15 B = 1 T simulation.15 simulation θ (rad).. plasmon frequency: mev 6.5 mev mev 4 mev θ (rad).1.5. scattering: 11 mev 5.5 mev 4 6 8 Energy (mev) 4 6 Energy (mev) rotation can be controlled by the plasmon frequency higher-mobility samples produce larger rotation defects are useful! I. Crassee et al. Nano Lett. 1, 47 (1)
Graphene-based magneto-optical applications Types of devices Absorption modulators Polarization modulators Faraday isolators (valves) Spheres of application Telecommunications Biosensing Security Astronomy Advantages of epitaxial graphene Samples very large Chemical potential homogeneous SiC is transparent Disadvantages of epitaxial graphene Gating is relatively difficult Controlled multilayer growth is tricky H. Da & C.W.Qiu, APL 1, 4116 (1) A. Fallahi & Perruisseau-Carrier, APL 11, 3165 (1) D. L. Sounas & C. Caloz, IEEE Trans. Microw. Theory Tech. 6, 91 (1) Y. Zhou et al, Phys.Chem. Chem. Phys. (13)
Fabry-Perot enhanced Faraday rotation in graphene interference in the substrate Rotation up to 9 o Rotation and transmission increase simultaneously Theory of FR in graphene in a cavity: A. Ferreira et al, PRB 84, 3541 (11) For details: Nicolas Ubrig, poster on Wednesday
Summary and outlook Magneto-optics (MO) is useful for routine characterization Giant THz Faraday rotation (present record is 9 o ) Robust (magneto-)plasmons due to nanoscale defects (i.e. steps and wrinkles) Strong interplay between MO and plasmonic effects (cyclotron mass about 1 smaller than in noble metals) Graphene is promising for MO applications