Ultra-fast response of nano-carbons under dynamical strong electric field
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1 Ultra-fast response of nano-carbons under dynamical strong electric field Yoshiyuki Miyamoto NEC Nano Electronics Res. Labs. Acknowledgements Dr. Nakamura (RIST, Tokyo) Prof. Tománek (Michigan Univ.) Prof. Zhang (Sichuan Univ.) All calculations were done by the Earth Simulator
2 1. Motivation 2.Simulation of pulse laser shot 3.Energy conservation rule in TDDFT simulation 4.Application 1: mono graphene exfoliation from bulk graphite 5.Application 2: E-field enhancement of light inside carbon nanotube with resonant frequency 6.Summary
3 1. Motivation (not only the scale!) Nonequilibrium Dynamics Speed per processor Response to Pulse ion collision molecular device conductance Defects Impurities in crystal Photo-chemistry Femtosecond Laser Ion Beam Fabrication contact Resistivity parasitic capacitance Charge trap Memory, gate Surface energy Plasmon-current conversion Epitaxial growth CNT, nano-wire Nano-fabrication Whole device simulation Emerging materials equilibrium Scale 10atoms 10 2 atoms 10 3 atoms 10 4 atoms Current level of simulation Parallel computing 3 NEC Corporation 2008
4 Compute electronic excitation and subsequent femtosecond dynamics Imaginary number! Need of massive number of fast processors time We cannot compute time-evolution in parallel manner! future Causality principle! past current 4 NEC Corporation 2008
5 TDDFT under strong pulse! Pioneering works: Prof. Yabana (Tskuba Univ.) Bertsch, et al., PRB , (2000). Castro et al., Eur. Phys. J. D 28, 211 (2004). 5 NEC Corporation 2008
6 For numerical stability what should we check? Energy conservation! MD simulation must conserve TDDFT term 6 NEC Corporation 2008
7 7 NEC Corporation 2008 Example of TDDFT-MD 96 C atoms under R.T. and excitation
8 With time-varying external field Goes to zero! Remains as non-zero! 8 NEC Corporation 2008
9 Work by external field is Thus a new conservation rule is Miyamoto, Zhang, Phys. Rev. B77, (2008) 1. This holds regardless to xc-functional form (but within adiabatic xc-functional) 2. Inductance has not been included (j B j ind ) current density functional theory 9 NEC Corporation 2008
10 + 10-layer graphite - Fictitious charge (+) Fictitious charge (-) Pulse shape Test calculation: AB-stacked graphite 2x2 cell in lateral directions under pulse E-field Ecut=60 Ry TM type pseudopotentials Single k-point dt=1.84 x 10-4 fs 10 NEC Corporation 2008
11 11 NEC Corporation 2008 R. K. Raman, et al., PRL101, (2008)
12 Laser pulse induced structural change! λ= 800 nm τ=50 fs 12 NEC Corporation 2008
13 Analysis of structural change λ= 800 nm Energy conservation rule Transferred energy to graphite = 87.9 mj/cm 2 13 NEC Corporation 2008
14 Why different from experiments? (No initial shrink) Laser fluence : exp. 77mJ/cm 2 present simulation 87.9 mj/cm 2 Pulse width: exp 25 fs, present simulation 50fs Needed research Change of wavelength Change of pulse width Change of power/pulse Combination of pulse with controlled phase 14 NEC Corporation 2008
15 Application 2: optical-field inside nanotube Applied E-field Esinωt Induced E-field 15 NEC Corporation 2008
16 Demonstration: Screening against static E-field Applied field V TDDFT HXC ( r, t; V appl ) V appl ( r ) V DFT HXC ( r ) Induced field 0.97 fs Very fast screening by depolarization, but still takes a time comparable to a frequency of E-field of light +5 V -5 V 16 NEC Corporation 2008
17 Can nanotubes completely screen cross-polarized light? Cross-excitations is atctually measured, so let s say NO! Absorption Applied E-field is no longer static! Absorption & luminescence E 22 E 11 E 12 E 11 Murakami et al., PRL 94, (2005) Lefebvre and Finnie, PRL 98, (2007) 17 NEC Corporation 2008
18 Cross-polarization of CNT did not take attentions due to smaller oscillator strength and depolarization effect, which was considered in early famous AB-effect works! H. Ajiki and T. Ando, Jpn. J. Appl. Phys. 34, Suppl, 34-1, 107 (1994). H. Ajiki and T. Ando, Physica B 201, 349 (1994). Question for theorists: Why E-field with cross-polarization can survive? What suppresses depolarization? Exciton has been suggested to weaken depolarization. S. Uryu and T. Ando, PRB 74, (2006). While excitons with cross-polarization are not strongly localized as those with parallel polarization. S. Kilina et al., Adv. Funct. Mater, 17, 3405 (2007); PNAS 105, 6797 (2008). 18 NEC Corporation 2008
19 Free from adjustable parameters: ab-inito approach for response of nanotube against time-varying E-field E x (r,t) (8,0) tube V ext (r,t) Periodic boundary conditions: inter-wall 10 Å in x 6 Å in y y x Combination with TDDFT and time-varying sawtooth-type external field Plane-wave, TM-type pps. (Sugino-Miyamoto code) O. Sugino, Y. Miyamoto PRB 59, 2579 (1999), 66, (E) (2002). Checking energy conservation rule (Total Energy Work) Y. Miyamoto, H. Zhang, PRB 77, (2008) 19 NEC Corporation 2008
20 Please let me remark This approach does not correctly include excitonic effect. We should have strong depolarization. Really? Hand writing by E. K. U. Gross 20 NEC Corporation 2008
21 Result E applied vs. E total (=E applied + E induced ) 800 nm light to (8,0) nanotube with cross-polarization No accumulation of potential FFT Given freq fs FFT peak 2 fs Off resonance! 21 NEC Corporation 2008
22 Result E applied vs. E total (=E applied + E induced ) 600 nm light to (8,0) nanotube with cross-polarization fs significant charge redistribution! Enhancement of E-field inside nanotube! Induced E-filed inside nanotube exceeds applied E-field. 22 NEC Corporation 2008
23 Further adjustment of frequency gives significant E-field enhancement! Period = fs =591nm=2.08 ev The resonant energy 2.08 ev is close to E 21 energy of (8,0) tube. (Cf. LDA gap is 1.75 ev.) 23 NEC Corporation 2008
24 (8,0) 800 nm The enhancement is also the case in larger diameter (14,0) tube. (8,0) 600 nm (14,0) 822 nm 24 NEC Corporation 2008
25 Application of E-field enhancement β-carotene inside nanotube B. W. Smith, M. Monthloux, and D. E. Luzzi Nature 396, 323 (1998) K. Yanagi et al., PRB74, (2006) Q: Can we shed light on stronger? A: Maybe yes with frequency of light of resonances. 25 NEC Corporation 2008
26 1. Simulation of pulse laser shot 2.Energy conservation rule in TDDFT simulation 3.Application 1: mono graphene exfoliation from bulk graphite 4.Application 2: E-field enhancement of light inside carbon nanotube with resonant frequency 26 NEC Corporation 2008
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