June 9, 2011, Crete, WavePro. Sergey Maksimenko, G. Ya. Slepyan Institute for Nuclear Problems, Belarus State University, Minsk, Belarus

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1 June 9, 2011, Crete, WavePro Carbon Nanotube as a Terahertz Delay Line: Manifestations and Potentiality in Nanoelectromagnetics Sergey Maksimenko, G. Ya. Slepyan Institute for Nuclear Problems, Belarus State University, Minsk, Belarus sergey.maksimenko@gmail.com

2 Motivation Milestones in the development of electrodynamics have always been related to practical problems arising from new ideas relating to the transmission and processing of electromagnetic signals. Advances in quantum electronics led to the development of the theory of open quasi-optical resonators. The implementation of the fiber optic communication led to the development of the theory of open dielectric waveguides. Progress in microwave microelectronics stimulated research on the electrodynamics of microstrips and other planar structures. Metamaterials and plasmonic structures initiate new exciting steps in electrodynamics. Simulation of electromagnetic processes on nanoscale is one of the main research directions for modern electrodynamics.

3 NANOELECTRODYNAMICS is currently emerging as a synthesis of macroscopic electrodynamics and microscopic theory of electronic properties of different nanostructures. Electromagnetic field diffraction Confinement of the charge carrier motion Diffraction Theory Boundary-value problems for complex-shaped regions: Complex geometry, ordinary electronics Condensed Matter Physics Quasi-particle concept: Electrons, phonons, magnons Complex electronics, ordinary geometry NANOELECTRODYNAMICS The present-day challenge is to incorporate into the theory a complex character of the charge carriers carriers dispersion and inhomogeneity of electromagnetic field on the nano(subwavelength) scale.

4 e CARBON NANOTUBE τ 3 τ 1 (m,0) -zigzag, (m,m) - armchair τ 2 R c a 1 a 2 e R c =ma 1 +na 2 SWCNT (m,n) Basic Physical Properties Length: 1-10 mkm Diameter: 1-3 nm Conductivity type: metallic or semiconductor Current-carrying capacity: A/cm 2 Free pass length: mkm Thermal conductivity: W/mK (~1000 for diamond)

5 nanoelectromagnetics Theoretical modeling of the CNT conductivity is the crucial problem in the electrodynamics of CNTs This problem is analyzed by the system of kinetic equations for the density matrix: t cc ee z p cc cv eez t pp z z cv i ee i ee z z [ R ( R cv * cv ( cv vv R cv cc vc ), ) ( R cc R vv ) cv ] i vc cv. vc where, is the frequency of the transition, ρ υυ + ρ cc = 1, and indexes v and c correspond to π-electron in the valence and conduction bands, respectively.

6 Dynamical conductivity of CNT The CNT conductivity below the optical transitions band Wllk Well-known property zigzag of zigzag amchair CNTs to be metallic or semiconducting dependently on the radius no ormalized axial conductivity ,1 0, (m,0) CNs 1: Metallic CNs (m=3q) 2: Semiconducting CNs (m3q) 1E m Slepyan et al., PRB 1999 conductivity nor rmalized axial (m,m) m) CNTs The axial conductivity, based on quantum transport theory m Conductivity of zigzag metallic CNT in the range of interband transitions tivity normalize ed axial conduct CN (9,0) 1: Re( zz ) 2: Im( zz ) ,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 1

7 Effective boundary conditions for CNTs In optical range b, Rcn, b нм 2 l 4 0 1, (1 / ) H H E R 0 R 0 zz z R k i z c H H 0, E E 0 z R0 z R0 z, R0 z, R0 Spatial dispersion parameter l 0 ~ 10-5 for metallic CNTs Solution of the conductivity problem accounting for the spatial confinement couples classical electrodynamics and physics of nanostructures

8 Nanoelectromagnetics Complex-valued slow-wave wave coefficient for a polar-symmetric surface wave v ph c k h k h ih : Re() 2: -Re()/Im() CN (9,0) Im() << Re() THz 100 THz 1 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01 kb b=0.142 nm is the C-C bond length axial component of the time-averaged Poynting vector for surface wave

9 What can we learn from the picture? CARBON NANOTUBE as an EM device (mostly in THz range): Electromagnetic slow-wave wave line: v ph /c~0.02 Dispersionless surface wave nanowaveguide Monomolecular traveling wave tube Terahertz-range range antenna Interconnects Thermal antenna : Re() 2: -Re()/Im() A spontaneous decay 1 rate10 controller CN (9,0) 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01

10 Long wavelength limit: geometrical resonances A vibrator antenna radiates effectively if its length equals to an integer number of halfwaves; for perfectly conducting wire it is kl=m, m=1,2,3.. Geometrical resonances: hl=m Because of the large slow-wave effect, h/k=c/v ph =1/~50, at optical lengths ~ 1 mkm the geometrical resonances are shifted to THz L=1m CNT terahertz antenna!

11 Experimental observations of THz peak in CNT-based composites Phys. Rev. B 74, (2006) Bommeli F., et al. Synt. Met. 86, 2307 (1997). (b) Real part of the conductivity together with the Drude and Lorentz contributions to the overall fit (solid line). T. Kampfrath, phys. stat. t sol. (b) 244, No. 11, (2007)

12 Comparison with experiment: THz peak The predicted amplitudes of resonance lines due to first two optical transitions of the semiconducting SWCNTs coincide reasonably well with the experimental values. 12

13 NANO - Traveling wave tube, Backward wave oscillator, Free electron laser: basic idea 300MHz 300GHz z Relativistic electron beam is the lasing medium Traveling-wave tubes, R Kompfner 1952 Rep. Prog. Phys The main elements of a TWT are (1) an electron gun, (2) a focusing structure that keeps the electrons in a linear path, (3) slowing-down system (4) an electron collector Large slow-down: 1/b > 100 Ballistic electron motion

14 Intrinsic properties of CNTs It is well-known, that electron beam at certain conditions can emit radiation In systems which modify photon states and slow down electromagnetic wave (Cherenkov, Smith-Purcell, quasi-cherenkov mechanisms); In systems which modify electron states (undulator, synchrotron and gyrotron systems) Combination in CNTs of three key properties, a strong slowing down of surface electromagnetic waves, ballisticity of the electron flow over typical CNT length, and extremely high electron current density, allows proposing them as candidates for the development of nano-sized Chernekov-type emitters nano-twt, nano-bwo and nano-fel.

15 Gain per unit length is extremely large comparing with macrodevices Threshold current and instability increment of generation j=10 10 A/cm 2 L= m Radiation generation is already possible at the current stage of the nanotechnology development

16 Thermal radiation from a single-wall CNT Motivation Noise properties and operational limits of CNT based devices are substantially determined by the thermal fluctuations of electromagnetic field (a) Thermal radiation spectra of metallic (15,0) CNT in the cross-section z 0 =0. The CNT polarizability is given on the inset. (b) Thermal radiation from CNT (solid line) and black--body radiation (dashed line) in the near-- field zone. The presence of singled out resonances illustrated by Fig. (a) allows us to propose metallic CNTs as far-field and near-field thermal antennas for the terahertz range

17 Where we go? Nano scale circuits components Functionalized, filled, coated and doped CNTs, MWCNTs, CNT bundles, telescopic junctions, nanorings, ribbons, etc. CNT-based composites and metamaterials Maxwell Garnet theory accounting for the length and diameter dispersion and percolation effect, regular structures Instabilities in CNTs monomolecular travelling wave tube, nanofel Photothermal effect Electromagnetic heating of CNTs and CNT thermo- dynamics, heat transfer on nanoscale A theory of quantum circuits Parcell effect, lifetime,

18 Acknowledgments I would like to thank our co-workers from the Institute for Nuclear Problems, BSU, Minsk Konstantin Batrakov, Polina Kuzhir, Mikhail Shuba and our international collaborators Akhlesh Lakhtakia, Christian Thomsen, George Hanson Support of the Research: ISTC (Intern. Science and Technology Center) В-1708 EU FP BY-NanoERA CACOMEL TERACAN 18