Modélisation et étude des propriétés optiques des nanotubes de carbone Modelling and study of

Mode´lisation et e´tude des proprie´te´s optiquesdes nanotubes de carboneModelling and study of optical properties ofcarbon nanotubesBenjamin Ricaud´Universite du Sud Toulon VarCentre de Physique The´orique, 22 Octobre 200766Carbon nanotubesTubes made of carbon atoms with = radiuses, = chiralities.◮ Different properties.◮ How to sort nanotubes.Benjamin Ricaud -2/26- 22 Octobre 2007 ,Optical spectrum◮ A way to sort nanotubes. Monochromatic light sent on CN, lowtemp.I ω0I ω1◮ Optical absorption spectrum /ω◮ Optical absorption spectrum related to radius & chirality.◮ explain a part of the optical absorption spectrum (Infrared).−(Absorption by e )Benjamin Ricaud -3/26- 22 Octobre 2007 ,Optical response, physical explanationSending light and looking at the absorption of semiconductor CN.− −◮ Without e -e interaction:E◮ periodic lattice⇒ bands& gaps Conduction band −e◮ Semiconductor: G. state=valence bands full, E(k)cconduction bands empty.Eg◮ Absorption↔ Energy.− − E(k)◮ vWith e -e interaction (weak):+Valence band h k◮ “excitons”. Wannier (1937), Elliot(1957), Mahan.− + E◮ exciton, coupled e -h : H φ = E φexc n n nConduction band◮ Absorption spectrum at 0K with Eg=gap, η=controlE(k)cadiabaticity:En2X |ψ (0)|nα(ω)∼2 2(E + E +~ω)[(E + E −~ω) +(~η) ] E(k)n g n g vn+Valence band h k[Haug, Koch]◮ Nanotubes: Exciton eigenstates depend on r.Benjamin Ricaud -4/26- 22 Octobre 2007 ,Benjamin Ricaud -5 ...