1 / 18

QUANTUM COHERENT CONDUCTION IN CNTs An Amateur’s View

QUANTUM COHERENT CONDUCTION IN CNTs An Amateur’s View. Learning Seminar Series on Carbon Nanotubes. T.Williams: SZFKI 19-09-2005. CONTENTS. 1. Four striking experiments on 1-D conduction in CNTs 2. Band structure of graphene and CNTs 3. Why armchair (n,n) CNTs are metallic

chance
Download Presentation

QUANTUM COHERENT CONDUCTION IN CNTs An Amateur’s View

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. QUANTUM COHERENT CONDUCTION IN CNTsAn Amateur’s View Learning Seminar Series on Carbon Nanotubes T.Williams: SZFKI 19-09-2005

  2. CONTENTS 1. Four striking experiments on 1-D conduction in CNTs 2. Band structure of graphene and CNTs 3. Why armchair (n,n) CNTs are metallic 4. Quantum of conduction e2/h per 1-D channel 5. Ballistic 1-D thermal conduction and quantum of conductance (π2/3)kB2T/h 6. Evidence for superconductivity in CNTs 7. Indications of Tomonaga-Luttinger liquid behaviour in CNTs

  3. Yu et al, Nano Letters 2005 Liang et al Nature 2001 1-D ballistic thermal conductance 1-D Quantum conductance and interference Ropes Kociak et al PRL 2001 Bockrath et al Nature 1999 1-D Superconductivity 1-D Tomonaga-Luttinger Liquid

  4. EF GRAPHENE BAND STRUCTURE Carbon: atom = 1s22s22p2 ; graphene = 1s2 (2s2p2)σ2pπ

  5. + = px 2s 2s2p2σx orbital - - + + + 2s + px 2s2p2 σ bonding Carbon: atom = 1s22s22p2 ; graphene = 1s2 (2s2p2)σ2pπ

  6. - + + + + - - - 2p π* antibonding 2p π bonding 2p π bonding

  7. k a2 k=3π/2a0 a1 W-S Zone (n,n) tube: c=na1+na2 k1 K M Γ EF Brillouin Zone k2 k Armchair tubes are quasi-metallic k

  8. kFP=kK =3π/2a0 E(k) around Fermi point k K point =Fermi point k

  9.     k k kK.ž = 3π/2a0 CARRIER DENSITY Neutral system = quasi-metallic = zero gap semiconductor 4 n=2 electrons per atom X 2 atoms per unit cell = 8 electrons = 2 spin states X 4 bands filled to Fermi point EFermi   k Degenerate semiconductor Electron metal Hole metal δQ = 0 δQ = +εe/unit cell δQ = -εe/unit cell

  10. IMPOSING CHARGE δQTotal = C Vg : L 2R Vgate s C  L/ln(R/s) (S0=area of graphene unit cell) If Efermi << Eexc subband , only four 1-D conduction channels = 2 bands X 

  11. No back scattering I12 Rsvr2 EF Rsvr1 EF+δeV I21 a b b a eV EF QUANTUM OF CONDUCTANCE Key: v = W/ħk e2/h = gQ ≈ 40μS = 1/25kΩ (Landauer formula)

  12. VDS IDS Au, Pt Al2O3 Au CONFIGURATION OF TRANSPORT EXPERIMENTS VG CNT Contacts: sometimes ohmic R  kΩ GQ , quantum int. ,superc. often tunnel R  102 kΩ CB, TLL STM tunnel

  13. e-ikz s2 s1 e+ikz QUANTUM OF CONDUCTANCE, QUANTUM INTERFERENCE k = kK + (k/W)eVG = kK + eVG/ħvF

  14. No back scattering I12 Rsvr2 Temp T Rsvr1 T+δT I21 ω k 1-D THERMAL CONDUCTANCE Power flow per mode: Number of modes: Total energy flux: Quantum of thermal conductance per channel

  15. 1-D BALLISTIC PHONON CONDUCTION At T<6K, 4 channels, at 100K estimate of 7 channels

  16. EVIDENCE FOR SUPERCONDUCTIVITY Nota: CNT ropes

  17. EVIDENCE FOR TOMANAGA-LUTTINGER LIQUID BEHAVIOUR Nota: CNT ropes

  18. WHAT TO BELIEVE? WHAT TO DO? WHAT CAN WE DO?

More Related