Carbon nanotubes: Models, correlations and the local density of states
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1 Carbon nanotubes: Models, correlations and the local density of states Alexander Struck in collaboration with Sebastián A. Reyes Sebastian Eggert
2 Outline Carbon structures Modelling of a carbon nanotube Effective ladder model Correlations in a carbon nanotube and the local density of states A.Struck models for carbon nanotubes
3 Carbon structures Graphene : 2D carbon layer (planar, sp2 hybridization in chemical bond 0D: Fullerene 1D: Carbon nanotube 3D: Graphite A.Struck models for carbon nanotubes
4 Graphene: electronic properties Lattice with 2-atom basis reciprocal lattice vectors Hamiltonian (nearest neighbour hopping) A.Struck models for carbon nanotubes
5 Graphene: electronic properties Lattice with 2-atom basis reciprocal lattice vectors Hamiltonian (nearest neighbour hopping) Stationary states: if A.Struck models for carbon nanotubes
6 Graphene: electronic properties Dispersion 6 Fermi points, 2 independent A.Struck models for carbon nanotubes
7 From graphene to CNT Wrap the sheet around Roll-up vector Periodic boundary conditions at the seam! Armchair CNT Zigzag CNT A.Struck models for carbon nanotubes
8 Armchair CNT: minimal model New band structure: only one free momentum k, the other is fixed to discrete modes from pbc Keep only two bands: Two-species extended Hubbard model Solve with DMRG A.Struck Standing waves in armchair carbon nanotubes
9 Armchair CNT with interactions Tight binding description A.Struck - Standing waves in armchair carbon nanotubes
10 Mean field phase diagram of a (clean) armchair CNT M. P. López Sancho et. al., Phys. Rev. B 63, (2001) A.Struck - Standing waves in armchair carbon nanotubes
11 Mean field phase diagram of a (clean) armchair CNT M. P. López Sancho et. al., Phys. Rev. B 63, (2001) A.Struck - Standing waves in armchair carbon nanotubes
12 Detecting interactions: The local density of states Central quantity in STM measurements Direct indicator for electron-electron interactions Quantifier for Luttinger liquid behaviour I. Schneider, A.Struck, M.Bortz, S.Eggert, Phys. Rev. Lett. 101, (2008) I. Schneider, S.Eggert, Phys. Rev. Lett. (2010) A.Struck - Lattice defects, boundaries and interactions in carbon nanotubes
13 Detecting interactions: The local density of states In carbon nanotubes A.Struck - Lattice defects, boundaries and interactions in carbon nanotubes
14 Detecting interactions: The local density of states (remapped to carbon lattice) A.Struck - Lattice defects, boundaries and interactions in carbon nanotubes
15 Detecting interactions: The local density of states (remapped to carbon lattice) A.Struck - Lattice defects, boundaries and interactions in carbon nanotubes
16 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
17 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
18 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
19 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
20 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
21 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
22 Spectral resolution of LDOS A.Struck Standing waves in armchair carbon nanotubes
23 Conclusion Effective Hubbard ladder models allow for DMRG studies of LDOS spectra in carbon nanotubes LDOS patterns strongly indicate electron interactions in the nanotube Literature: S.A.Reyes, A. Struck, S. Eggert, Lattice defects and boundaries in conducting carbon nanotubes, Phys. Rev. B 80, (2009) I. Schneider, A.Struck, M.Bortz, S.Eggert, Local density of states for finite quantum wires, Phys. Rev. Lett. 101, (2008) A.Struck Standing waves in armchair carbon nanotubes
24 A.Struck models for carbon nanotubes
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