Spectrum and Franck–Condon factors of interacting suspended single-wall carbon nanotubes

Abstract

A low-energy theory of suspended carbon nanotube quantum dots in weak tunnelling coupling with metallic leads is presented. The focus is on the dependence of the spectrum and the Franck-Condon factors on the geometry of the junction including several vibronic modes. The relative size and the relative position of the dot and its associated vibrons strongly influence the electromechanical properties of the system. A detailed analysis of the complete parameters space reveals different regimes: in the short vibron regime the tunnelling of an electron into the nanotube generates a plasmon-vibron excitation, whereas in the long vibron regime polaron excitations dominate the scenario. The small, position-dependent Franck-Condon couplings of the small vibron regime convert into uniform, large couplings in the long vibron regime. Selection rules for the excitations of the different plasmon-vibron modes via electronic tunnelling events are also derived.

Magnetic field control of the Franck-Condon coupling of few-electron quantum states

“…Models discussing strong electron-vibron coupling in carbon nanotube quantum dots typically assume an inhomogeneuous charge distribution relative to the vibration mode envelope, or more generally, a different localization of electron and vibron wave function, see, e.g., Refs. [9,30,32,37]. This is consistent with the occurrence of Franck-Condon sidebands in devices with local gates close to the nanotube [14,18,19].…”

“…A large number of extensions to this model has been developed to take into account specific details of transport spectra, see, e.g., Refs. [8,19,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]; however, for now we focus our analysis on the simplest theoretical case, assuming a single harmonic oscillator mode and fast relaxation into the vibrational ground state. In this case, the current step heights or conductance peak amplitudes follow the Poisson formula [4,10], P n = (e −g g n )/n!, n = 0, 1, 2, .…”

Out-of-equilibrium density dynamics of a quenched fermionic system

“…The validity of LLs as low energy theories for 1D systems of fermions, bosons and spin, has been demonstrated experimentally by means of anomalous tunneling effects 32,33 , or by observing spin-charge separation [34][35][36] . Moreover, the LL theory represents a very useful tool for the study of a wide range of 1D systems, including integer 37 and fractional 38 quantum Hall effects and two dimensional topological insulators [39][40][41][42] , weakly interacting quantum wires 32 , even in the presence of spin-orbit coupling [43][44][45][46][47][48] , carbon nanotubes 33,49,50 , eventually including electron phonon coupling 51,52 , spin chains 53,54 and, complemented with its spin incoherent version 55,56 , Wigner crystals [57][58][59][60][61][62][63] . The validity of the LL picture as a low energy theory for 1D Hamiltonians is however limited to the low energy excitations of gapless phases 29,31 .…”

The Electronic Structure of Short Carbon Nanotubes: The Effects of Correlation

“…A similar approach was already applied to closed polyacenes structures [13] whereas most of previous works on nanotubes [14][15][16][17][18][19][20][21][22] or nanoribbons [23] principally rely on density functional theory or tight binding results. The main conclusion of studies on There also have been some studies in the solid-state community on the energy spectrum [24] and properties of single walled nanotubes [25] using sophisticated analytic tools. Similar structures as those considered consist in an antiferromagnetic coupling of two electrons localized in the edge orbitals.…”