Enhanced NMR relaxation of Tomonaga-Luttinger liquids and the magnitude of the carbon hyperfine coupling in single-wall carbon nanotubes

Abstract

Recent transport measurements [Churchill \textit{et al.} Nat. Phys. \textbf{5}, 321 (2009)] found a surprisingly large, 2-3 orders of magnitude larger than usual ${}^{13}$C hyperfine coupling (HFC) in ${}^{13}$C enriched single-wall carbon nanotubes (SWCNTs). We formulate the theory of the nuclear relaxation time in the framework of the Tomonaga-Luttinger liquid theory to enable the determination of the HFC from recent data by Ihara \textit{et al.} [Ihara \textit{et al.} EPL \textbf{90}, 17004 (2010)]. Though we find that $1/T_1$ is orders of magnitude enhanced with respect to a Fermi-liquid behavior, the HFC has its usual, small value. Then, we reexamine the theoretical description used to extract the HFC from transport experiments and show that similar features could be obtained with HFC-independent system parameters.

5 pages plus 2 supplementary materials

References in corpus (8)

• Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots
• Nuclear magnetism and electron order in interacting one-dimensional conductors
• Hyperfine Interactions in Graphene and Related Carbon Nanostructures
• Nuclear Magnetism and Electronic Order in 13C Nanotubes
• Hyperfine-induced valley mixing and the spin-valley blockade in carbon-based quantum dots
• Spin gap and Luttinger liquid description of the NMR relaxation in carbon nanotubes
• The low energy spectrum of finite size metallic SWNTs
• The spectrum of interacting metallic carbon nanotubes: Exchange effects and universality

Cited by in corpus (7)

• Attractive Tomonaga-Luttinger Liquid in a Quantum Spin Ladder
• Hyperfine and spin-orbit coupling effects on decay of spin-valley states in a carbon nanotube
• Shape-sensitive Pauli blockade in a bent carbon nanotube
• Current hot spot in the spin-valley blockade in carbon nanotubes
• Nonlocal Damping of Helimagnets in One-Dimensional Interacting Electron Systems
• Orbital hyperfine interaction and qubit dephasing in carbon nanotube quantum dots
• Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by 13C NMR