Relaxation and Dephasing in a Two-Electron \(^{13}C\) Nanotube Double Quantum Dot

We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13 C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time T 1 first decreases with a parallel magnetic field and then goes through a minimum in a field of 1.4 T. We attribute both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which at high field enhances relaxation due to bending-mode phonons. The inhomogeneous dephasing time T * 2 is consistent with previous data on hyperfine coupling strength in 13 C nanotubes.