Electron Spin Resonance Signal of Luttinger Liquids and Single-Wall Carbon Nanotubes

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid state of correlated metals is presented. The ESR measurables such as the signal intensity and the linewidth are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line broadening which is related to the spin-symmetry breaking and the electron-electron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the noninteracting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions.

Figure 1

The ESR signal intensity, Eq. (5) is shown as a function of the magnetic field for $K_s=1.1$ (corresponding to $\gamma =0.0045$), $k_{B}T/\hslash \omega =0.1$ (blue), 1 (red), 5 (black), and 25 (magenta). The resonance occurs at $g{\mu }_{B}B/\hslash \omega =1/K_s\approx 0.91$ for small temperatures.