Thermal Einstein-de Haas Effect Induced by Chiral Phonons in Carbon Nanotubes

Abstract

We investigate the effects of chirality on phonon thermal transport in semiconducting chiral single-walled carbon nanotubes (SWCNTs) using lattice dynamics combined with Boltzmann transport theory. We find that transverse acoustic and optical phonon modes, which are degenerate in nonchiral zigzag and armchair SWCNTs, are split in chiral SWCNTs, giving rise to finite phonon angular momentum associated with circular motion of individual atoms. This angular momentum is most efficiently generated in small-diameter nanotubes with intermediate chiral angles. Consequently, chiral SWCNTs are predicted to undergo thermally induced rigid-body rotation with an experimentally observable angular velocity via the thermal Einstein-de Haas effect.

Figures (5)

• Figure 1: (Color online) Illustrations of the unit-cell structures of left- (L-) and right-handed (R-) chiral (10,$-4$) and (6,4) SWCNTs, shown in blue and red, respectively. The chiral angle $\theta$ lies in the ranges $30^\circ < \theta < 60^\circ$ for L-handed structures and $0^\circ < \theta < 30^\circ$ for R-handed structures.
• Figure 2: Phonon dispersion relations of (11,0), (8,4), and (6,6) SWCNTs with unit-cell lengths $a = 0.43$, $1.15$, and $0.25$ nm, respectively.
• Figure 3: (Color online) (a) Phonon angular momentum $l_{q\lambda}^{x}$ for (10,$-4$) and (6,4) SWCNTs with unit-cell length $a = 1.89$ nm. The blue and red colors represent the amplitudes of phonon angular momentum for left- and right-handed chiral phonon modes, respectively. (b) $l_{q\lambda}^{x}$ for (8,4), (16,8), and (20,10) SWCNTs with a fixed chiral angle $\theta = 19.1^\circ$ and unit-cell length $a = 1.14$ nm. The corresponding tube diameters are $d_{\rm t} = 0.85$, $1.68$, and $2.10$ nm, respectively.
• Figure 4: (Color online) Dependence of $|\kappa_{\rm AM}|/\tau_{\rm ph}$ on the tube diameter $d_{\rm t}$ for chiral SWCNTs with four different chiral angles $\theta$ at $300$ K. The corresponding values of $\theta$ are $8.95^\circ$, $13.9^\circ$, $19.1^\circ$, and $23.4^\circ$. The solid curves represent power-law fits of the form $|\kappa_{\rm AM}|/\tau_{\rm ph} = |A| d_{\rm t}^{B}$, where $A$ and $B$ are fitting parameters.
• Figure 5: (Color online) Dependence of $|\kappa_{\rm AM}|/\tau_{\rm ph}$ on the chiral angle $\theta$ for chiral SWCNTs at $300$ K. The corresponding tube diameters are $d_{\rm t} = 1.2$ and $1.8$ nm. The red and blue curves represent sinusoidal fits of the form $|\kappa_{\rm AM}|/\tau_{\rm ph} = |C|\sin(D\theta)$, where $C$ and $D$ are fitting parameters. The fitting parameters $(C,D)$ are $(-10.2,\,6.0)$ and $(-4.67,\,6.0)$, respectively.