Anomalous phonon behavior of carbon nanotubes: First-order influence of external load

摘要: External loads typically have an indirect influence on phonon curves, i.e., they the curves by changing state about which linearization is performed. In this paper, we show that in nanotubes, axial load has a direct first-order long-wavelength behavior of transverse acoustic (TA) mode. particular, when tube force-free, TA mode frequencies vary quadratically with wave number and curvature (second derivative) proportional to square-root nanotube's bending stiffness. When non-zero external force, linearly slope force. Therefore, curves—and associated transport properties—are not material properties but rather can be directly tuned loads. addition, out-of-plane shear deformation does contribute unusual are exclusively due ben...