= Carbon-nanotube Dirac mass
{title2=$m_{\rm eff}=\hbar|q_\perp|/v_F$}
Circumferential momentum quantization of a <graphene> <Dirac cone> produces nanotube dispersion $E_\pm(q_\parallel)=\pm\sqrt{(\hbar v_Fq_\parallel)^2+(\hbar v_Fq_\perp)^2}$. Comparing with a massive one-dimensional <Dirac Hamiltonian> identifies the displayed <effective mass> and gap $2m_{\rm eff}v_F^2$. This is an emergent band mass, not a changed vacuum <electron> rest mass. A quantization line through the valley gives zero mass in the ideal zone-folding model; curvature, strain and interactions can change that idealization.
Back to article page
