X-ray-edge singularities in nanotubes and quantum wires with multiple subbands

Band theory predicts a (epsilon-Delta)(-1/2) van Hove singularity in the tunneling density of states at the minimum energy (Delta) of an unoccupied subband in a one-dimensional quantum wire. With interactions, an orthogonality catastrophe analogous to the x-ray edge effect for core levels in a metal strongly reduces this singularity to the form (epsilon - Delta)(beta-112), with beta approximate to 0.3 for typical carbon nanotubes. Despite the anomalous tunneling characteristic, good quasiparticles corresponding to the unoccupied subband states do exist.