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

Band theory predicts a (ε-Δ)^-1/2 van Hove singularity in the tunneling density of states at the minimum energy (Δ) 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 (ε-Δ)^β-1/2, with β≈0.3 for typical carbon nanotubes. Despite the anomalous tunneling characteristic, good quasiparticles corresponding to the unoccupied subband states do exist.