``X-Ray Edge'' Singularities in Nanotubes and Quantum Wires with Multiple Subbands

Abstract

Band theory predicts an inverse square root van Hove singularity in the tunneling density of states at the minimum energy 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 by a power B of the energy above threshold, with B approximately 0.3 for typical carbon nanotubes. Despite the anomalous tunneling characteristic, good quasiparticles corresponding to the unoccupied subband states do exist.