Gapped Phases of Quantum Wires

TL;DR

This paper explores the rich phase diagram of a two-subband quantum wire, revealing conditions for charge-density wave and superconducting phases, and analyzing their effects on conductance and tunneling density of states.

Contribution

It provides a detailed theoretical analysis of gapped phases in two-subband quantum wires, including the interplay of interactions and resulting electronic properties.

Findings

Inter-subband interactions can induce gapped charge-density wave or superconducting phases.

Total charge mode remains gapless, maintaining universal conductance of 2e^2/h per subband.

Tunneling density of states exhibits a hard gap with non-universal singularities, affected by boundary effects.

Abstract

We investigate possible nontrivial phases of a two-subband quantum wire. It is found that inter- and intra-subband interactions may drive the electron system of the wire into a gapped state. If the nominal electron densities in the two subbands are sufficiently close to each other, then the leading instability is the inter-subband charge-density wave (CDW). For large density imbalance, the interaction in the inter-subband Cooper channel may lead to a superconducting instability. The total charge-density mode, responsible for the conductance of an ideal wire, always remains gapless, which enforces the two-terminal conductance to be at the universal value of 2e^2/h per occupied subband. On the contrary, the tunneling density of states (DOS) in the bulk of the wire acquires a hard gap, above which the DOS has a non-universal singularity. This singularity is weaker than the square-root divergency characteristic for non-interacting quasiparticles near a gap edge due to the "dressing" of massive modes by a gapless total charge density mode. The DOS for tunneling into the end of a wire in a CDW-gapped state preserves the power-law behavior due to the frustration the edge introduces into the CDW order. This work is related to the vast literature on coupled 1D systems, and most of all, on two-leg Hubbard ladders. Whenever possible, we give derivations of the important results by other authors, adopted for the context of our study.