Nature of the many-body excitations in a quantum wire: theory and experiment

TL;DR

This paper combines theoretical analysis and experimental measurements to explore the nature of many-body excitations in a quantum wire, revealing a hierarchy of excitations beyond low energies and confirming the presence of spin-charge separation and parabolic dispersion.

Contribution

It introduces a detailed theoretical model of many-body excitations beyond low energy in quantum wires and validates it through momentum-resolved tunneling experiments.

Findings

Identification of a hierarchy of excitations with spectral weights proportional to interaction-related length scales.

Observation of a parabolic dispersion mode consistent with a renormalized single particle.

Detection of second-level excitations with power-law spectral features and their rapid decay at high momentum.

Abstract

The natural excitations of an interacting one-dimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analysed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to non-linear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.