Hierarchy of modes in an interacting system

TL;DR

This paper reveals a hierarchical structure of excitations in interacting 1D fermionic systems, demonstrating both theoretical predictions and experimental evidence for multiple excitation levels with distinct spectral features.

Contribution

It introduces a theoretical hierarchy of excitation modes in 1D interacting fermions and provides experimental evidence for second-level excitations in a GaAs heterostructure.

Findings

Hierarchy levels separated by powers of /Lb2

First-level excitations form a parabolic mode

Experimental evidence of second-level excitations with spectral signatures

Abstract

Studying interacting fermions in 1D at high energy, we find a hierarchy in the spectral weights of the excitations theoretically and we observe evidence for second-level excitations experimentally. Diagonalising a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. 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 measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.