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

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.

23 pages, 10 figures, 2 tables

References in corpus (13)

• Spin-charge separation and localization in one-dimension
• Universal theory of nonlinear Luttinger liquids
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• Dynamic response of one-dimensional interacting fermions
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• Spectral function of spinless fermions on a one-dimensional lattice
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• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
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Cited by in corpus (14)

• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit
• Nonlinear spectra of spinons and holons in short GaAs quantum wires
• Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor
• Microscopic metallic air-bridge arrays for connecting quantum devices
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Splitting of Fermi point of strongly interacting electrons in one dimension: A nonlinear effect of spin-charge separation
• Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions
• Many-body theory of magneto-elasticity in one dimension
• Semiconductor nanodevices as a probe of strong electron correlations
• Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality
• Finite-temperature spectroscopy of dirty helical Luttinger liquids
• Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D Regime
• Dominant end-tunneling effect in two distinct Luttinger liquids coexisting in one quantum wire