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

Research output: Contribution to journal › Article › peer-review

## Standard

**Nature of the many-body excitations in a quantum wire : theory and experiment.** / Tsyplyatyev, O.; Schofield, A. J.; Jin, Y.; Moreno, M.; Tan, W. K.; Anirban, A. S.; Ford, C. J. B.; Griffiths, J. P.; Farrer, I.; Jones, G. A. C.; Ritchie, D. A.

Research output: Contribution to journal › Article › peer-review

## Harvard

*Physical Review B*, vol. 93, no. 7, 075147. https://doi.org/10.1103/PhysRevB.93.075147

## APA

*Physical Review B*,

*93*(7), [075147]. https://doi.org/10.1103/PhysRevB.93.075147

## Vancouver

## Author

## Bibtex

}

## RIS

TY - JOUR

T1 - Nature of the many-body excitations in a quantum wire

T2 - theory and experiment

AU - Tsyplyatyev, O.

AU - Schofield, A. J.

AU - Jin, Y.

AU - Moreno, M.

AU - Tan, W. K.

AU - Anirban, A. S.

AU - Ford, C. J. B.

AU - Griffiths, J. P.

AU - Farrer, I.

AU - Jones, G. A. C.

AU - Ritchie, D. A.

N1 - 23 pages, 10 figures, 2 tables

PY - 2016/2/24

Y1 - 2016/2/24

N2 - 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.

AB - 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.

KW - cond-mat.str-el

U2 - 10.1103/PhysRevB.93.075147

DO - 10.1103/PhysRevB.93.075147

M3 - Article

VL - 93

JO - Physical Review B

JF - Physical Review B

SN - 1098-0121

IS - 7

M1 - 075147

ER -