Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0507065 · Science

Spin-Charge Separation and Localization in One Dimension

Ophir M. Auslaender, Hadar Steinberg, Amir Yacoby, Yaroslav Tserkovnyak, B. I. Halperin, K. W. Baldwin, Loren N. Pfeiffer, K. W. West

Published Mar 31, 2005• 403 citations
arXivHTMLPDF

Abstract

We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained by tunneling between two parallel wires in an GaAs/AlGaAs heterostructure while varying electron density. We observed two spin modes and one charge mode of the coupled wires and mapped the dispersion velocities of the modes down to a critical density, at which spontaneous localization was observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that was not observed. The measured spin velocity was smaller than theoretically predicted.

DOI
10.1126/science.1107821

Related papers

Tunneling spectroscopy of quantum wires: Spin‐charge separation and localization

Amir Yacoby, Ophir M. Auslaender, Hadar Steinberg +5 more

Abstract Using a double wire geometry we probe the quantum many‐body modes in ballistic wires and their dependence on Coulomb interactions. The wires are fabricated using the cleaved edge overgrowth method. We clearly observe two spin modes and one charge mode of the coupled wires. We map the dispersion velocities of the modes down to a critical density at which spontaneous localization is observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that is not observed. Surprisingly, the suppression of the spin velocities does not depend on density. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)•Nov 1, 2006•2 citations

Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor

Pedro M. T. Vianez, Yiqing Jin, M. Moreno +9 more

An electron is usually considered to have only one form of kinetic energy, but could it have more, for its spin and charge, by exciting other electrons? In one dimension (1D), the physics of interacting electrons is captured well at low energies by the Tomonaga-Luttinger model, yet little has been observed experimentally beyond this linear regime. Here, we report on measurements of many-body modes in 1D gated wires using tunneling spectroscopy. We observe two parabolic dispersions, indicative of separate Fermi seas at high energies, associated with spin and charge excitations, together with the emergence of two additional 1D "replica" modes that strengthen with decreasing wire length. The interaction strength is varied by changing the amount of 1D intersubband screening by more than 45%. Our findings not only demonstrate the existence of spin-charge separation in the whole energy band outside the low-energy limit of the Tomonaga-Luttinger model but also set a constraint on the validity of the newer nonlinear Tomonaga-Luttinger theory.

arXiv:2102.05584•Science Advances•Jun 17, 2022•14 citations

Probing spin-charge separation in tunnel-coupled parallel quantum wires

Ulrich Zülicke, Michele Governale

Interactions in one-dimensional (1D) electron systems are expected to cause a dynamical separation of electronic spin and charge degrees of freedom. A promising system for experimental observation of this non-Fermi-liquid effect consists of two quantum wires coupled via tunneling through an extended uniform barrier. Here we consider the minimal model of an interacting 1D electron system exhibiting spin-charge separation, and calculate the differential tunneling conductance as well as the density-density response function. Both quantities exhibit distinct strong features arising from spin-charge separation. Our analysis of these features within the minimal model neglects interactions between electrons of opposite chirality, and therefore applies directly to chiral 1D electron systems realized, e.g., at the edge of integer quantum Hall systems. Physical insight gained from our results is useful for interpreting current experiment in quantum wires, as our main conclusions still apply with nonchiral interactions present. In particular, we discuss the effect of charging due to applied voltages, and the possibility to observe spin-charge separation in a time-resolved experiment.

arXiv:cond-mat/0105066•Physical review. B, Condensed matter•Apr 25, 2002•23 citations

Momentum-resolved tunneling between Luttinger liquids

David Carpentier, Claudia S. Peça, Leon Balents

We study tunneling between two nearby cleaved edge quantum wires in a perpendicular magnetic field. Due to Coulomb forces between electrons, the wires form a strongly-interacting pair of Luttinger liquids. We calculate the low-temperature differential tunneling conductance, in which singular features map out the dispersion relations of the fractionalized quasiparticles of the system. The velocities of several such spin-charge separated excitations can be explicitly observed. Moreover, the proposed measurement directly demonstrates the splintering of the tunneling electrons into a multi-particle continuum of these quasiparticles, carrying separately charge from spin. A variety of corrections to the simple Luttinger model are also discussed.

arXiv:cond-mat/0103193•Mar 8, 2001•0 citations

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

Oleksandr Tsyplyatyev, A. J. Schofield, Yuan Jin +8 more

The natural excitations of an interacting one-dimensional system at low energy are the hydrodynamic modes of a Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where the 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 analyzed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized 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 a crossover to a Luttinger liquid at low energy by calculating the local density of states through all energy scales: from linear to nonlinear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure the momentum-resolved tunneling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe a 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 a structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.

arXiv:1508.07125•Physical review. B./Physical review. B•Feb 24, 2016•16 citations

Inelastic light scattering by spin-density, charge-density, and single-particle excitations in GaAs quantum wires

A. Schmeller, Alejandro Rodolfo Goñi, Aron Pinczuk +5 more

We report the observations of inelastic light scattering by the elementary excitations of the one-dimensional electron gas. The quantum wires are fabricated from a modulation-doped single GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum well electron-beam lithography and shallow electron-cyclotron-resonance reactive-ion etching. In spectra of intersubband excitations we observe a clear separation of spin-density and charge-density collective modes. The splitting associated with the lateral potential of the wires is also seen in transitions to states of the first excited level of the parent quantum well. Determinations of electron-electron interactions in intersubband excitations of the one-dimensional electron gas show large corrections due to the exchange terms (or vertex corrections) that represent the excitonic binding of the particle-hole pairs.

Physical review. B, Condensed matter•May 15, 1994•85 citations
We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained by tunneling between two parallel wires in an GaAs/AlGaAs heterostructure while varying electron density. We observed two spin modes and one charge mode of the coupled wires and mapped the dispersion velocities of the modes down to a critical density, at which spontaneous localization was observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that was not observed. The measured spin velocity was smaller than theoretically predicted.
Abstract Using a double wire geometry we probe the quantum many‐body modes in ballistic wires and their dependence on Coulomb interactions. The wires are fabricated using the cleaved edge overgrowth method. We clearly observe two spin modes and one charge mode of the coupled wires. We map the dispersion velocities of the modes down to a critical density at which spontaneous localization is observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that is not observed. Surprisingly, the suppression of the spin velocities does not depend on density. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An electron is usually considered to have only one form of kinetic energy, but could it have more, for its spin and charge, by exciting other electrons? In one dimension (1D), the physics of interacting electrons is captured well at low energies by the Tomonaga-Luttinger model, yet little has been observed experimentally beyond this linear regime. Here, we report on measurements of many-body modes in 1D gated wires using tunneling spectroscopy. We observe two parabolic dispersions, indicative of separate Fermi seas at high energies, associated with spin and charge excitations, together with the emergence of two additional 1D "replica" modes that strengthen with decreasing wire length. The interaction strength is varied by changing the amount of 1D intersubband screening by more than 45%. Our findings not only demonstrate the existence of spin-charge separation in the whole energy band outside the low-energy limit of the Tomonaga-Luttinger model but also set a constraint on the validity of the newer nonlinear Tomonaga-Luttinger theory.
Interactions in one-dimensional (1D) electron systems are expected to cause a dynamical separation of electronic spin and charge degrees of freedom. A promising system for experimental observation of this non-Fermi-liquid effect consists of two quantum wires coupled via tunneling through an extended uniform barrier. Here we consider the minimal model of an interacting 1D electron system exhibiting spin-charge separation, and calculate the differential tunneling conductance as well as the density-density response function. Both quantities exhibit distinct strong features arising from spin-charge separation. Our analysis of these features within the minimal model neglects interactions between electrons of opposite chirality, and therefore applies directly to chiral 1D electron systems realized, e.g., at the edge of integer quantum Hall systems. Physical insight gained from our results is useful for interpreting current experiment in quantum wires, as our main conclusions still apply with nonchiral interactions present. In particular, we discuss the effect of charging due to applied voltages, and the possibility to observe spin-charge separation in a time-resolved experiment.
We study tunneling between two nearby cleaved edge quantum wires in a perpendicular magnetic field. Due to Coulomb forces between electrons, the wires form a strongly-interacting pair of Luttinger liquids. We calculate the low-temperature differential tunneling conductance, in which singular features map out the dispersion relations of the fractionalized quasiparticles of the system. The velocities of several such spin-charge separated excitations can be explicitly observed. Moreover, the proposed measurement directly demonstrates the splintering of the tunneling electrons into a multi-particle continuum of these quasiparticles, carrying separately charge from spin. A variety of corrections to the simple Luttinger model are also discussed.
The natural excitations of an interacting one-dimensional system at low energy are the hydrodynamic modes of a Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where the 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 R2/L2{\mathcal{R}}^{2}/{L}^{2}R2/L2, where R\mathcal{R}R is a length-scale related to interactions and LLL 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 analyzed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized 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 a crossover to a Luttinger liquid at low energy by calculating the local density of states through all energy scales: from linear to nonlinear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure the momentum-resolved tunneling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe a 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 a structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.
We report the observations of inelastic light scattering by the elementary excitations of the one-dimensional electron gas. The quantum wires are fabricated from a modulation-doped single GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum well electron-beam lithography and shallow electron-cyclotron-resonance reactive-ion etching. In spectra of intersubband excitations we observe a clear separation of spin-density and charge-density collective modes. The splitting associated with the lateral potential of the wires is also seen in transitions to states of the first excited level of the parent quantum well. Determinations of electron-electron interactions in intersubband excitations of the one-dimensional electron gas show large corrections due to the exchange terms (or vertex corrections) that represent the excitonic binding of the particle-hole pairs.