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/0103193

Momentum-resolved tunneling between Luttinger liquids

David Carpentier, Claudia S. Peça, Leon Balents

Published Mar 8, 2001• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.cond-mat/0103193

Related papers

Momentum Resolved tunneling in a Luttinger Liquid

S. A. Grigera, A. J. Schofield, Silvio Rabello +1 more

We consider momentum resolved tunneling between a Luttinger liquid and a two dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a non-interacting one dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when $γ_ρ=0$. We argue that this measurement provides an important experimental signature of spin-charge separation.

arXiv:cond-mat/0312299•Dec 11, 2003•0 citations

Momentum-resolved tunneling between a Luttinger liquid and a two-dimensional electron gas

S. A. Grigera, A. J. Schofield, Silvio Rabello +1 more

We consider momentum resolved tunneling between a Luttinger liquid and a two-dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two-dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a noninteracting one-dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when ${\ensuremath{\gamma}}_{\ensuremath{\rho}}=0$. We argue that this measurement provides an important experimental signature of spin-charge separation.

Physical Review B•Jun 18, 2004•8 citations

Theory of momentum resolved tunneling into a short quantum wire

Gregory A. Fiete, Jiang Qian, Yaroslav Tserkovnyak +1 more

Motivated by recent tunneling experiments in the parallel wire geometry, we calculate results for momentum resolved tunneling into a short one-dimensional wire, containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to $N=4$ electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. We also investigate the limit of large $N$ using a Luttinger-liquid type analysis. We consider the low-density regime, where the system is close to the Wigner crystal limit, and where the energy scale for spin excitations can be much lower than for charge excitations, and we consider temperatures intermediate between the relevant spin energies and charge excitations, as well as temperatures below both energy scales.

arXiv:cond-mat/0501684•Physical Review B•Jul 8, 2005•49 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

Quantum interference and spin-charge separation in a disordered Luttinger liquid

A. G. Yashenkin, I. V. Gornyi, A. D. Mirlin +1 more

We study the influence of spin on the quantum interference of interacting electrons in a single-channel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional-bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of inelastic electron-electron interactions and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.

arXiv:0808.1093•Physical Review B•Nov 7, 2008•12 citations

Tunneling into a nonequilibrium Luttinger liquid with impurity

Stéphane Ngo Dinh, Dmitry Bagrets, A. D. Mirlin

We evaluate tunneling rates into/from a voltage $(U)$ biased quantum wire containing a weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}U$. The tunneling rates are split in two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge ${E}_{F}\ensuremath{-}U$ is negative if Coulomb interaction is not too strong.

arXiv:0910.3917•Physical Review B•Feb 24, 2010•31 citations
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.
We consider momentum resolved tunneling between a Luttinger liquid and a two dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a non-interacting one dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when γρ=0γ_ρ=0γρ​=0. We argue that this measurement provides an important experimental signature of spin-charge separation.
We consider momentum resolved tunneling between a Luttinger liquid and a two-dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two-dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a noninteracting one-dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when ${\ensuremath{\gamma}}_{\ensuremath{\rho}}=0$. We argue that this measurement provides an important experimental signature of spin-charge separation.
Motivated by recent tunneling experiments in the parallel wire geometry, we calculate results for momentum resolved tunneling into a short one-dimensional wire, containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to N=4N=4N=4 electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. We also investigate the limit of large NNN using a Luttinger-liquid type analysis. We consider the low-density regime, where the system is close to the Wigner crystal limit, and where the energy scale for spin excitations can be much lower than for charge excitations, and we consider temperatures intermediate between the relevant spin energies and charge excitations, as well as temperatures below both energy scales.
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 the influence of spin on the quantum interference of interacting electrons in a single-channel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional-bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of inelastic electron-electron interactions and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.
We evaluate tunneling rates into/from a voltage (U)(U)(U) biased quantum wire containing a weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}U$. The tunneling rates are split in two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge ${E}_{F}\ensuremath{-}U$ is negative if Coulomb interaction is not too strong.