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:1402.5626 · Physical Review B

Fractional shot noise in partially gapped Tomonaga-Luttinger liquids

Eyal Cornfeld, Izhar Neder, Eran Sela

Published Mar 23, 2015• 24 citations
arXivHTMLPDF

Abstract

We depict a family of one-dimensional systems where one can create and detect fractional charges. These charges are produced via interacting one-dimensional conductors connected to noninteracting leads. At certain electron densities, some distinct modes develop an energy gap due to electron-electron interactions. This gap allows for tunneling events inside the conductor, which generate electric current noise. The resulting fractional noise's Fano factor depends only on the identification of the gapped mode, and is insensitive to additional interactions in the conductor. These effects can be realized in either quantum wires or edges of quantum Hall systems.

DOI
10.1103/physrevb.91.115427

Related papers

Fractional charge in the noise of Luttinger liquid systems (Invited Paper)

Björn Trauzettel, Inès Safi A, Fabrizio Dolcini +1 more

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g the Luttinger liquid interaction parameter, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections of plasmons at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.

arXiv:cond-mat/0505722•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 23, 2005•1 citation

Current Noise in Non-Chiral Luttinger Liquids: Appearance of Fractional Charge

Fabrizio Dolcini

The current noise of a voltage‐biased interacting quantum wire connected to leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency ω relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g the electron interaction strength, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also to Andreev‐type reflections at the contacts. The frequency dependence of the noise needs to be analyzed to extract the fractional charge e* = eg of the bulk excitations.

AIP conference proceedings•Jan 1, 2005•0 citations

Fractional Charge Determination via Quantum Shot Noise Measurements

Moty Heiblum

Charge excitations in a two dimensional electron gas, under a quantizing magnetic field and in the fractional quantum Hall effect regime, flow in one dimensional-like strips along the edges of the sample. These excitations (quasiparticles) may be independent or condense into an interacting chiral Luttinger liquid. Adding a backscattering potential, which reflects a forward propagating quasiparticle to a backward propagating one, partitions the stream of quasiparticles and induces quantum shot noise. The noise is proportional to quasiparticles charge and may be affected by their mutual interactions. The dependence of the determined charge on the temperature, excitation energy, and partitioning will be describes for a few fractional states, revealing in some cases a universal behavior.

arXiv:0912.4868•WORLD SCIENTIFIC eBooks•Aug 1, 2010•5 citations

Tunneling and quantum noise in one-dimensional Luttinger liquids

Claudio Chamon, Denise E. Freed, Xiao-Gang Wen

We study nonequilibrium noise in the transmission current through barriers in one-dimensional Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or nonequilibrium) contour. We show that the charges tend to reorganize as a dipole gas,which we use to describe the tunneling statistics. The dipole-gas picture allows us to have a unified description of the low-frequency shot noise and the high-frequency Josephson noise. The correlation between the charges within a dipole (intradipole) contributes to the high-frequency Josephson noise, which has an algebraic singularity at \ensuremath{\omega}=${\mathit{e}}^{\mathrm{*}}$V/\ensuremath{\Elzxh}, whereas the correlations between dipoles (interdipole) are responsible for the low-frequency noise. We show that an independent or noninteracting dipole approximation gives a Poisson distribution for the locations of the dipole centers of mass, which gives a flat noise spectrum at low frequencies and corresponds to uncorrelated shot noise. Including interdipole interactions gives an additional 1/${\mathit{t}}^{2}$ correlation between the tunneling events that results in an \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity, but its form should remain \ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} to all orders in perturbation theory. A counting argument also suggests that the leading algebraic singularity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$ should be \ensuremath{\propto}\ensuremath{\Vert}\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$${\mathrm{\ensuremath{\Vert}}}^{2\mathit{g}\mathrm{\ensuremath{-}}1}$ to all orders in perturbation theory.

arXiv:cond-mat/9408064•Physical review. B, Condensed matter•Jan 15, 1995•157 citations

Appearance of Fractional Charge in the Noise of Nonchiral Luttinger Liquids

Björn Trauzettel, Inès Safi A, Fabrizio Dolcini +1 more

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in the presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency omega relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g is the Luttinger liquid interaction parameter, and L is the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but it also depends on Andreev-type reflections at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=eg of the bulk excitations.

arXiv:cond-mat/0402479•Physical Review Letters•Jun 4, 2004•70 citations

Detection of Spin Entanglement via Spin-Charge Separation in Crossed Tomonaga-Luttinger Liquids

Alexander Schroer, Bernd Braunecker, A. Levy Yeyati +1 more

We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.

arXiv:1404.4524•Physical Review Letters•Dec 23, 2014•10 citations
We depict a family of one-dimensional systems where one can create and detect fractional charges. These charges are produced via interacting one-dimensional conductors connected to noninteracting leads. At certain electron densities, some distinct modes develop an energy gap due to electron-electron interactions. This gap allows for tunneling events inside the conductor, which generate electric current noise. The resulting fractional noise's Fano factor depends only on the identification of the gapped mode, and is insensitive to additional interactions in the conductor. These effects can be realized in either quantum wires or edges of quantum Hall systems.
The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g the Luttinger liquid interaction parameter, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections of plasmons at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.
The current noise of a voltage‐biased interacting quantum wire connected to leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency ω relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g the electron interaction strength, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also to Andreev‐type reflections at the contacts. The frequency dependence of the noise needs to be analyzed to extract the fractional charge e* = eg of the bulk excitations.
Charge excitations in a two dimensional electron gas, under a quantizing magnetic field and in the fractional quantum Hall effect regime, flow in one dimensional-like strips along the edges of the sample. These excitations (quasiparticles) may be independent or condense into an interacting chiral Luttinger liquid. Adding a backscattering potential, which reflects a forward propagating quasiparticle to a backward propagating one, partitions the stream of quasiparticles and induces quantum shot noise. The noise is proportional to quasiparticles charge and may be affected by their mutual interactions. The dependence of the determined charge on the temperature, excitation energy, and partitioning will be describes for a few fractional states, revealing in some cases a universal behavior.
We study nonequilibrium noise in the transmission current through barriers in one-dimensional Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or nonequilibrium) contour. We show that the charges tend to reorganize as a dipole gas,which we use to describe the tunneling statistics. The dipole-gas picture allows us to have a unified description of the low-frequency shot noise and the high-frequency Josephson noise. The correlation between the charges within a dipole (intradipole) contributes to the high-frequency Josephson noise, which has an algebraic singularity at \ensuremath{\omega}=e∗{\mathit{e}}^{\mathrm{*}}e∗V/\ensuremath{\Elzxh}, whereas the correlations between dipoles (interdipole) are responsible for the low-frequency noise. We show that an independent or noninteracting dipole approximation gives a Poisson distribution for the locations of the dipole centers of mass, which gives a flat noise spectrum at low frequencies and corresponds to uncorrelated shot noise. Including interdipole interactions gives an additional 1/t2{\mathit{t}}^{2}t2 correlation between the tunneling events that results in an \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity, but its form should remain \ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} to all orders in perturbation theory. A counting argument also suggests that the leading algebraic singularity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$ should be \ensuremath{\propto}\ensuremath{\Vert}\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$${\mathrm{\ensuremath{\Vert}}}^{2\mathit{g}\mathrm{\ensuremath{-}}1}$ to all orders in perturbation theory.
The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in the presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency omega relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g is the Luttinger liquid interaction parameter, and L is the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but it also depends on Andreev-type reflections at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=eg of the bulk excitations.
We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.