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/0205344 · Physical Review Letters

Narrow-Gap Luttinger Liquid in Carbon Nanotubes

Leonid S Levitov, Alexei M. Tsvelik

Published Jan 2, 2003• 62 citations
arXivHTMLPDF

Abstract

Electron interactions reinforce minigaps induced in metallic nanotubes by an external field and turn the gap field dependence into a universal power law. An exactly solvable Gross-Neveau model with an SU(4) symmetry is derived for neutral excitations near half filling. Charge excitations, described by a sine-Gordon perturbation of Luttinger liquid theory, are composite solitons formed by the charged and neutral fields with two separate length scales. Charge compressibility at finite density, evaluated in terms of intersoliton interaction, exhibits a crossover from overlapping to nonoverlapping soliton state. Implications for the Coulomb blockade measurements are discussed.

DOI
10.1103/physrevlett.90.016401

Related papers

Interaction induced dimerization in zigzag single wall carbon nanotubes

Sam T. Carr, Alexander O. Gogolin, A. A. Nersesyan

We derive a low-energy effective model of metallic zigzag carbon nanotubes at half filling. We show that there are three important features characterizing the low-energy properties of these systems: the long-range Coulomb interaction, umklapp scattering, and an explicit dimerization generated by interactions. The ratio of the dimerization induced gap and the Mott gap induced by the umklapp interactions is dependent on the radius of the nanotube and can drive the system upon increasing dimerization strength from a Haldane spin-liquid phase through a quantum phase transition with $\mathrm{SU}{(2)}_{1}$ quantum symmetry to a dimerized phase. We consider the physical properties of the phases on either side of this transition, which should be relevant for realistic nanotubes.

arXiv:0707.3784•Physical Review B•Dec 21, 2007•12 citations

Field-induced SU(4) to SU(2) Kondo crossover in a half-filling nanotube dot: Spectral and finite-temperature properties

Yoshimichi Teratani, Rui Sakano, T. HATA +4 more

We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a ${T}^{2}$ coefficient of conductance becomes zero at quarter-filling, whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU(4) scaling behavior at ${\ensuremath{\mu}}_{B}B<{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$ and it exhibits the SU(2) universality at ${\ensuremath{\mu}}_{B}B\ensuremath{\gg}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$, where ${T}_{K}^{\mathrm{SU}(4)}$ is the SU(4) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for ${\ensuremath{\mu}}_{B}B\ensuremath{\gtrsim}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$.

arXiv:2003.12715•Physical review. B./Physical review. B•Oct 6, 2020•17 citations

Measuring Fractional Charge in Carbon Nanotubes

Cristina Bena B, Smitha Vishveshwara, Leon Balents +1 more

The Luttinger model of the one-dimensional Fermi gas is the cornerstone of modern understanding of interacting electrons in one dimension. In fact, the enormous class of systems whose universal behavior is adiabatically connected to it are now deemed Luttinger liquids. Recently, it has been shown that metallic single-walled carbon nanotubes are almost perfectly described by the Luttinger Hamiltonian. Indeed, strongly non-Fermi liquid behavior has been observed in a variety of DC transport experiments, in very good agreement with theoretical predictions. Here, we describe how fractional quasiparticle charge, a fundamental property of Luttinger liquids, can be observed in impurity-induced shot noise.

arXiv:cond-mat/0008188•APS March Meeting Abstracts•Aug 11, 2000•1 citation

Field-Enhanced Kondo Correlations in a Half-Filling Nanotube Dot: Evolution of an SU(N) Fermi-Liquid Fixed Point

Yoshimichi Teratani, Rui Sakano, Ryo Fujiwara +5 more

Carbon nanotube quantum dot has four-fold degenerate one-particle levels, which bring a variety to the Kondo effects taking place in a wide tunable-parameter space. We theoretically study an emergent SU(2) symmetry that is suggested by recent magneto-transport measurements, carried out near two electrons filling. It does not couple with the magnetic field, and emerges in the case where the spin and orbital Zeeman splittings cancel each other out in two of the one-particle levels among four. This situation seems to be realized in the recent experiment. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs as magnetic field increases at two impurity-electrons filling. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. Furthermore, we consider how the singlet ground state evolves during such a crossover. Specifically, we reexamine the SU(N) Kondo singlet for M impurity-electrons filling in the limit of strong exchange interactions. We find that the nondegenerate Fermi-liquid fixed point of Nozières and Blandin can be described as abosonic Perron–Frobenius vector for M composite pairs, each of which consists of one impurity-electron and one conduction-hole. This interpretation in terms of the Perron–Frobenius theorem can also be extended to the Fermi-liquid fixed-point without the SU(N) symmetry.

arXiv:1607.02305•Journal of the Physical Society of Japan•Sep 1, 2016•13 citations

Quantum Entanglement in Carbon Nanotubes

Cristina Bena B, Smitha Vishveshwara, Leon Balents +1 more

With the surge of research in quantum information, the issue of producing entangled states has gained prominence. Here, we show that judiciously bringing together two systems of strongly interacting electrons with vastly differing ground states-the gapped BCS superconductor and the Luttinger liquid-can result in quantum entanglement. We propose three sets of measurements involving single-walled metallic carbon nanotubes which have been shown to exhibit Luttinger liquid physics, to test our claim and as nanoscience experiments of interest in and of themselves.

arXiv:cond-mat/0202102•Physical Review Letters•Jun 26, 2002•164 citations

Zigzag carbon nanotubes with generic electron-electron interactions

Judith E. Bunder, James Murray Hill

A Hamiltonian is derived for a zigzag carbon nanotube with an arbitrary number of weak electron-electron charge and spin interactions, which become significant in ultraclean systems. The renormalization group and bosonization are used to determine the ground-state phase diagram. Our phase diagram contains some exotic phases which have not previously been predicted in carbon nanotubes with physically possible interaction profiles. Phases of the undoped case include Mott insulators and a variety of density wave states. In the doped case a Tomanaga-Luttinger liquid is possible.

Physical Review B•Oct 6, 2009•5 citations
Electron interactions reinforce minigaps induced in metallic nanotubes by an external field and turn the gap field dependence into a universal power law. An exactly solvable Gross-Neveau model with an SU(4) symmetry is derived for neutral excitations near half filling. Charge excitations, described by a sine-Gordon perturbation of Luttinger liquid theory, are composite solitons formed by the charged and neutral fields with two separate length scales. Charge compressibility at finite density, evaluated in terms of intersoliton interaction, exhibits a crossover from overlapping to nonoverlapping soliton state. Implications for the Coulomb blockade measurements are discussed.
We derive a low-energy effective model of metallic zigzag carbon nanotubes at half filling. We show that there are three important features characterizing the low-energy properties of these systems: the long-range Coulomb interaction, umklapp scattering, and an explicit dimerization generated by interactions. The ratio of the dimerization induced gap and the Mott gap induced by the umklapp interactions is dependent on the radius of the nanotube and can drive the system upon increasing dimerization strength from a Haldane spin-liquid phase through a quantum phase transition with SU(2)1\mathrm{SU}{(2)}_{1}SU(2)1​ quantum symmetry to a dimerized phase. We consider the physical properties of the phases on either side of this transition, which should be relevant for realistic nanotubes.
We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures TTT can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a T2{T}^{2}T2 coefficient of conductance becomes zero at quarter-filling, whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields BBB. We find that the conductance shows the SU(4) scaling behavior at ${\ensuremath{\mu}}_{B}B<{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$ and it exhibits the SU(2) universality at ${\ensuremath{\mu}}_{B}B\ensuremath{\gg}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$, where TKSU(4){T}_{K}^{\mathrm{SU}(4)}TKSU(4)​ is the SU(4) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for ${\ensuremath{\mu}}_{B}B\ensuremath{\gtrsim}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$.
The Luttinger model of the one-dimensional Fermi gas is the cornerstone of modern understanding of interacting electrons in one dimension. In fact, the enormous class of systems whose universal behavior is adiabatically connected to it are now deemed Luttinger liquids. Recently, it has been shown that metallic single-walled carbon nanotubes are almost perfectly described by the Luttinger Hamiltonian. Indeed, strongly non-Fermi liquid behavior has been observed in a variety of DC transport experiments, in very good agreement with theoretical predictions. Here, we describe how fractional quasiparticle charge, a fundamental property of Luttinger liquids, can be observed in impurity-induced shot noise.
Carbon nanotube quantum dot has four-fold degenerate one-particle levels, which bring a variety to the Kondo effects taking place in a wide tunable-parameter space. We theoretically study an emergent SU(2) symmetry that is suggested by recent magneto-transport measurements, carried out near two electrons filling. It does not couple with the magnetic field, and emerges in the case where the spin and orbital Zeeman splittings cancel each other out in two of the one-particle levels among four. This situation seems to be realized in the recent experiment. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs as magnetic field increases at two impurity-electrons filling. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. Furthermore, we consider how the singlet ground state evolves during such a crossover. Specifically, we reexamine the SU(N) Kondo singlet for M impurity-electrons filling in the limit of strong exchange interactions. We find that the nondegenerate Fermi-liquid fixed point of Nozières and Blandin can be described as abosonic Perron–Frobenius vector for M composite pairs, each of which consists of one impurity-electron and one conduction-hole. This interpretation in terms of the Perron–Frobenius theorem can also be extended to the Fermi-liquid fixed-point without the SU(N) symmetry.
With the surge of research in quantum information, the issue of producing entangled states has gained prominence. Here, we show that judiciously bringing together two systems of strongly interacting electrons with vastly differing ground states-the gapped BCS superconductor and the Luttinger liquid-can result in quantum entanglement. We propose three sets of measurements involving single-walled metallic carbon nanotubes which have been shown to exhibit Luttinger liquid physics, to test our claim and as nanoscience experiments of interest in and of themselves.
A Hamiltonian is derived for a zigzag carbon nanotube with an arbitrary number of weak electron-electron charge and spin interactions, which become significant in ultraclean systems. The renormalization group and bosonization are used to determine the ground-state phase diagram. Our phase diagram contains some exotic phases which have not previously been predicted in carbon nanotubes with physically possible interaction profiles. Phases of the undoped case include Mott insulators and a variety of density wave states. In the doped case a Tomanaga-Luttinger liquid is possible.