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/0606214 · Physical Review B

Non-Fermi-liquid behavior in transport across carbon nanotube quantum dots

Leonhard Mayrhofer, Milena Grifoni

Published Sep 19, 2006• 22 citations
arXivHTMLPDF

Abstract

A low energy theory for nonlinear transport in finite-size single-wall carbon nanotubes, based on a microscopic model for the interacting ${p}_{z}$ electrons and successive bosonization, is presented. Due to the multiple degeneracy of the energy spectrum diagonal as well as off-diagonal (coherences) elements of the reduced density matrix contribute to the nonlinear transport. A four-electron periodicity with a characteristic ratio between adjacent peaks, as well as nonlinear transport features, in quantitative agreement with recent experiments, are predicted.

DOI
10.1103/physrevb.74.121403

Related papers

Strongly interacting Luttinger liquid states as those inherent in carbon nanotubes

Igor N. Karnaukhov, Victor I. Kolomytsev, Cees G. H. Diks

The electronic transport properties of single-walled nanotubes (SWNTs) are characterized by the critical exponent $\ensuremath{\Theta}$, describing the behavior of the single-particle spectral function near the Fermi energy as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{\ensuremath{\Theta}}$. Experimentally obtained $\ensuremath{\Theta}$ values have been reported in the range of 0.43--0.48 for metallic SWNTs. However, these values are much larger than the theoretical upper limit of the exponent, ${\ensuremath{\Theta}}_{\mathrm{max}}=1∕8$, for the Hubbard model. Here, we show that the observed electronic transport properties can be explained by taking into account a specific hard-core Coulomb interaction. For a many-body system with a hard-core potential, we analytically calculate the critical exponents using the Bethe ansatz and conformal field theory. We find strongly interacting Luttinger liquid states that are characterized by large $\ensuremath{\Theta}$ values, consistent with the empirical results, suggesting that these states are actually realized in metallic SWNTs and organic conductors.

Physical Review B•Mar 8, 2007•1 citation

Theory of nonequilibrium transport in the SU(N) Kondo regime

Christophe Mora, Pavel Vitushinskiy, X. Leyronas +2 more

Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an $\text{SU}(N)$ Kondo model, focusing on the case $N=4$ relevant to carbon nanotube dots. We show that for general $N$, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.

arXiv:0906.2791•Physical Review B•Oct 23, 2009•88 citations

On quantum optical properties of single-walled carbon nanotube

Zhenyu Guo, Zhirui Gong, C. P. Sun

We study quantum optical properties of the single-walled carbon nanotube (SWCNT) by introducing the effective interaction between the quantized electromagnetic field and the confined electrons in the SWCNT. Our purpose is to explore the quantum natures of electron transport in the SWCNT by probing its various quantum optical properties relevant to quantum coherence, such as the interference of the scattered and emitted photons, and the bunching and anti-bunching of photons which are characterized by the higher order coherence functions. In the strong field limit, we study the interband Rabi oscillation of electrons driven by a classical light. We also investigate the possible lasing mechanism in superradiation of coherent electrons in a SWCNT driven by a light pump or electron injection, which generate electron population inversion in the higher energy-band of SWCNT.

arXiv:0904.2231•Apr 15, 2009•0 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

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

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
A low energy theory for nonlinear transport in finite-size single-wall carbon nanotubes, based on a microscopic model for the interacting pz{p}_{z}pz​ electrons and successive bosonization, is presented. Due to the multiple degeneracy of the energy spectrum diagonal as well as off-diagonal (coherences) elements of the reduced density matrix contribute to the nonlinear transport. A four-electron periodicity with a characteristic ratio between adjacent peaks, as well as nonlinear transport features, in quantitative agreement with recent experiments, are predicted.
The electronic transport properties of single-walled nanotubes (SWNTs) are characterized by the critical exponent $\ensuremath{\Theta}$, describing the behavior of the single-particle spectral function near the Fermi energy as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{\ensuremath{\Theta}}$. Experimentally obtained $\ensuremath{\Theta}$ values have been reported in the range of 0.43--0.48 for metallic SWNTs. However, these values are much larger than the theoretical upper limit of the exponent, ${\ensuremath{\Theta}}_{\mathrm{max}}=1∕8$, for the Hubbard model. Here, we show that the observed electronic transport properties can be explained by taking into account a specific hard-core Coulomb interaction. For a many-body system with a hard-core potential, we analytically calculate the critical exponents using the Bethe ansatz and conformal field theory. We find strongly interacting Luttinger liquid states that are characterized by large $\ensuremath{\Theta}$ values, consistent with the empirical results, suggesting that these states are actually realized in metallic SWNTs and organic conductors.
Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an SU(N)\text{SU}(N)SU(N) Kondo model, focusing on the case N=4N=4N=4 relevant to carbon nanotube dots. We show that for general NNN, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.
We study quantum optical properties of the single-walled carbon nanotube (SWCNT) by introducing the effective interaction between the quantized electromagnetic field and the confined electrons in the SWCNT. Our purpose is to explore the quantum natures of electron transport in the SWCNT by probing its various quantum optical properties relevant to quantum coherence, such as the interference of the scattered and emitted photons, and the bunching and anti-bunching of photons which are characterized by the higher order coherence functions. In the strong field limit, we study the interband Rabi oscillation of electrons driven by a classical light. We also investigate the possible lasing mechanism in superradiation of coherent electrons in a SWCNT driven by a light pump or electron injection, which generate electron population inversion in the higher energy-band of SWCNT.
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.
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.
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.