Kondo effects in carbon nanotubes: From SU(4) to SU(2) symmetry

Jong Soo Lim, Mahn-Soo Choi, M. Y. Choi, Rosa López, Ramón Aguado

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube (NT). The K- K′ double orbital degeneracy of a NT, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudospin. Screening of this pseudospin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. In order to have such an exotic Kondo effect it is crucial that this orbital quantum number be conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may occur. Here we investigate in detail the role of mixing and asymmetry in the tunneling coupling and analyze how different Kondo effects, from an SU(4) symmetry to a two-level SU(2) Kondo effect, emerge depending on the mixing and/or asymmetry. We use four different theoretical approaches to address both the linear and nonlinear conductance for different values of external magnetic field. Our results point out clearly the experimental conditions to observe exclusively SU(4) Kondo physics. Although we focus on NT quantum dots (QDs) our results also apply to vertical quantum dots. We also mention that a finite amount of orbital mixing corresponds, in pseudospin language, to having noncollinear leads with respect to the orbital "magnetization" axis which defines the two pseudospin orientations in the carbon nanotube QD. In this sense, some of our results are also relevant to the problem of a Kondo QD coupled to noncollinear ferromagnetic leads.

Original languageEnglish
Article number205119
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume74
Issue number20
DOIs
Publication statusPublished - 2006 Dec 5

Fingerprint

Kondo effect
Carbon Nanotubes
Carbon nanotubes
carbon nanotubes
Semiconductor quantum dots
orbitals
quantum dots
symmetry
Nanotubes
nanotubes
asymmetry
Single electron transistors
single electron transistors
Graphite
Band structure
Graphene
quantum numbers
conservation
Magnetization
Conservation

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Kondo effects in carbon nanotubes : From SU(4) to SU(2) symmetry. / Lim, Jong Soo; Choi, Mahn-Soo; Choi, M. Y.; López, Rosa; Aguado, Ramón.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 74, No. 20, 205119, 05.12.2006.

Research output: Contribution to journalArticle

Lim, Jong Soo ; Choi, Mahn-Soo ; Choi, M. Y. ; López, Rosa ; Aguado, Ramón. / Kondo effects in carbon nanotubes : From SU(4) to SU(2) symmetry. In: Physical Review B - Condensed Matter and Materials Physics. 2006 ; Vol. 74, No. 20.
@article{c8a00acf36b242c78fe8aa2d3d9977d4,
title = "Kondo effects in carbon nanotubes: From SU(4) to SU(2) symmetry",
abstract = "We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube (NT). The K- K′ double orbital degeneracy of a NT, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudospin. Screening of this pseudospin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. In order to have such an exotic Kondo effect it is crucial that this orbital quantum number be conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may occur. Here we investigate in detail the role of mixing and asymmetry in the tunneling coupling and analyze how different Kondo effects, from an SU(4) symmetry to a two-level SU(2) Kondo effect, emerge depending on the mixing and/or asymmetry. We use four different theoretical approaches to address both the linear and nonlinear conductance for different values of external magnetic field. Our results point out clearly the experimental conditions to observe exclusively SU(4) Kondo physics. Although we focus on NT quantum dots (QDs) our results also apply to vertical quantum dots. We also mention that a finite amount of orbital mixing corresponds, in pseudospin language, to having noncollinear leads with respect to the orbital {"}magnetization{"} axis which defines the two pseudospin orientations in the carbon nanotube QD. In this sense, some of our results are also relevant to the problem of a Kondo QD coupled to noncollinear ferromagnetic leads.",
author = "Lim, {Jong Soo} and Mahn-Soo Choi and Choi, {M. Y.} and Rosa L{\'o}pez and Ram{\'o}n Aguado",
year = "2006",
month = "12",
day = "5",
doi = "10.1103/PhysRevB.74.205119",
language = "English",
volume = "74",
journal = "Physical Review B-Condensed Matter",
issn = "1098-0121",
publisher = "American Institute of Physics Publising LLC",
number = "20",

}

TY - JOUR

T1 - Kondo effects in carbon nanotubes

T2 - From SU(4) to SU(2) symmetry

AU - Lim, Jong Soo

AU - Choi, Mahn-Soo

AU - Choi, M. Y.

AU - López, Rosa

AU - Aguado, Ramón

PY - 2006/12/5

Y1 - 2006/12/5

N2 - We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube (NT). The K- K′ double orbital degeneracy of a NT, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudospin. Screening of this pseudospin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. In order to have such an exotic Kondo effect it is crucial that this orbital quantum number be conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may occur. Here we investigate in detail the role of mixing and asymmetry in the tunneling coupling and analyze how different Kondo effects, from an SU(4) symmetry to a two-level SU(2) Kondo effect, emerge depending on the mixing and/or asymmetry. We use four different theoretical approaches to address both the linear and nonlinear conductance for different values of external magnetic field. Our results point out clearly the experimental conditions to observe exclusively SU(4) Kondo physics. Although we focus on NT quantum dots (QDs) our results also apply to vertical quantum dots. We also mention that a finite amount of orbital mixing corresponds, in pseudospin language, to having noncollinear leads with respect to the orbital "magnetization" axis which defines the two pseudospin orientations in the carbon nanotube QD. In this sense, some of our results are also relevant to the problem of a Kondo QD coupled to noncollinear ferromagnetic leads.

AB - We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube (NT). The K- K′ double orbital degeneracy of a NT, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudospin. Screening of this pseudospin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. In order to have such an exotic Kondo effect it is crucial that this orbital quantum number be conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may occur. Here we investigate in detail the role of mixing and asymmetry in the tunneling coupling and analyze how different Kondo effects, from an SU(4) symmetry to a two-level SU(2) Kondo effect, emerge depending on the mixing and/or asymmetry. We use four different theoretical approaches to address both the linear and nonlinear conductance for different values of external magnetic field. Our results point out clearly the experimental conditions to observe exclusively SU(4) Kondo physics. Although we focus on NT quantum dots (QDs) our results also apply to vertical quantum dots. We also mention that a finite amount of orbital mixing corresponds, in pseudospin language, to having noncollinear leads with respect to the orbital "magnetization" axis which defines the two pseudospin orientations in the carbon nanotube QD. In this sense, some of our results are also relevant to the problem of a Kondo QD coupled to noncollinear ferromagnetic leads.

UR - http://www.scopus.com/inward/record.url?scp=33751519284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751519284&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.74.205119

DO - 10.1103/PhysRevB.74.205119

M3 - Article

AN - SCOPUS:33751519284

VL - 74

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 20

M1 - 205119

ER -