Interacting electrons in a semiconducting carbon nanotube dot: A 2-band approach

Roy, Mervyn; Maksym, P. A.

doi:10.1016/j.physe.2007.09.160

Cited by 4 publications

(6 citation statements)

References 3 publications

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“…(2) gives the intraband effective interaction. We ignore the interband interaction because its effect is small [3,4]. In this case the band index acts like a pseudospin and our Hamiltonian is block diagonal in both the total electron spin and the pseudospin.…”

Section: Effective Mass Description Of a Nanotube Dotmentioning

confidence: 99%

Calculation of the few-electron states in semiconductor carbon nanotube quantum dots by exact diagonalisation

Roy

Maksym

2010

J. Phys.: Conf. Ser.

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Abstract. The 3 and 4-electron states of a gated semiconducting carbon nanotube quantum dot are calculated by exact diagonalisation of a modified effective mass Hamiltonian. A typical nanotube quantum dot is examined and the few-electron states are Wigner molecule-like. The exact diagonalisation method and the rate of convergence of the calculation are discussed. IntroductionIn a gated semiconductor nanotube (SNT) quantum dot, electrons or holes are confined electrostatically. The occupancy of this type of dot can be precisely controlled and, importantly, a semiconducting nanotube dot can be completely emptied of electrons. This means that SNT quantum dots are excellent systems in which to study the physics of a few interacting particles.Like traditional semiconductor quantum dots, SNT dots behave like artificial atoms but there are some differences that make semiconducting carbon nanotube dots unique. First, the SNT bandstructure is unusual, primarily because nanotubes are rolled graphene sheets and the nanotube bandstructure is derived from that of graphene. Second, the geometry of SNT dots is also unusual: the nanotube length is very much greater than its diameter and so SNT dots are quasi-1 dimensional objects. In Ref. [1] we demonstrated that the electronic correlation was large in a large proportion of all physically accessible SNT quantum dots. Taken together with the tube geometry, this means that SNT dots are ideal systems in which to observe quasi-1D Wigner (or all-electron) molecules.In our approach, we describe the few particle states in a SNT quantum dot with a 1 dimensional, 2 band, effective mass Hamiltonian [1]. However, because the electron correlation is strong and the few-particle states are Wigner molecule-like, care must be taken in the calculation of the electron states: exact diagonalisation, or configuration interaction (CI), techniques must be used to include the correlation effects correctly. In this paper we give an overview of our effective mass description of SNT dots and then discuss the exact diagonalisation scheme in detail. We examine the convergence of the few-electron states and discuss a way of truncating the full CI basis which improves the convergence of the few-electron energy.

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Section: Effective Mass Description Of a Nanotube Dotmentioning

confidence: 99%

Calculation of the few-electron states in semiconductor carbon nanotube quantum dots by exact diagonalisation

Roy

Maksym

2010

J. Phys.: Conf. Ser.

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“…One dimensional nanotube (NT) dots are, however, very different to the 2D semiconductor dots that have been used to study effects such as the formation of all electron (Wigner) molecules [2,3] and electronic shell filling analogous to that observed in atoms [4]. The reduced dimensionality of NT dots alters the form of the effective Coulomb interaction [5], it affects the allowed symmetries of the states [6] and the types of confinement that can be engineered.In particular, NT dots can be used to fabricate room temperature single electron transistors because of the large single particle level spacings which can be engineered [7]. They are promising candidates for spin qubits [8] and also exhibit interesting shell filling effects due to the approximately degenerate [8] K, K ′ sub-bands.…”

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“…So far we have considered the CB constructed from states near K but we can also write down equivalent equations for states near K ′ . The K and K ′ CBs are coupled by the Coulomb interaction, but the effective interband interaction is small [5] and we neglect it. Our Hamiltonian is block diagonal in the total spin.…”

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confidence: 99%

“…This effective interaction includes the effect of both the NT band structure and the cylindrical geometry of the tube. Here, we neglect the interband Coulomb scattering because its effect on the N -particle ground-state energy is small [5]. In this case, the band index acts simply as an extra label by which states can be distinguished (a "pseudospin").…”

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Semiconducting carbon nanotube quantum dots: Calculation of the interacting electron states by exact diagonalisation

Roy

Maksym

2009

Europhys. Lett.

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Abstract. -In semiconducting carbon nanotube quantum dots that contain a few interacting electrons the electron-electron correlation is always important. The states of up to 6 interacting electrons in such a dot are calculated by exact diagonalisation of a 2-band, effective mass Hamiltonian. The addition energy and the few electron density are investigated for a wide range of dots with different physical properties and, in a large proportion of these dots, the electrons are found to form Wigner molecules.Introduction. -It is now possible to form one dimensional quantum dots from high quality semiconducting carbon nanotubes [1]. Quantum dots are tunable artificial atoms that provide an ideal laboratory for exploring the physics of atoms and molecules and have many potential applications, for example in quantum computing. As dots can be used to controllably confine small numbers of charge carriers they have stimulated much interest in the quantum states of a few interacting electrons. One dimensional nanotube (NT) dots are, however, very different to the 2D semiconductor dots that have been used to study effects such as the formation of all electron (Wigner) molecules [2,3] and electronic shell filling analogous to that observed in atoms [4]. The reduced dimensionality of NT dots alters the form of the effective Coulomb interaction [5], it affects the allowed symmetries of the states [6] and the types of confinement that can be engineered.In particular, NT dots can be used to fabricate room temperature single electron transistors because of the large single particle level spacings which can be engineered [7]. They are promising candidates for spin qubits [8] and also exhibit interesting shell filling effects due to the approximately degenerate [8] K, K ′ sub-bands. This has been examined in detail in metallic NT dots [9,10] but, only recently has it been possible to accurately measure the addition energy [1] or the differential conductance [11] of semiconducting NT dots.In the Coulomb blockade [4] regime the occupancy of all types of NT dot can be controlled to the level of a single electron. Importantly, however, semiconductor NT

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2-electron Wigner molecules in carbon nanotube quantum dots: Excited states

Roy¹,

Maksym²

2010

Physica E: Low-dimensional Systems and Nanostructures

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Interacting electrons in a semiconducting carbon nanotube dot: A 2-band approach

Cited by 4 publications

References 3 publications

Calculation of the few-electron states in semiconductor carbon nanotube quantum dots by exact diagonalisation

Calculation of the few-electron states in semiconductor carbon nanotube quantum dots by exact diagonalisation

Semiconducting carbon nanotube quantum dots: Calculation of the interacting electron states by exact diagonalisation

2-electron Wigner molecules in carbon nanotube quantum dots: Excited states

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