Four-Electron Shell Structures and an Interacting Two-Electron System in Carbon-Nanotube Quantum Dots

Moriyama, Satoshi; Fuse, Tomoko; Suzuki, Masaki; Aoyagi, Yoshinobu; Ishibashi, Koji

doi:10.1103/physrevlett.94.186806

Cited by 112 publications

(128 citation statements)

References 20 publications

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“…Near zero magnetic field the sign of || / dB dV g changes every time an electron is added (or removed), indicating that CCW and CW states are filled alternately. Similar addition sequences were explained in the past by repulsive electron-electron interactions driving electrons to occupy different orbits [2][3][4][5][6][7]9,26 (Fig. 3b).…”

mentioning

confidence: 71%

“…With increasing || B the spectrum splits into pairs of CCW and CW states (going down and up in energy respectively), each pair having a smaller internal spin splitting. Indications of approximate four-fold degeneracy have been observed in high-field measurements of electron addition spectra [2][3][4][5][6][7][8][9][10] and inelastic cotunneling 4,10 in nanotube QDs. However, in previous experiments disorder-induced splitting of the orbital degeneracy and electron-electron interactions in multi-electron QDs have masked the intrinsic symmetries at low energies.…”

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confidence: 99%

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Coupling of spin and orbital motion of electrons in carbon nanotubes

Kuemmeth

Ilani

Ralph

et al. 2008

Nature

558

761

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Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion leading to the wellknown fine structure in their spectra. The electronic states in defect-free carbon nanotubes (NTs) are widely believed to be four-fold degenerate 1-10 , due to independent spin and orbital symmetries, and to also possess electron-hole symmetry 11 . Here we report measurements demonstrating that in clean NTs the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin-orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and anti-parallel alignment for holes. Our measurements are consistent with recent theories 12,13 that predict the existence of spin-orbit coupling in curved graphene and describe it as a spin-dependent topological phase in NTs. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of qubits in NTs and providing a mechanism for all-electrical control of spins 14 in NTs.Carbon-based systems are promising candidates for spin based applications such as spinqubits [14][15][16][17][18][19] and spintronics 20-23 as they are believed to have exceptionally long spin coherence times due to weak spin-orbit interactions and the absence of nuclear spin in the 12 C atom. Carbon NTs may play a particularly interesting role in this context because in addition to spin they offer a unique two-fold orbital degree of freedom that can also be used for quantum manipulation. The latter arises from the two equivalent dispersion cones (K and K') in graphene, which lead to doubly-degenerate electronic orbits that encircle the nanotube circumference in a clockwise (CW) and counter-clockwise (CCW) fashion 24 (Fig 1a). Together, the two-fold spin degeneracy and two-fold orbital degeneracy are generally assumed to yield a four-fold-degenerate electronic energy spectrum in clean NTs. Understanding the fundamental symmetries of this spectrum is at the heart of successful manipulation of these quantum degrees of freedom.A powerful way to probe the symmetries is by confining the carriers to a quantum dot (QD) and applying a magnetic field parallel to the tube axis, || B 4,5,8,10,24,25 . The confinement creates bound states and the field interrogates their nature by coupling independently to their spin and orbital moments. In the absence of spin-orbit coupling, such a measurement should yield for a defect-free NT the energy spectrum shown in figure 1b. At 0 || = B the NT spectrum should be four-fold degenerate. With increasing || B the spectrum splits into pairs of CCW and CW states

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mentioning

confidence: 71%

mentioning

confidence: 99%

Coupling of spin and orbital motion of electrons in carbon nanotubes

Kuemmeth

Ilani

Ralph

et al. 2008

Nature

558

761

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“…17, we now take into account the K-K ′ orbital degeneracy commonly observed 20,28,29,30,31,32 in SWNTs, by considering a two-orbitals model i.e. hamiltonian (2) with d ∈ {K, K ′ } and ξ K ′ σ = ξ Kσ .…”

Section: Quantum Dot With a Doubly-degenerate Levelmentioning

confidence: 99%

“…Refs. 20,28,29,30,31,32), one can solve this discrepancy. In this framework, we expect non-regular MR(V g ) oscillations if the experiment is repeated on a larger V g −range.…”

Section: Introductionmentioning

confidence: 99%

Magnetoresistance of a quantum dot with spin-active interfaces

Cottet

Choi

2006

Phys. Rev. B

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We study the zero-bias magnetoresistance (MR) of an interacting quantum dot connected to two ferromagnetic leads and capacitively coupled to a gate voltage source Vg. We investigate the effects of the spin-activity of the contacts between the dot and the leads by introducing an effective exchange field in an Anderson model. This spin-activity makes easier negative MR effects, and can even lead to a giant MR effect with a sign tunable with Vg. Assuming a twofold orbital degeneracy, our approach allows to interpret in an interacting picture the MR(Vg) measured by S. Sahoo et al. [Nature Phys. 2, 99 (2005)] in single wall carbon nanotubes with ferromagnetic contacts. If this experiment is repeated on a larger Vg−range, we expect that the MR(Vg) oscillations are not regular like in the presently available data, due to Coulomb interactions.

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“…All electrical transport measurements were carried out at a base temperature of 30 mK and electron temperature of ∼240 mK, allowing us to use the results for one sample as a reference for the other under the same measurement conditions [25]. We measured the dc current I through a device by applying dc bias voltage V sd with a dc voltage source and current amplifier.…”

Section: Electrical Propertiesmentioning

confidence: 99%

Fabrication of quantum-dot devices in graphene

Moriyama

Morita

Watanabe³

et al. 2010

Science and Technology of Advanced Materials

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We describe our recent experimental results on the fabrication of quantum-dot devices in a graphene-based two-dimensional system. Graphene samples were prepared by micromechanical cleavage of graphite crystals on a SiO 2 /Si substrate. We performed micro-Raman spectroscopy measurements to determine the number of layers of graphene flakes during the device fabrication process. By applying a nanofabrication process to the identified graphene flakes, we prepared a double-quantum-dot device structure comprising two lateral quantum dots coupled in series. Measurements of low-temperature electrical transport show the device to be a series-coupled double-dot system with varied interdot tunnel coupling, the strength of which changes continuously and non-monotonically as a function of gate voltage.

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Four-Electron Shell Structures and an Interacting Two-Electron System in Carbon-Nanotube Quantum Dots

Cited by 112 publications

References 20 publications

Coupling of spin and orbital motion of electrons in carbon nanotubes

Coupling of spin and orbital motion of electrons in carbon nanotubes

Magnetoresistance of a quantum dot with spin-active interfaces

Fabrication of quantum-dot devices in graphene

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