Interplay of the Kondo Effect and Strong Spin-Orbit Coupling in Multihole Ultraclean Carbon Nanotubes

Cleuziou, Jean-Pierre; Nguyen, Ngoc-Viet; Florens, Serge; Wernsdorfer, Wolfgang

doi:10.1103/physrevlett.111.136803

Cited by 37 publications

(38 citation statements)

References 33 publications

(99 reference statements)

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“…3(h)). For this shell we find ∆ SO = 120-170 µeV, ∆ KK = 50-100 µeV, |g orb | = 2.4-2.9 and exchange splitting J = 50-200 µeV, which are consistent with values previously reported [14,15,[28][29][30][31] the tangent of the midpoint of the right segment in the SEM image within experimental uncertainty.…”

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confidence: 91%

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

et al. 2016

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We demonstrate experimentally that non-collinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near four-fold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.Controlling local magnetic fields on the nanoscale is currently of strong interest in quantum information and spintronics. Local fields are important for operating spin quantum bits, spin-filters and realizing topological states of matter. Several approaches to address the spin degree of freedom in this manner have been pursued involving techniques based on on-chip strip lines [1], nuclear spin ensembles [2], micromagnetic stray [3][4][5] and exchange fields [6,7], g-factor engineering [8] and spin-orbit coupling [9,10].A particularly interesting situation arises in double dots coupled to a central superconducting electrode. Here the control of the local spin directions, inducing non-collinear spin projection axes for the two dots, is predicted to give rise to unconventional superconductivity [11], poor man's Majorana physics [12] and novel schemes for transport based spin-entanglement detection of Cooper pairs [13].These geometries can favorably be realized with carbon nanotubes when utilizing spin-orbit interactions (SOI) [14][15][16][17][18][19] to control [20] and filter spins [21]. In contrast to other quantum dot systems (e.g. semiconducting nanowires), the effect of SOI on the four-fold degenerate energy spectrum (due to spin s =↑, ↓ and valley τ = K, K ) of nanotubes is well-understood [22] and gives rise to spin-orbit magnetic fields oriented along the nanotube axis. In this Letter we demonstrate the realization of non-collinear magnetic fields using the spinorbit fields in a bent carbon nanotube double quantum dot. The non-collinearity of the fields originates from the geometry-defined angle between the two quantum dot tube segments. Furthermore, the spin alignment can be controlled and rotated by applying an external magnetic field.In this paper we present data from the hybrid carbon nanotube device [23] shown in Fig. 1(a). Nanotubes are grown using chemical vapor deposition [24] (CVD) on a doped Si chip with a 0.5 µm thermal oxide cap. In the growth process nanotubes are bound to the substrate in random orientations by van der Waals forces. Many of the tubes are in this way fixated in curved configurations. The nanotubes are subsequently located using scanning electron microscopy (SEM) at an acceleration voltage of 1.5 kV and metal leads are defined by e-beam lithography at 20 kV. The two na...

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confidence: 91%

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

et al. 2016

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“…Unconventional Kondo physics in nanotubes was first experimentally studied by Jarillo-Herrero et al (2005b) and later by Jarillo-Herrero et al (2005a), , , Makarovski and Finkelstein (2008), Cleuziou et al (2013), and Schmid et al (2015). 25 For all but the last two experiments, the spin-orbit interaction was thought to be negligible and thus …”

Section: Methodsmentioning

confidence: 99%

“…Instead, values as large as 3.4 meV have been reported, with several devices yielding results up to 16 times larger than expected (Jhang et al, 2010;Steele et al, 2013). Other experiments have found Δ SO within the expected range Cleuziou et al, 2013;Lai, Churchill, and Marcus, 2014). Furthermore, in some cases the calculations even predict the wrong sign for both couplings Δ 0 SO and Δ 1 SO (Kuemmeth et al, 2008;Jespersen, GroveRasmussen, Paaske et al, 2011).…”

Section: H Open Questionsmentioning

confidence: 98%

“…The observed behavior in both the Kondo and mixed-valence regimes has been reproduced by numerical renormalization group (NRG) calculations within an SU(4) Anderson model for various lead couplings, supporting this interpretation . Figure 44(c) systematically studies the transition from SU(4) to SU(2) Kondo physics in a clean narrow-gap device (Cleuziou et al, 2013). The crossover is measured across seven shells, thereby varying both the spin-orbit interaction (decreases with filling, see Fig.…”

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Quantum transport in carbon nanotubes

et al. 2015

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Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike in conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and valley freedom. The interplay between the two is the focus of this review. The energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are explained, together with their consequences for transport measurements through nanotube quantum dots. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behavior. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, open questions for the field are also clearly stated. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a low level.

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“…4a and a cross-section is shown in the middle panel. Because spin and orbital degrees of freedom are degenerated, two channels contribute to transport, and Kondo resonance emerges at every filling factor, N = 1, 2 and 3 electrons [4][5][6][7] . At odd filling, the channels are half transmitted (T 1 = T 2 = 0.5), yielding the same conductance G Q as in the SU(2) symmetry.…”

Section: The Kondo Effectmentioning

confidence: 99%

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

et al. 2015

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Interacting quantum many-body systems constitute a fascinating research field because they form quantum liquids with remarkable properties and universal behaviour The idea is that they behave as an ensemble of non-interacting 'quasi-particles'. However, non-equilibrium properties have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi liquid theory extended to the non-equilibrium regime in a zero-dimensional system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) (ref. The Kondo effect19 is a typical example of a quantum manybody effect, where a localized spin is screened by the surrounding conduction electrons at low temperature to form a unique correlated ground state. The Kondo state is described well by the Fermi liquid theory at equilibrium 1,9 , which makes it an ideal testbed to go beyond equilibrium. To unveil the universal behaviour of nonequilibrium Fermi liquid 11 , we have used the current fluctuations or shot noise in a Kondo-correlated nanotube quantum dot 18 . When electrons are transmitted through this system, the scattering induces the shot noise, which sensitively reflects the nature of the quasi-particles 20 , as shown in the upper panel of Fig. 1a. A remarkable prediction of the non-equilibrium Fermi liquid theory is that the residual interaction between quasi-particles creates an additional scattering of two quasi-particles which enhances the noise (see the lower panel of Fig. 1a) 10,12-15 . This two-particle scattering is characterized by an effective charge e * larger than e (electron charge). This value, closely related to the Wilson ratio, is universal for the Fermi liquid in the Kondo regime as it depends only on the symmetry group of the system [13][14][15] . Although some aspects of Kondo-associated noise have been reported 8,16,17 , a rigorous, selfconsistent treatment in a regime where universal results apply is at the core of the present work. Actually, by investigating the same nanotube quantum dot in the spin degenerate SU(2) Kondo regime and in the spin-orbit degenerate SU(4) regime, the noise is proved to contain distinct signatures of these two symmetries, confirming theoretical developments of Fermi liquid theory out of equilibrium.In our experiment, we measured the conductance and current noise through a carbon nanotube quantum dot grown by chemical vapour deposition 21 . Iron catalyst was deposited on an oxidized undoped silicon wafer and exposed to 10 mbar of acetylene for 9 s at 900• C. The nanotube was connected with a Pd(6 nm)/Al(70 nm) bilayer deposited by e-gun evaporation. The distance between the contacts is 400 nm and a side gate electrode is deposited to tune the potential of the quantum dot (see Fig. 1b). A magnetic field of 0.08 T is applied to suppress superconductivity of the contacts. To measure accurately the shot noise, our sample is connected to a resonant (2.58 MHz) LC circuit thermalized at the mixing chambe...

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Interplay of the Kondo Effect and Strong Spin-Orbit Coupling in Multihole Ultraclean Carbon Nanotubes

Cited by 37 publications

References 33 publications

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

Quantum transport in carbon nanotubes

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

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