Orbital hyperfine interaction and qubit dephasing in carbon nanotube quantum dots

Csiszár, Gábor; Pályi, András

doi:10.1103/physrevb.90.245413

Cited by 8 publications

(13 citation statements)

References 63 publications

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“…In a nanowire with free carriers (electrons) and localized spins, such as spins of atomic nuclei, these two subsystems are coupled by the hyperfine interaction. [24][25][26] With parameters typical for semiconducting nanowires, this interaction is weak on the scale of the electronic Fermi energy. It can then be recast as the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction, [27][28][29][30] the electron mediated pairwise interaction between localized spins (see also Ref.…”

Section: Introductionmentioning

confidence: 99%

Antiferromagnetic nuclear spin helix and topological superconductivity inC13nanotubes

et al. 2015

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We investigate the RKKY interaction arising from the hyperfine coupling between localized nuclear spins and conduction electrons in interacting 13 C carbon nanotubes. Using the Luttinger liquid formalism, we show that the RKKY interaction is sublattice dependent, consistent with the spin susceptibility calculation in noninteracting carbon nanotubes, and it leads to an anti-ferromagnetic nuclear spin helix in finite-size systems. The transition temperature reaches up to tens of millikelvins, due to a strong boost by a positive feedback through the Overhauser field from ordered nuclear spins. Similar to GaAs nanowires, the formation of the helical nuclear spin order gaps out half of the conduction electrons, and is therefore observable as a reduction of conductance by a factor of two in a transport experiment. The nuclear spin helix leads to a density wave combining spin and charge degrees of freedom in the electron subsystem, resulting in synthetic spin-orbit interaction, which induces non-trivial topological phases. As a result, topological superconductivity with Majorana fermion bound states can be realized in the system in the presence of proximity-induced superconductivity without the need of fine tuning the chemical potential. We present the phase diagram as function of system parameters, including the pairing gaps, the gap due to the nuclear spin helix, and the Zeeman field perpendicular to the helical plane.

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Section: Introductionmentioning

confidence: 99%

Antiferromagnetic nuclear spin helix and topological superconductivity inC13nanotubes

et al. 2015

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“…As discussed in the main text, the reason is as follows. Hyperfine interaction in carbon nanotubes acts on both the spin and valley degrees of freedom [34,35]. Therefore it mixes the three energetically aligned states |T b1 , |T b2 and |M 2 , resulting in new eigenstates |M 2 , |M 3 , |M 4 ( Fig.…”

Section: Magnetic Field Dependencementioning

confidence: 99%

“…3(b). We now include hyperfine interaction, which acts on both spin and valley degrees of freedom [34,35]. At B = 0, the three energetically aligned states |T b1 , |T b2 , and |M 2 mix to form new eigenstates |M 2 , |M 3 , |M 4 , each overlapping with |S and therefore contributing to the current via spinindependent inelastic interdot tunnelling.…”

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confidence: 99%

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube

et al. 2017

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The decay of spin-valley states is studied in a suspended carbon nanotube double quantum dot via leakage current in Pauli blockade and via dephasing and decoherence of a qubit. From the magnetic field dependence of the leakage current, hyperfine and spin-orbit contributions to relaxation from blocked to unblocked states are identified and explained quantitatively by means of a simple model. The observed qubit dephasing rate is consistent with the hyperfine coupling strength extracted from this model and inconsistent with dephasing from charge noise. However, the qubit coherence time, although longer than previously achieved, is probably still limited by charge noise in the device.The co-existence in carbon nanotubes of spin and valley angular momenta opens a host of possibilities for quantum information [1][2][3][4], coherent coupling to mechanics [5,6], and on-chip entanglement [7,8]. Spin-orbit coupling [9] provides electrical control, but introduces a relaxation channel. However, measurements of dephasing and decoherence [10][11][12] show that spin and valley qubit states couple surprisingly strongly to lattice nuclear spins and to uncontrolled electric fields, e.g. from thermal switchers. Realising these possibilities requires such effects to be mitigated. Here we study leakage current in a Pauli blockaded double quantum dot to identify spin-orbit and hyperfine contributions to spin-valley relaxation [3,13,14]. By suspending the nanotube, we decouple it from the substrate [11]. Measuring a spinvalley qubit defined in the double dot, we find dephasing and decoherence rates nearly independent of temperature, and show that charge noise cannot explain the observed dephasing, supporting the conclusion that despite the low density of 13 C spins, hyperfine interaction causes rapid dephasing in nanotubes [10,11].The measured device [ Fig. 1(a-b)] is a carbon nanotube suspended by stamping between two contacts and over five gate electrodes G1-G5 [3,[15][16][17]. Gate voltages V G1 − V G5 , together with Schottky barriers at the contacts, define a double quantum dot potential. The dot potentials are predominantly controlled by gates G1 (for the left dot) and G4-5 (for the right dot), while the interdot tunnel barrier is controlled by gates G2-3. For fast manipulation, gates G1 and G5 are connected via tees to waveform generator outputs and a vector microwave source. The device is measured in a magnetic field B = (B X , B Y , B Z ), with Z chosen along the nanotube and X normal to the substrate. Experiments were in a dilution refrigerator at 15 mK unless stated.To map charge configurations of the double quantum dot, we measure the current I through the nanotube with source-drain bias V SD = 8 mV applied between the contacts [ Fig. 1(c)]. As a function of V G1 and V G4 , the honeycomb Coulomb peak pattern is characteristic of a double quantum dot, with honeycomb vertices marking transitions between particular electron or hole occupations [18]. A horizontal stripe of suppressed current around V G4 = 200 mV indicates depl...

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“…Therefore, NMR in graphene samples was demonstrated for 13 C specially enriched samples [23]. On the other hand, from the theoretical point of view, several studies analyzed the nuclear spin-lattice relaxation time and the Knight shift related to the electron -nuclear spin interaction in graphene samples [28,30,34,35].…”

Section: Discussionmentioning

confidence: 99%

NMR parameters in gapped graphene systems

2016

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We calculate the nuclear spin-lattice relaxation time and the Knight shift for the case of gapped graphene systems. Our calculations consider both the massive and massless gap scenarios. Both the spin-lattice relaxation time and the Knight shift depend on temperature, chemical potential, and the value of the electronic energy gap. In particular, at the Dirac point, the electronic energy gap has stronger effects on the system nuclear magnetic resonance parameters in the case of the massless gap scenario. Differently, at large values of the chemical potential, both gap scenarios behave in a similar way and the gapped graphene system approaches a Fermi gas from the nuclear magnetic resonance parameters point of view. Our results are important for nuclear magnetic resonance measurements that target the 13 C active nuclei in graphene samples.

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Orbital hyperfine interaction and qubit dephasing in carbon nanotube quantum dots

Cited by 8 publications

References 63 publications

Antiferromagnetic nuclear spin helix and topological superconductivity inC13nanotubes

Antiferromagnetic nuclear spin helix and topological superconductivity inC13nanotubes

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube

NMR parameters in gapped graphene systems

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