Electronic Tunnelling in Superconductor/Quantum-Dot Josephson Junction Side-Coupled to Majorana Nanowire

Chi, Feng; Jia, Qiang-Sheng; Liu, Jia; Gao, Qingguo; Yi, Zichuan; Li, Liming

doi:10.3390/coatings13030612

Cited by 5 publications

(8 citation statements)

References 44 publications

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“…where the first term in the right of Equation ( 1) is for the QD with quantized energy level ε d and creation (annihilation) operator d † (d). The second and third terms are for the superconductors acting as leads with energy gap ∆, quasi-particle energy ε kβσ (β = L/R, spin σ =↑ / ↓, wave vector k) and creation (annihilation) operator C † kβσ (C kβσ ) [6,8,47,48]. The forth term in the right side of Equation ( 1) stands for hopping between the QD and the superconductors with amplitude V kβ and phase factor φ β .…”

Section: Model and Methodsmentioning

confidence: 99%

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Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire

Gao,

Zhang,

et al. 2023

Nanomaterials

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The dc Josephson current is generated from phase difference between two superconductors separated by a mesoscopic thin film (Josephson junction) without external bias voltage. In the presence of a temperature gradient across the superconductors, a thermal phase is induced under the condition of open circuit. This is very similar to the Seebeck effect in the usual thermoelectric effect, and the thermal phase is thus named as thermophase Seebeck coefficient (TPSC). Here we find obvious enhancement and sign change of the TPSC unique to the Josephson junction composing of two superconductors connected to a semiconductor quantum dot (QD), which is additionally side-coupled to a nanowire hosting Majorana bound states (MBSs), the system denoted by S-MQD-S. These result arise from the newly developed states near the Fermi level of the superconductors due to the QD-MBS hybridization when the dot level is within the superconducting gap. The sign change of the TPSC provides a strong evidence of the existence of MBSs, and is absent if the QD is coupled to regular fermion, such as another QD (system denoted by S-DQD-S). We show that the magnitude and sign of the TPSC are sensitive to the physical quantities including interaction strength between the QD and MBSs, direct overlap between the MBSs, system equilibrium temperature, as well as hopping amplitude between the QD and the superconductors. The obtained results are explained with the help of the current-carrying density of the states (CCDOS), and may be useful in interdisciplinary research areas of Josephson and Majorana physics.

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Section: Model and Methodsmentioning

confidence: 99%

“…The forth term in the right side of Equation ( 1) stands for hopping between the QD and the superconductors with amplitude V kβ and phase factor φ β . The last term in the right of Equation ( 1) is for the MBSs formed at the ends of the nanowire and their interaction with the QD [46][47][48][49][50],…”

Section: Model and Methodsmentioning

confidence: 99%

Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire

Gao,

Zhang,

et al. 2023

Nanomaterials

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“…It is known that the difference between the phase factors gives rise to the Josephson current. As for the middle Majorana junction, we assume that both of the MBSs on it interact with the electrons on the QD, and [33,34,42,44]…”

Section: Model and Methodsmentioning

confidence: 99%

“…Although the magnitude of the Josephson current in the abovementioned two-terminal Josephson junctions can be efficiently adjusted, the current's period is difficult to alter. In view of this issue and those previously published works concerning multiple-terminal Josephson junctions [14,[41][42][43], here, we propose a QD/Majorana-trijunction hybridized device to control both the magnitude and the period of the Josephson current. We emphasize that the proposed device is within the reach of present-day nanofabrication technologies, and the unique functions brought about by the additional third junction are difficult to realize in those two-terminal setups.…”

Section: Introductionmentioning

confidence: 96%

Tunable Josephson Current through a Semiconductor Quantum Dot Hybridized to Majorana Trijunction

Gao,

Zhang

2023

Coatings

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We investigate theoretically the Josephson current through one semiconductor quantum dot (QD) coupled to triple nanowires (junctions) with Majorana bound states (MBSs) prepared at their ends. We find that not only the strength but also the period of the Josephson current flowing between the left and right Josephson junctions via the dot can be fully controlled in terms of the third junction side-coupled to the QD. When the phase factor is zero in the third junction, which acts as a current regulator, the Josephson current is a 2π-period function of the difference in phases of the left and right junctions. Now, the magnitude of the current is suppressed by hybridization between the QD and the regulator junction. The period of the current becomes 4π under the condition of nonzero phase factor in the regular junction, and thus either the magnitude or the sign (flow direction) of the current can be controlled in this trijunction device. This is difficult to realize in the usual tow-terminal structure. It is also found that the direct overlap between the MBSs in the regulator junction generally enhances the current’s amplitude, but those in the left and right Majorana junctions suppress the current. The above results are explained with the help of the device’s energy diagram and the current carrying density of states (CCDOS) and might be applied for adjusting the current density in the superconducting coated conductors technologies.

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“…The presence of MBSs requires the conductance to take the value of

, which is measured through the QD via normal leads [ 15 ]. Several theoretical designs based on either single QDs–TSNWs or double QD interferometer–TSNW setups [ 16 ] have been considered in order to probe the MBSs via transport properties such as (thermal) [ 16 , 17 , 18 , 19 , 20 , 21 ] conductance [ 16 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 ], current noise [ 22 , 35 , 36 , 37 , 38 ] and Josephson current [ 39 , 40 ]. Details on the experimental detection of MBSs via transport characteristics measurements have been reported elsewhere [ 8 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ].…”

Section: Introductionmentioning

confidence: 99%

Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States

et al. 2023

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We theoretically analyze phonon-assisted tunneling transport in a quantum dot side connected to a Majorana bound state in a topological superconducting nanowire. We investigate the behavior of the current through the dot, for a range of experimentally relevant parameters, in the presence of one long-wave optical phonon mode. We consider the current-gate voltage, the current-bias voltage and the current-dot–Majorana coupling characteristics under the influence of the electron–phonon coupling. In the absence of electron–phonon interaction, the Majorana bound states suppress the current when the gate voltage matches the Fermi level, but the increase in the bias voltage counteracts this effect. In the presence of electron–phonon coupling, the current behaves similarly as a function of the renormalized gate voltage. As an added feature at large bias voltages, it presents a dip or a plateau, depending on the size of the dot–Majorana coupling. Lastly, we show that the currents are most sensitive to, and depend non-trivially on the parameters of the Majorana circuit element, in the regime of low temperatures combined with low voltages. Our results provide insights into the complex physics of quantum dot devices used to probe Majorana bound states.

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Electronic Tunnelling in Superconductor/Quantum-Dot Josephson Junction Side-Coupled to Majorana Nanowire

Cited by 5 publications

References 44 publications

Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire

Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire

Tunable Josephson Current through a Semiconductor Quantum Dot Hybridized to Majorana Trijunction

Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States

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