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Register a new userMajorana dc Josephson current mediated by a quantum dot
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The Josephson supercurrent through the hybrid Majorana--quantum dot--Majorana junction is investigated. We particularly analyze the effect of spin-selective coupling between the Majorana and quantum dot states, which emerges only in the topological phase and will influence the current through bent junctions and/or in the presence of magnetic fields in the quantum dot. We find that the characteristic behaviors of the supercurrent through this system are quite counterintuitive, remarkably differing from the resonant tunneling, e.g., through the similar (normal phase) superconductor--quantum dot--superconductor junction. Our analysis is carried out under the influence of full set-up parameters and for both the $2pi$ and $4pi$ periodic currents. The present study is expected to be relevant to future exploration of applications of the Majorana-nanowire circuits.
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A quantum dot weakly coupled to two normal metal leads exhibits resonant transmission when one of the dot energy levels lies within the applied bias window. But when the quantum dot is sidecoupled to the transport channel, transmission in the channel is suppressed when a dot energy lies in the bias window. A steady current can also be driven in a transport channel by connecting it to superconducting reservoirs and applying a Josephson phase difference instead of a voltage bias. An interesting question is to investigate the transport across quantum dot connected to two superconductors maintained at a superconducting phase difference. To incorporate the geometry where quantum dot is sidecoupled, we consider a quantum dot with two sites connected to the superconductors in two geometrical configurations: (A) the one where both the sites are in the transport channel and (B) the other where only one site is in the transport channel and the second site sidecoupled. We find that both the configurations show resonant transmission for Josephson current and give qualitatively same result when the onsite energies of the two sites in the dot are equal. The two configurations exhibit distinct Josephson current characteristics when the onsite energies of the two sites are equal in magnitude and opposite in sign. We understand the obtained results. The systems studied are within the reach of current experiments.
We study a time-reversal-invariant topological superconductor island hosting spatially separated Majorana Kramers pairs, with weak tunnel couplings to two s-wave superconducting leads. When the topological superconductor island is in the Coulomb blockade regime, we predict that a Josephson current flows between the two leads due to a non-local transfer of Cooper pairs mediated by the Majorana Kramers pairs. Interestingly, we find that the sign of the Josephson current is controlled by the joint parity of all four Majorana bound states on the island. Consequently, this parity-controlled Josephson effect can be used for qubit read-out in Majorana-based quantum computing.
The demonstration of the non-Abelian properties of Majorana bound states (MBS) is a crucial step toward topological quantum computing. We theoretically investigate how Majorana fusion rules manifest themselves in the current-voltage characteristics of a topological Josephson junction. The junction is built on U-shaped quantum spin Hall edges and hosts a Majorana qubit formed by four MBS. Owing to Majorana fusion rules, inter- and intra-edge couplings among adjacent MBS provide two orthogonal components in the rotation axis of the Majorana qubit. We show that the interplay of the dynamics of the superconductor phase difference and the Majorana qubit governs the Josephson effect. Strikingly, we identify sequential jumps of the voltage across the junction with increasing DC current bias without external AC driving. Its role is replaced by the intrinsic Rabi oscillations of the Majorana qubit. This phenomenon, DC Shapiro steps, is a manifestation of the non-trivial fusion rules of MBS.
The Josephson current through an Aharonov-Bohm (AB) interferometer, in which a quantum dot (QD) is situated on one arm and a magnetic flux $Phi$ threads through the ring, has been investigated. With the existence of the magnetic flux, the relation of the Josephson current and the superconductor phase is complex, and the system can be adjusted to $pi$ junction by either modulating the magnetic flux or the QDs energy level $varepsilon_d$. Due to the electron-hole symmetry, the Josephson current $I$ has the property $I(varepsilon_d,Phi)=I(-varepsilon_d,Phi+pi)$. The Josephson current exhibits a jump when a pair of Andreev bound states aligns with the Fermi energy. The condition for the current jump is given. In particularly, we find that the position of the current jump and the position of the maximum value of the critical current $I_c$ are identical. Due to the interference between the two paths, the critical current $I_c$ versus the QDs level $varepsilon_d$ shows a typical Fano shape, which is similar to the Fano effect in the corresponding normal device. But they also show some differences. For example, the critical current never reaches zero for any parameters, while the current in the normal device can reach zero at the destruction point.
We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multi-electron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tuneability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system.
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