We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin–orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to $50\%$, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.

Electronic transport through T-shaped double quantum dots (TDQDs) connected to normal metallic leads is studied theoretically by using a nonequilibrium Green’s function method. It is assumed that the Coulomb interaction exists only in the central QD (QD-1) sandwiched between the leads, and it is absent in the other reference QD (QD-2) side-coupled to QD-1. We also consider the impacts of Majorana bound states (MBSs), which are prepared at the opposite ends of a topological superconductor nanowire (hereafter called a Majorana nanowire) connected to QD-2, on the electrical current and differential conductance. Our results show that by the combined effects of the Coulomb interaction in QD-1 and the MBSs, a negative differential conductance (NDC) effect emerges near the zero-bias point, where MBSs play significant roles. Now, the electrical current decreases despite the increasing bias voltage. The NDC is prone to occur under conditions of low temperature, and both of the two QDs’ energy levels are resonant to the leads’ zero Fermi energy. Its magnitude, which is characterized by a peak-to-valley ratio, can be enhanced up to 3 by increasing the interdot coupling strength, and it depends on the dot-MBS hybridization strength nonlinearly. This prominent NDC combined with the previously found zero-bias anomaly (ZBA) of the differential conductance is useful in designing novel quantum electric devices, and it may also serve as an effective detection means for the existence of MBSs, which is still a challenge in solid-state physics.

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 $2\pi$-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 $4\pi$ 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.

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.

We study the electron tunneling (ET) and local Andreev reflection (AR) processes in a quantum dot (QD) coupled to the left and right ferromagnetic leads with noncollinear ferromagnetisms. In particular, we consider that the QD is also side-coupled to a nanowire hosting Majorana bound states (MBSs) at its ends. Our results show that when one mode of the MBSs is coupled simultaneously to both spin-up and spin-down electrons on the QD, the height of the central peak is different from that if the MBS is coupled to only one spin component electrons. The ET and AR conductances, which are mediated by the dot–MBS hybridization, strongly depend on the angle between the left and right magnetic moments in the leads. Interaction between the QD and the MBSs will result in sign change of the angle-dependent tunnel magnetoresistance. This is very different from the case when the QD is coupled to regular fermonic mode, and can be used for detecting the existence of MBSs, a current challenge in condensed matter physics under extensive investigations.

We study theoretically the Josephson diode effect (JDE) realized in a system composed of parallel-coupled double quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of the proximity-caused superconductivity, strong Rashba spin-orbit interaction and Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arisen from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respective to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and can hardly occur in system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, and depends on the overlap amplitude between the MBSs and the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabitication technologies and may find practical use in interdisciplinary field of Majorana and Josephson physics.