The Spin‐Dependent Coupling in the Hybrid Quantum Dot–Majorana Wire System

Abstract

The transport properties of a quantum dot coupled to two metallic contacts and side‐coupled to a topological superconductor wire hosting Majorana zero energy modes (Majorana wire) have been studied. The spin‐dependent tunneling amplitude between quantum dot and Majorana wire has been assumed. The polarization of tunneling amplitudes causes the polarization of spin‐dependent zero‐bias conductance, but the total conductance of a quantum dot depends very weakly on the polarization of tunneling amplitudes. The complex behavior of the zero‐bias anomaly of conductance in the presence of an external magnetic field is shown. The zero‐bias conductance peaks at high external magnetic field can be the fingerprint of the presence of Majorana fermions.

Electronic Transport Through Double Quantum Dot Coupled to Majorana Bound States and Ferromagnetic Leads

“…The Hamiltonian of the studied system shown in Figure 1, which is composed of the DQD each of which connected to the left and right ferromagnetic leads and to one mode of the MBSs, can be written as the following form [21,24],…”

“…The last term in Eq. 1 is for the MBSs realized at opposite ends of the TSNW and their couplings to the DQD [21,24],…”

“…For example, Baranger and his co-author proved that the value of the conductance in a single QD, which is coupled to the left and right leads, will remain at half of its quantum value e 2 /2h, regardless of the positions of the dot's energy levels [21]. If both the spin directions of electrons on the QD are coupled to the MBSs [20,[22][23][24] with different hybridization amplitudes, which depend on the spin-orbit interaction length in the TSNW, they will interfere with each other through the MBSs and then will change the current significantly. For electron-hole symmetry, the zero-bias conductance is 3e 2 /2h which is the sum of e 2 /2h for one spin direction and e 2 /h for the opposite spin direction.…”

“…Single QD has been successfully inserted in between the ferromagnetic leads [32], and abnormal sign change of the TMR may be realized in experiments. There are also investigations on the Kondo effect in a single QD coupled to ferromagnetic leads [24] and showed that the impacts of the ferromagnetism on the leads will induce more interesting result due to the presence of the MBSs [33]. As a natural extension, we study properties of the electrical current and TMR in a DQD coupled to ferromagnetic leads and MBSs (see Figure 1).…”

“…As a natural extension, we study properties of the electrical current and TMR in a DQD coupled to ferromagnetic leads and MBSs (see Figure 1). Different from some previous work [31,33], we consider that the case that spin-up and spin-down electrons on the QD are coupled to the MBSs with different hybridization amplitudes [20,[22][23][24]. Our results show that the sign and the amplitude of the TMR can be adjusted in a large regime by variation of several system parameters, especially the spin polarization of the DQD-MBS hybridization, which is useful in detection of the MBSs, as well as in the design of spintronic devices or information processes.…”