We investigate the electronic transport properties of a ferromagnet/normal/ferromagnet junction on the surface of a topological insulator with a gate voltage exerted on the normal segment. It is found that the conductance oscillates with the width of normal segment and gate voltage, and the maximum of conductance gradually decreases while the minimum of conductance approaches zero as the width increases. The conductance can be controlled by tuning the gate voltage like a spin field-effect transistor. It is found that the magnetoresistance ratio can be very large, and can also be negative owing to the anomalous transport. In addition, when there exists a magnetization component in the surface plane, it is shown that only the component parallel to the junction interface has an influence on the conductance.

We study new types of Josephson junctions composed of helical p-wave superconductors with and -pairing symmetries using quasi-classical Green’s functions with generalized Riccati parametrization. The junctions can host rich ground states: π phase, 0 + π phase, φ0 phase and φ phase. The phase transition can be tuned by rotating the magnetization in the ferromagnetic interface. We present the phase diagrams in the parameter space formed by the orientation of the magnetization or by the magnitude of the interfacial potentials. The selection rules for the lowest order current which are responsible for the formation of the rich phases are summarized from the current-phase relations based on the numerical calculation. We construct a Ginzburg–Landau type of free energy for the junctions with d-vectors and the magnetization, which not only reveals the interaction forms of spin-triplet superconductivity and ferromagnetism, but can also directly lead to the selection rules. In addition, the energies of the Andreev bound states and the novel symmetries in the current-phase relations are also investigated. Our results are helpful both in the prediction of novel Josephson phases and in the design of quantum circuits.

We demonstrate that zero-energy Majorana bound state, in the ferromagnetic insulator (FI)-superconductor (SC) junction formed on the edge of two-dimensional topological insulator, exhibits three types of spin-triplet pairing correlations and its spin polarization direction is position independent in ferromagnetic insulator. When an electron is injected with a spin (anti-)parallel to this direction, equal-spin Andreev reflection exhibits the widest (narrowest) resonance peak. Similar behaviour is found when the coupling between two Majorana bound states in a FI-SC-FI junction is invoked, though an additional weak spin-singlet pairing correlation is generated. These signatures can readily facilitate the experimental detection of spin-triplet correlations and spin polarization of Majorana bound states. PACS numbers: 74.45.+c, 74.78.Na, 74.20.RP, 74.25.F-Introduction-. Majorana fermions are exotic particles that are their own antiparticles [1], and have been suggested to exist as Majorana bound states (MBSs) in condensed matter systems [2]. Two spatially separated MBSs can define a qubit that stores information non-locally and is robust against local sources of decoherence [5], which together with its non-Abelian statistics [3, 4] make it exhibit potential applications in quantum information and quantum computation [6]. Several theoretical proposals were raised to realize such states, like topological insulators proximity-coupled with superconductors [7-10], semiconductor-superconductor heterostructures [11][12][13][14], and magnetic-atomic chains on superconductors [15]. Recently, intensive theoretical and experimental efforts have been made to verify the existence of MBSs in these systems by employing charge transport properties [16][17][18][19][20][21][22][23][24][25][26][27][28]. However, few attention has been paid to the spin related phenomena of MBSs [29][30][31][32]. Furthermore, the in-depth classification of spin-triplet correlations and spin polarization of MBSs are yet unclear [33,34], especially those in twodimensional topological insulator systems. And these characteristics are closely related to the resulting unusual spinrelated transport, like the intriguing selective equal-spin Andreev reflection [29,31].

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