We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the hetero-structures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity without breaking time-reversal symmetry is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the interlayer interaction is repulsive, both of which can be satisfied in realistic systems. Edge channels are studied in a tight-binding model numerically, and the several predictions on experiments are also given. PACS numbers: 74.45.+c, 74.50.+r, 74.20.Rp The topological aspects of the electronic states in solids have recently attracted intensive interest. In addition to the quantum Hall effect [1,2], the anomalous Hall effect [3], spin Hall effect [4], and topological insulators (TI's) [5,6] turn out to be topological phenomena driven by the Berry curvatures [7] in momentum and/or real spaces. Especially, the topological insulators are realized in the time-reversal (T ) symmetric systems with the relativistic spin-orbit interaction (SOI), and are characterized by the Z 2 topological indices. On the other hand, the concept of the topological superconductors (TSC) or superfluidity (TSF) has been proposed in the context of 3 He [8]. Recently the p-wave superconductivity with broken T symmetry in Sr 2 RuO 4 has been discussed from this respect [9,10]. Helical topological superconductors with T symmetry have also been discussed [11]. On the other hand, the unified scheme of the classification of the TIs and TSCs according to the three symmetries (T symmetry, particle-hole symmetry, and chiral symmetry) and the dimension of the system has been established [12].The implementation or fabrication of the TSCs is an important issue especially because it is expected to support the Majorana fermions [13][14][15][16][17], a promising tool for the quantum information processes. An interesting recent proposal is the proximity-induced superconductivity of the surface state in the three dimensional TI [18]. Because of the electron fractionalization in the surface Dirac fermions, Majorana fermions are expected to appear at the interface between the ferromagnet and s-wave superconductors both of which are on top of TI. It is also proposed that the superconductivity in a doped TI Cu x Bi 2 Se 3 [19] can be topological [20][21][22][23][24]. Besides, the possible TSC in noncentrosymmetric superconductors with the Rashba spin splitting has been discussed [25,26]. The basic idea is that the spin direction rotates with the momentum for the spin split bands, leading to the p ± ip pairing form when the superconducting order parameter is projected onto each of the bands. However, it has been clarified that due to the interference between the two order parameters in the two spin split ...

We study theoretically the proximity effect of a one-dimensional metallic quantum wire (in the absence of spin-orbit interaction) lying on top of an unconventional superconductor. Three different material classes are considered as a substrate: (i) a chiral superconductor in class D with broken time-reversal symmetry; a class DIII superconductor (ii) with and (iii) without a nontrivial Z2 number. Interestingly, we find degenerate zero energy Majorana bound states at both ends of the wire for all three cases. They are unstable against spin-orbit interaction in case (i) while they are topologically protected by time-reversal symmetry in cases (ii) and (iii). Remarkably, we show that non-local spin correlations between the two ends of the wire can be simply controlled by a gate potential in our setup. Introduction.-Proximity effects of superconductors and normal metals as well as semiconductors have been a subject of continued interest due to the rich physical phenomena of these hybrid systems. Especially, the topological nature of the superconducting proximity effect is an issue of current research activities [1-4] stimulated by the possible occurrence of Majorana fermions in solid state systems [5][6][7][8][9][10][11]. For example, the interface between an s-wave superconductor and the surface state of a three-dimensional topological insulator (TI) is predicted to offer a platform to realize Majorana fermions [1]. The underlying idea here is holographic principle that entails the reduction of electronic degrees of freedom, i.e., electron fractionalization, at the surface of a topologically non-trivial bulk state. Furthermore, the proximity effect of a TI to unconventional superconductors has also been studied theoretically [12]. Another (highly interesting) proposal is to use semiconductors with Rashba spin-orbit interaction in combination with s-wave superconductors for this purpose. In the presence of a sufficiently strong magnetic field, an inverted gap opens at the Γ-point in this system and topological superconductivity as well as Majorana fermions may appear when the Fermi energy lies inside the gap [13][14][15][16]. A recent experiment observed the zero-bias conductance peak at the edge of an InSb quantum wire (QW) coupled to an s-wave superconducting substrate, which might be the first experimental observation of a Majorana fermion [17]. It has also been shown theoretically that a one-dimensional Rashba quantum wire coupled to a d-wave superconductor hosts doubly degenerate Majorana bound states (MBSs) at the edge [18]. Besides these distinct works, there are various other research activities on the basis of QWs (for example Refs. [16,[19][20][21][22][23][24][25]). In all the cases listed above, spin-orbit interaction and/or the Zeeman energy in the QW is essential. Therefore, an open question is

Unconventional superconductivity induced by the magnetic moments in a conventional spin-singlet s-wave superconductor is theoretically studied. By choosing the spin directions of these moments, one can design spinless pairing states appearing within the s-wave superconducting energy gap. It is found that the helix spins produce px + py-wave state while the skyrmion crystal configuration px + ipy-wave like state. Nodes in the energy gap and the zero energy flat band of Majorana edge states exist in the former one, while the chiral Majorana channels along edges of the sample and the zero energy Majorana bound state at the core of the vortex appear in the latter case. PACS numbers: 74.45.+c, Introduction.-Unconventional superconducting states are one of the most important issues in current condensed matter physics. 1-3 Although most of the superconductors show the conventional spin-singlet s-wave pairing, strongly correlated materials sometimes show unconventional pairing since the on-site pairing is suppressed by the repulsive interaction. However, the discovery of the unconventional pairings relies on serendipity to some degree, and their theoretical designs and artificial fabrications are highly desired. Especially, recent intensive interest in the topological superconductivity and consequent Majorana fermions enhance the importance of this topics since Majorana fermions are the leading candidate for the platform of the quantum computation. [4][5][6][7][8][9] A promising proposal for realization of a topological superconducting state is the combined system of semiconducting nanowire with s-wave superconductor under an external magnetic field. The spin-orbit interaction and the magnetic field reduce the degrees of freedom of electrons concerning superconducting states, and effectively generate spinless p-wave superconductor. [10][11][12][13][14] As for one-dimensional system, signals suggesting Majorana fermions at the ends of the nanowire have been observed in some experimental setups. [15][16][17][18] There are other routes for creating topological superconductors; spin-singlet superconductor deposited on the topological insulator. 19,20 superfluid of cold atoms with lasergenerated effective spin-orbit interaction. 21 , aligned quantum dots connected by s-wave superconductors, 22 and magnetic moments in s-wave superconductors [23][24][25][26] or nodal superconductors. 27 The last ones are significantly distinct in that they don't explicitly require spin-orbit interaction in the system. With respect to the cooperation between magnetic moment and superconductivity, it has been known that the bound states are created around the impurities with the energy inside the bulk superconducting gap (not necessarily zero energy). [28][29][30] The modulation of the local density of states by a single magnetic impurity has been observed in the experiment. 31 The authors of Refs 24 and 26 considered the one-dimensional array of the magnetic impurities, and studied the possibility of Kitaev state with the Majorana bound states a...

We consider a superconductor proximity coupled to a two-dimensional ferromagnetic film with a skyrmion texture. Using the T-matrix calculations and numerical modeling we calculate the spinpolarized local density of states in the superconductor in the vicinity of the skyrmion. We predict the skyrmion bound states that are induced in the superconductor, similar to the well-known Yu-ShibaRusinov (YSR) states. The bound state wavefunctions have spatial power-law decay. It is suggested that superconductivity could facilitate an effective long-range interaction between skyrmions when bound state wavefunctions overlap.