Majorana Bound States and Nonlocal Spin Correlations in a Quantum Wire on an Unconventional Superconductor

Abstract

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

Topological phases of inhomogeneous superconductivity

“…If 0 = z < ( 2 − 2 0 )/ 0 we may still construct two-MF solutions satisfying the boundary conditions but they are delocalized; i.e., the decay length is infinite. Although M 1 and M 2 are orthogonal, there is no inherent symmetry in the system that prevents two MFs at the same end from splitting; e.g., they are not Kramers pairs protected by time-reversal symmetry [43][44][45][46][47][48][49][50]. One may show that an infinitesimal deviation away from a planar helix will split the MF energies away from zero.…”

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

“…[40,[50][51][52][53][54][55][56][71][72][73][74][75] for applications). However, there are several shortcomings of this approach.…”

Topological Majorana Two-Channel Kondo Effect

“…In a Rashba nanowire, the s ± -wave pairing in Fig. 1(a) can be proximity induced by a nodeless iron-based SC [20], or other unconventional ones [34,35]. This scheme constitutes an advantage of enjoying a higher T c [36,37].…”