Selective Equal-Spin Andreev Reflections Induced by Majorana Fermions

Abstract

In this work, we find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counter-propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors. [18,19]. Introduction-In this work, we point out another intriguing phenomenon due to the self-Hermitian property of MFs, namely, MF-induced selective equal spin Andreev reflections (SESARs). As depicted in Fig.1, when a spinful paramagnetic normal lead is coupled to a topological superconductor through its MF end state, electrons with spin pointing to a certain direction n are reflected as holes with the same spin (Fig.1a), where n is determined by the properties of the topological superconductor. The reflected holes are created due to missing electrons with spin polarization n below the Fermi energy. Therefore, these processes are called equal spin Andreev reflections. This is in sharp contrast to ordinary Andreev reflection processes [20], in which the reflected holes are created due to missing electrons below the Fermi energy which have opposite spins to the incoming electrons.Even more interestingly, at the normal lead/topological superconductor (N/TS) junction, electrons with opposite spin polarization − n are completely decoupled from the MF and they cannot participate in Andreev reflections (Fig.1b). In other words, the MF selects electrons with certain spin polarization n to undergo equal spin Andreev reflections. Therefore, we refer to this new phenomenon as MF-induced SESARs.Pure equal spin Andreev reflections can take place at a half-metal/superconductor interface [21-28] if spin is not conserved at the interface. This is because conducting electrons in a half-metal are fully spin-polarized and usual Andreev reflection processes cannot occur. Nevertheless, as we show below, inducing SESARs in paramagnetic leads is a special property of MFs. Importantly, as in the half-metal case and depicted in Fig.1a, the charge

Detection of Majorana zero mode in the vortex

“…This process was first proposed in a semiconductor wire/SC structure in which MZMs exist at two ends of the wire. 43 The proposed SSAR of the MZM in 1D wire can be generalized to a 2D TSC. In the latter case, the spin of the MZM in the vortex core has a spatial distribution and is not conserved.…”

“…Therefore, the Andreev reflection at the vortex center is expected to be spin-selective. [42][43][44] Via an spin-polarized STM, 45,46 we can inject spin-polarized tunneling current in STS measurements and observe the zero bias conductance change caused by the SSAR from the MZM when flipping the spin of the tunneling electrons. 47,48 It is worth noting that only a small magnetic field is sufficient to excite vortices on the TI surface and hence the spin-polarized MZM in the vortex core.…”

Signatures of Majorana States in Electron Transport through a Quantum Dot Coupled to a Topological Wire

“…(2) We assume that spin-down sector only of the dot is coupled to the MS due to its helical properties [9]. ε m ∼ e −L/ξ represents the coupling between two Majorana states, where L is the wire length and ξ is the superconducting coherence length.…”

Majorana Zero Mode Detected with Spin Selective Andreev Reflection in the Vortex of a Topological Superconductor

“…This introduces great difficulty in detection of the MZM by using normal STM=STS with a nonpolarized tip. He et al have recently proposed a novel property of MZM in a 1D system [16], where the Andreev reflection (AR) is spin selective. They showed that MZM induces selective equal spin AR, in which incoming electrons with certain spin polarization in the lead are reflected as counterpropagating holes with the same spin [7].…”

“…3(a). Therefore, the AR at r ¼ 0 is expected to be spin selective, and can be probed in spin polarized (SP) STM=STS [16][17][18].…”