Abstract
Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.
Highlights
A central subject in the physics of topological superconductivity [1,2,3,4] is the realization of fault-tolerant topological quantum computations [5,6,7,8,9] using Majorana zero modes [10,11,12]
We have demonstrated that a two-dimensional noncentrosymmetric (s + p)-wave superconductor in the presence of an in-plane magnetic field can host tunable Majorana corner modes (MCMs)
We show that the number of MCMs depends sensitively on the edge shape of the noncentrosymmetric superconductor
Summary
A central subject in the physics of topological superconductivity [1,2,3,4] is the realization of fault-tolerant topological quantum computations [5,6,7,8,9] using Majorana zero modes [10,11,12]. On the basis of this strategy, the presence of tunable MCMs has been demonstrated in Rashba bilayers coupled to superconductors [60], semiconductor–iron-basedsuperconductor hybrids [59], and spin-triplet helical p-wave superconductors [59,64] Even so, since these proposals have not yet been implemented experimentally, it is important to continue to propose alternative models hosting tunable MCMs. as the first objective of this paper, we demonstrate that a two-dimensional noncentrosymmetric (s + p)-wave superconductor [66,67,68,69,70,71,72] can harbor the tunable MCMs by applying in-plane magnetic fields.
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