Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections

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.

11 pages, 10 figures

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• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Sublattice-sensitive Majorana Modes
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits
• Interaction-driven first-order and higher-order topological superconductivity
• Tunable Majorana corner states driven by superconducting phase bias in a vertical Josephson junction
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
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