High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors

Abstract

The realization of Majorana corner modes generally requires unconventional superconducting pairing or $s$-wave pairing. However, the bulk nodes in unconventional superconductors and the low $T_c$ of $s$-wave superconductors are not conducive to the experimental observation of Majorana corner modes. Here we show the emergence of a Majorana corner mode at each corner of a two-dimensional topological insulator in proximity to a $d+i{d}^{\prime }$ pairing superconductor, such as heavily doped graphene or especially a twisted bilayer of a cuprate superconductor, e.g., Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$, which has recently been proposed as a fully gapped chiral $d_{x^2-y^2}+i{d}_{xy}$ superconductor with $T_c$ close to its native 90 K, and an in-plane magnetic field. By numerical calculation and intuitive edge theory, we find that the interplay of the proximity-induced pairing and Zeeman field can introduce opposite Dirac masses on adjacent edges of the topological insulator, which creates one zero-energy Majorana mode at each corner. Our scheme offers a feasible route to achieve and explore Majorana corner modes in a high-temperature platform without bulk superconductor nodes.

6 pages, 3 figures

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