High-temperature Majorana corner modes in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math> superconductor heterostructure: Application to twisted bilayer cuprate superconductors
Yu-Xuan Li, Cheng‐Cheng Liu
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 $d+i{d}^{\ensuremath{'}}$ pairing superconductor, such as heavily doped graphene or especially a twisted bilayer of a cuprate superconductor, e.g., ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$, which has recently been proposed as a fully gapped chiral ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ 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.