High-temperature topological superconductivity in twisted double layer copper oxides

Abstract

A great variety of novel phenomena occur when two-dimensional materials, such as graphene or transition metal dichalcogenides, are assembled into bilayers with a twist between individual layers. As a new application of this paradigm, we consider structures composed of two monolayer-thin $d$-wave superconductors with a twist angle $\theta$ that can be realized by mechanically exfoliating van der Waals-bonded high-$T_c$ copper oxide materials, such as Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$. On the basis of symmetry arguments and detailed microscopic modelling, we predict that for a range of twist angles in the vicinity of $45^{\mathrm{o}}$, such bilayers form a robust, fully gapped topological phase with spontaneously broken time-reversal symmetry and protected chiral Majorana edge modes. When $\theta \approx 45^{\mathrm{o}}$, the topological phase sets in at temperatures close to the bulk $T_c\simeq 90$ K, thus furnishing a long sought realization of a true high-temperature topological superconductor.

arXiv comment15 pages, 13 figures

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• Persistent Josephson tunneling between Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ flakes twisted by 45${}^{\circ }$ across the superconducting dome
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• Prominent Josephson tunneling between twisted single copper oxide planes of Bi${}_2$Sr${}_{2-x}$LaxCuO${}_{6+y}$
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• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
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• Doping dependence of chiral superconductivity in near $45^{\circ }$ twisted bilayer cuprates
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• Quasiperiodic circuit quantum electrodynamics
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field
• Tunable $t-t^{\prime }-U$ Hubbard models in twisted square homobilayers
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