High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

Abstract

We study the largest-angle twisted homo-bilayer (LA-THB) systems, hosting Moiréless quasi-crystal (QC) structure. We propose to use these materials to generate high-angular-momentum (HAM) topological superconductivities (TSCs) protected by their QC symmetries absent on conventional crystalline materials. This proposal is based on our universal Ginzburg-Landau theory based analysis which yields the general conclusion that, when each $D_n$-symmetric ($n$ is even) monolayer hosts SC with pairing angular momentum $l\le \frac{n}{2}$, the interlayer Josephson coupling will induce SC with pairing angular momentum $L=l$ or $L=n-l$ in the LA-THB, determined by microscopic details. The latter one is just the HAM TSC if $l>0$. Based on our revised perturbational-band theory, we develop general microscopic framework to study the QC LA-THBs involving electron-electron interactions, adopting which we study three examples, i.e. the 30${}^{\circ }$- twisted bilayer graphene, the 30${}^{\circ }$- twisted bilayer BC${}_3$, and the 45${}^{\circ }$- twisted bilayer cuprates. The $g+ig$- $h+ih$- and $d+id$- TSCs with HAM $L=4,5$ and $2$ can emerge in certain doping regimes in these systems, respectively.

4.2 pages, 3 figures, with Supplementary Materials. This is the generalized version of arXiv:2106.08542. In the old version, we only consider a special example, here we give a general theory

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Cited by in corpus (15)

• Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
• Charge 4e superconductivity and chiral metal in the $45^{\circ }$-twisted bilayer cuprates and similar bilayers
• Quasiperiodic pairing in graphene quasicrystals
• Classification of electronic nematicity in three-dimensional crystals and quasicrystals
• Making Chiral Topological Superconductivities from Non-topological Superconductivities Through the Twist
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• Unconventional superfluidity of superconductivity on Penrose lattice
• A critical nematic phase with pseudogap-like behavior in twisted bilayers
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Gapless superconductivity and its real-space topology in quasicrystals
• Topological phases in twisted Rashba superconductors
• Energy Spectrum Theory of Incommensurate Systems
• Electronic Reconstruction at the Quasicrystal-Moiré Crossover in Twisted Bilayer Graphene
• Hydrogen Doping Induced $p_x\pm i{p}_y$ Triplet Superconductivity in Quasi-One-Dimensional K${}_2$Cr${}_3$As${}_3$
• Site-selective correlations in interacting "flat-band" quasicrystals