Noncrystalline topological superconductors

Abstract

Topological insulators, featuring bulk-boundary correspondence, have been realized on a large number of noncrystalline materials, among which amorphous network, quasicrystals and fractal lattices are the most prominent ones. By contrast, topological superconductors beyond the realm of quantum crystals are yet to be harnessed, as their nucleation takes place around a well-defined Fermi surface with a Fermi momentum, the existence of which rests on the underlying translational symmetry. Here we identify a family of noncrystalline Dirac materials, devoid of time-reversal ($\mathcal{T}$) and translational symmetries, on which a suitable local or on-site pairing yields topological superconductors. We showcase this outcome on all the above mentioned noncrystalline platforms embedded in a two-dimensional flat space. The resulting noncrystalline topological superconductors possess quantized topological invariants (Bott index and local Chern marker) and harbor robust one-dimensional Majorana edge modes, analogs of $\mathcal{T}$-odd $p+ip$ pairing in noncrystalline materials.

Published version in PRB: 8 Pages, 5 Figures

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• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Josephson effect in a fractal geometry
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Topological insulators on fractal lattices: A general principle of construction
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Emergent fractals in dirty topological crystals
• Gapless superconductivity and its real-space topology in quasicrystals
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Stripe order in quasicrystals
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Site-selective correlations in interacting "flat-band" quasicrystals
• Superconducting order parameter in aperiodic binary systems
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Topological states and flat bands in exactly solvable decorated Cayley trees