Inner Skin Effects on Non-Hermitian Topological Fractals

Abstract

Non-Hermitian (NH) crystals, quasicrystals and amorphous network display an accumulation of a macroscopic number of states near one of its specific interfaces with vacuum, such as edge, surface, hinge or corner. This phenomenon is known as the NH skin effect, which can only be observed with open boundary condition. In this regard self-similar fractals, manifesting inner boundaries in the interior of the system, harbor a novel phenomenon, the \emph{inner skin effect} (ISE). Then the NH skin effect appears at the inner boundaries of the fractal lattice with periodic boundary condition. We showcase this observation by implementing prominent models for NH insulators and superconductors on representative planar Sierpinski carpet fractal lattices. They accommodate both first-order and second-order ISEs at inner edges and corners, respectively, for charged as well as neutral Majorana fermions. Furthermore, over extended parameter regimes ISEs are tied with nontrivial bulk topological invariants, yielding intrinsic ISEs. With the recent success in engineering NH topological phases on highly tunable metamaterial platforms, such as photonic and phononic lattices, as well as topolectric circuits, the proposed ISEs can be observed experimentally at least on fractal metamaterials with periodic boundary condition.

Published Version: 9 Pages, 5 Figures (Supplementary Materials as Ancillary File)

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• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
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• Topological insulators on fractal lattices: A general principle of construction
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
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• Model non-Hermitian topological operators without skin effect: A general principle of construction
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• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
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• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
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• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals