Chern and Majorana Modes of Quasiperiodic Systems

TL;DR

This paper explores how topological invariants like Chern numbers influence self-similar states and edge modes in quasiperiodic systems, revealing new phenomena such as Chern-beats and the interplay with Majorana modes.

Contribution

It introduces the concept of Chern-induced length scales affecting self-similar states and links topological invariants to zero-energy Majorana modes in quasiperiodic superconductors.

Findings

Chern numbers create doublets in self-similar band edge states.

Chern-beats and smooth fractal regions emerge due to topological length scales.

Majorana modes are related to zero-energy states influenced by topology.

Abstract

New types of self-similar states are found in quasiperiodic systems characterized by topological invariants-- the Chern numbers. We show that the topology introduces a competing length in the self-similar band edge states transforming peaks into doublets of size equal to the Chern number. This length intertwines with the quasiperiodicity and introduces an intrinsic scale, producing Chern-beats and nested regions where the fractal structure becomes smooth. Cherns also influence the zero-energy mode, that for quasiperiodic systems which exhibit exponential localization, is related to the ghost of the Majorana; the delocalized state at the onset to topological transition. The Chern and the Majorana, two distinct types of topological edge modes, exist in quasiperiodic superconducting wires.