Fibonacci sequence of twist angles in superconducting multi-layer graphene and hydrogenated graphitic fibers

TL;DR

This paper investigates the Fibonacci sequence pattern in twist angles of multi-layer graphene and hydrogenated graphitic fibers, revealing potential links to superconductivity and higher-order topological properties.

Contribution

It introduces the idea that twist angles in layered graphene structures follow a Fibonacci sequence, connecting geometric patterns to superconducting and topological phenomena.

Findings

Twist angles in layered graphene may follow Fibonacci sequence.

Superconducting properties are linked to specific twist angle patterns.

Hydrogenated graphite exhibits higher-order topological features.

Abstract

A range of twist angles between adjacent surfaces/volumes are intrinsic to natural graphite or artificially design in multi-layer graphene. In addition, stacking faults can be created by the application of mechanic, electric or magnetic fields. Charge and spin transport then occur in relation to the existing twist-angle pattern. In two dimensions, a saddle point in the electronic band structure leads to divergence in the density of states, known as van Hove singularities (vHs). The energy difference between vHs for the conduction and valence bands was found to increase with the twist angle between neighboring graphite domains with respect to the c axis (perpendicular to the graphite planes). In this work, we estimate for the superconducting (SC)-like nano-size multi-layer granular domain in hydrogenated graphitic fibers [1]. We show that this value for and the values found by others for few-layer graphene might actually form the Fibonacci mathematical sequence. Moreover, SC hydrogenated graphite can harbour higher-order topology as reflected in at least quadratic energy gap flattening. Charge transport and magnetization measurements on hydrogenated graphitic fibers have been done using a Quantum Design Physical Properties Measurement System.