English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The topological properties of the quantum Hall effect in a crystallinelattice, described by Chern numbers of the Hofstadter butterfly quantum phasediagram, are deduced by using a geometrical method to generate the structure ofquasicrystals: the cut and projection method. Based on this, we provide ageometric unified approach to the Hofstadter topological phase diagram at allfluxes. Then we show that for any flux, the bands conductance follow a twoletter symbolic sequence . As a result, bands conductance at different fluxesobey inflation/deflation rules as the ones observed to build quasicrystals. Thebands conductance symbolic sequences are given by the Sturmian coding of theflux and can be found by considering a circle map, a billiard or trajectorieson a torus. Simple and fast techniques are thus provided to obtain Chernnumbers at any magnetic flux. This approach rationalize the previously observedtopological equivalences between the Fibonacci and Harper potentials (alsoknown as the almost Mathieu operator problem) or with other trigonometricpotential, as well as the relationship with Farey sequences and trees.

physical review. b./physical review. b

A higher-dimensional quasicrystalline approach to the Hofstadter and  Fibonacci butterflies topological phase diagram and band conductance:  symbolic sequences, Sturmian coding and self-similar rules at all magnetic  fluxes