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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In two, three and even four spatial dimensions, the transverse responsesexperienced by a charged particle on a lattice in a uniform magnetic field arefully controlled by topological invariants called Chern numbers, whichcharacterize the energy bands of the underlying Hofstadter Hamiltonian. Theseremarkable features, solely arising from the magnetic translational symmetry,are captured by Diophantine equations which relate the fraction of occupiedstates, the magnetic flux and the Chern numbers of the system bands. Here weinvestigate the close analogy between the topological properties of HofstadterHamiltonians and the diffraction figures resulting from optical gratings. Inparticular, we show that there is a one-to-one relation between the abovementioned Diophantine equation and the Bragg condition determining thefar-field positions of the optical diffraction peaks. As an interestingconsequence of this mapping, we discuss how the robustness of diffractionfigures to structural disorder in the grating is a direct analogue of therobustness of transverse conductance in the Quantum Hall effect.

Linking topological features of the Hofstadter model to optical diffraction figures