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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The Hofstadter problem is the lattice analog of the quantum Hall effect andis the paradigmatic example of topology induced by an applied magnetic field.Conventionally, the Hofstadter problem involves adding $\sim 10^4$ T magneticfields to a trivial band structure. In this work, we show that when a magneticfield is added to an initially topological band structure, a wealth ofremarkable possible phases emerges. Remarkably, we find topological phaseswhich cannot be realized in any crystalline insulators. We prove that threadingmagnetic flux through a Hamiltonian with nonzero Chern number enforces a phasetransition at fixed filling and that a 2D Hamiltonian with nontrivial Kane-Meleinvariant produces a 3D TI or 3D weak TI phase in periodic flux. We then studyfragile topology protected by the product of two-fold rotation andtime-reversal and show that there exists a 3D higher order TI phase wherecorner modes are pumped by flux. We show that a model of twisted bilayergraphene realizes this phase. Our results rely primarily on the magnetictranslation group which exists at rational values of the flux. The advent ofMoir\'e lattices also renders our work relevant experimentally. In Moir\'elattices, it is possible for fields of order $1-30$ T to reach one flux perplaquette and allow access to our proposed Hofstadter topological phase.

Hofstadter Topology: Non-crystalline Topological Materials at High Flux