page_title: Hofstadter's butterfly
section_title: Confirmation
hierarchical_section_title: Hofstadter's butterfly / Confirmation
caption_attribution_description: English: This is an early rendering of w:Hofstadter's butterfly. He named it Gplot in 1974.
context_page_description: In condensed matter physics, Hofstadter's butterfly describes the spectral properties of non-interacting two-dimensional electrons in a magnetic field. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of computer graphics. The name reflects the visual resemblance of the figure on the right to a swarm of butterflies flying to infinity.
  The Hofstadter butterfly plays an important role in the theory of the integer quantum Hall effect, and David J. Thouless won the Nobel Prize in physics in 2016 for the discovery that the wings of the butterfly are characterized by Chern integers, the quantized Hall conductances discovered in 1980 by Klaus von Klitzing for which he won the Nobel Prize in 1985. The colors in the diagram reflect the different Chern numbers.
context_section_description: In 1997 the Hofstadter butterfly was reproduced in experiments with microwave guide equipped by an array of scatterers. Similarity of the mathematical description of the microwave guide with scatterers and of Bloch's waves in magnetic field allowed to reproduce the Hofstadter butterfly for periodic sequences of the scatterers.
  In 2013, three separate groups of researchers independently reported evidence of the Hofstadter butterfly spectrum in graphene devices fabricated on hexagonal boron nitride substrates.  In this instance the butterfly spectrum results from interplay between the applied magnetic field, and the large scale moiré pattern that develops when the graphene lattice is oriented with near zero-angle mismatch to the boron nitride.
  In September 2017, John Martinis group in Google, in collaboration with Angelakis group in CQT Singapore, published results from a simulation of 2D electrons in a magnetic field using interacting photons in 9 superconducting qubits. The simulation recovered Hofstadter's butterfly, as expected.
caption: Rendering of the butterfly by Hofstadter
exif: {}