All articles tagged with #hofstadter butterfly
The article discusses the ten martini conjecture, a challenging problem in quantum physics and mathematics related to the energy levels of electrons in magnetic fields, which was eventually proven using advanced number theory and geometric methods, confirming the fractal patterns known as Hofstadter butterflies as real phenomena.
Researchers have discovered that layered 2D materials, such as graphene and boron nitride, can exhibit a wide range of electron behaviors and even quasicrystal patterns when stacked at specific angles. These moiré materials have allowed scientists to observe the Hofstadter butterfly, a theoretical concept from the 1970s, in experimental data for the first time. The discovery of quasicrystals in these materials opens up new possibilities for studying electron behavior and potentially finding applications in areas such as superconductivity. Additionally, researchers have found that twisting a thin film of graphite can create a hybrid 2D-3D structure with altered electron behavior, further blurring the boundary between dimensions.