Usuario:El bosón/Taller

What happens to the quantum mechanical motion of electrons in a crystalline lattice when an external magnetic field is applied? This problem exhibits a remarkable and puzzling property. The general nature of the energy spectrum depends on whether the magnetic field, expressed in natural units, is a rational number. This defies common wisdom, as the energy of an electron is expected to be a smooth function of external parameters, such as the magnetic field. In this Milestone paper, Hofstadter reveals that the electron spectrum plotted as a function of the magnetic field exhibits a recursive, self-replicating structure. It is widely known as Hofstadter’s butterfly – one of the most impressive and iconic images in condensed matter physics. The fractal nature of Hofstadter’s butterfly is very delicate. It can be destroyed by impurities or magnetic field fluctuations, leading its creator to express some reservations about the possibility for its experimental observation. Yet, it has been detected in recent years in a number of systems as diverse as microwave guides, patterned GaAs/AlGaAs heterostructures, moiré superlattices, and cold atom systems in optical lattices. No less importantly, this type of analysis has played a major role in the understanding of the integer quantum Hall effect. (Phys. Rev B)