Linking topological features of the Hofstadter model to optical diffraction figures
【Abstract】
In two, three and even four spatial dimensions, the transverse responses experienced by a charged
particle on a lattice in a uniform magnetic field are fully controlled by topological invariants
called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian.
These remarkable features, solely arising from the magnetic translational symmetry, are captured by
Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern
numbers of the system bands. Here we investigate the close analogy between the topological
properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings.
In particular, we show that there is a one-to-one relation between the above mentioned Diophantine
equation and the Bragg condition determining the far-field positions of the optical diffraction
peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction
figures to str...
【Author】
Francesco Di Colandrea, Alessio D’Errico, Maria Maffei, Hannah M Price, Maciej Lewenstein, Lorenzo Marrucci, Filippo Cardano, Alexandre Dauphin and Pietro Massignan
【Journal】
New Journal of Physics(IF：3.8) Time：2022-01-25
