Year: 2021
Type: article
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 structural disorder in the grating is a direct analogue of the robustness of transverse conductance in the quantum Hall effect.
Source: New Journal of Physics
Institutions: University of Naples Federico II, Institut polytechnique de Grenoble, Centre National de la Recherche Scientifique, Institut Néel, Université Grenoble Alpes, University of Birmingham, Institució Catalana de Recerca i Estudis Avançats, Institute of Photonic Sciences, Barcelona Institute of Science and Technology, Institute of Applied Science and Intelligent Systems, Universitat Politècnica de Catalunya
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,195
Funders: National Science Foundation, Fundación Cellex, Foundational Questions Institute, “la Caixa” Foundation, Centres de Recerca de Catalunya, Royal Society, Agence Nationale de la Recherche, Generalitat de Catalunya, Ministerio de Economía y Competitividad, Narodowe Centrum Nauki, Narodowym Centrum Nauki, QuantERA, Horizon 2020 Framework Programme, Agència de Gestió d'Ajuts Universitaris i de Recerca, European Regional Development Fund, Agencia Estatal de Investigación, H2020 Marie Skłodowska-Curie Actions
Awards: G1175115578, G1309967896, G1341588127, G148743912, G1495698476, G1622782223, G162601807, G1694298633, G1871477277, G1888088267, G1908469581, G1909050264, G2038104832, G2064873908, G2163055958, G2262748287, G2355262757, G2357050330, G2469010403, G2494840282, G2673512141, Structured electric-dipole-based chirality, G2713276326, G2744780120, G2763573136, G288263039, G3005324705, G3007892998, G300979063, G3261693824, G3288897321, G3302599245, G34346518, G3480869486, G3546882995, G3639969887, G3674674691, G3939077204, G408490004, G410571670, G4179535065, G425668148, G4353981422, G4391008399, G451917667, G4526231891, G4630312626, G5080475149, G5426121769, G5505639174, G5539308778, G5554424168, G5852091828, G5967599077, G6079324567, G6482940084, G6656126374, G6727213032, G6790183914, G69051668, G7021218639, G7084143925, G7181734937, G7226647862, G7425137858, G7438636020, G7898799392, G8180681537, G8283979283, Kavli Institute for Theoretical Physics, G853839195, G8637226926, G8676624529, G8684520763, G8765903826, G885552189, G929308097, G948124368, G9487005
OpenAlex ID: W4200417997