Bloch-like waves in random-walk potentials based on supersymmetry
arXiv:1501.02591 · doi:10.1038/ncomms9269
Abstract
Bloch's theorem was a major milestone that established the principle of bandgaps in crystals. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations for Bloch's theorem, this restriction was disproven by the discoveries of amorphous media and quasicrystals. While network and liquid models have been suggested for the interpretation of Bloch-like waves in disordered media, these approaches based on searching for random networks with bandgaps have failed in the deterministic creation of bandgaps. Here, we reveal a deterministic pathway to bandgaps in random-walk potentials by applying the notion of supersymmetry to the wave equation. Inspired by isospectrality, we follow a methodology in contrast to previous methods: we transform order into disorder while preserving bandgaps. Our approach enables the formation of bandgaps in extremely-disordered potentials analogous to Brownian motion, and also allows the tuning of correlations while maintaining identical bandgaps, thereby creating a family of potentials with 'Bloch-like eigenstates'.
References in corpus (21)
- Local Density Fluctuations, Hyperuniformity, and Order Metrics
- Designer disordered materials with large complete photonic band gaps
- Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
- Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
- Supersymmetric Optical Structures
- Supersymmetric mode converters
- Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
- Supersymmetry-generated complex optical potentials with real spectra
- Long range correlations in DNA : scaling properties and charge transfer efficiency
- Two families of superintegrable and isospectral potentials in two dimensions
- SUSY-inspired one-dimensional transformation optics
- Quantum Phase Extraction in Isospectral Electronic Nanostructures
- Ultra-high-Q TE/TM dual-polarized photonic crystal nanocavities
- Amorphous Photonic Lattices: Band Gaps, Effective Mass and Suppressed Transport
- Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
- Intertwined isospectral potentials in an arbitrary dimension
- Observation of supersymmetric scattering in photonic lattices
- Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
- Supersymmetric transparent optical intersections
- Talbot self-imaging in -symmetric complex crystals
- Anderson Localization Triggered by Spin Disorder---with an Application to Eu_x Ca_1-x B_6
Cited by in corpus (30)
- Hyperuniformity and its Generalizations
- Supersymmetric Laser Arrays
- Topological hyperbolic lattices
- Acoustic omni meta-atom for top-down, decoupled access to all octants of a wave parameter space
- Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
- Low-dimensional optical chirality in complex potentials
- Symmetry in optics and photonics: a group theory approach
- Metadisorder for designer light in random-walk systems
- Interdimensional optical isospectrality inspired by graph networks
- Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
- Unidirectional scattering with spatial homogeneity using photonic time disorder
- Effective Elastic Wave Characteristics of Composite Media
- Supercharge optical arrays
- Perfect Transmission through Disordered Media
- Inverse design of disordered stealthy hyperuniform spin chains
- Digital building blocks for controlling random waves based on supersymmetry
- Acceleration toward polarization singularity inspired by relativistic ExB drift
- Continuous supersymmetric transformations in optical waveguides
- Absence of Anderson localization in certain random lattices
- Parity anomaly laser
- Supersymmetric correspondence in spectra on a graph and its line graph: From circuit theory to spoof plasmons on metallic lattices
- Target decoupling in a coupled optical system resistant to random perturbation
- Deep-subwavelength engineering of stealthy hyperuniformity
- Supersymmetry, half-bound states, and grazing incidence reflection
- Low-dimensional gap plasmons for enhanced light-graphene interactions
- Supersymmetric relativistic quantum mechanics in time-domain
- Linear and nonlinear dynamics of isospectral granular chains
- Supersymmetrically bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states
- Universal Scaling of Electron Transmission for Nearly Ballistic and Quantum Dragon Nanodevices
- Localization of states, Bloch wave and quantum phase transitions in SUSY deformed potentials in non-Hermitian optical systems