Invisible defects in complex crystals

Abstract

We show that invisible localized defects, i.e. defects that can not be detected by an outside observer, can be realized in a crystal with an engineered imaginary potential at the defect site. The invisible defects are synthesized by means of supersymmetric (Darboux) transformations of an ordinary crystal using band-edge wave functions to construct the superpotential. The complex crystal has an entire real-valued energy spectrum and Bragg scattering is not influenced by the defects. An example of complex crystal synthesis is presented for the Mathieu potential.

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Physics counterpart of the PT non-hermitian tight-binding chain
• Nonlinear Bloch-wave interaction and Bragg scattering in optically-induced lattices
• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Electron and Spin Transport in the Presence of Complex Absorbing Potential

Cited by in corpus (31)

• Supersymmetric mode converters
• $PT$-symmetric invisible defects and confluent Darboux-Crum transformations
• Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Observation of supersymmetric scattering in photonic lattices
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• Unidirectional reflectionlessness and invisibility in the TE and TM modes of a PT-symmetric slab system
• Supersymmetric transparent optical intersections
• Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings
• Unidirectional Invisibility and PT-Symmetry with Graphene
• Supersymmetric Bragg gratings
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Long-range entangled zero-mode state in a non-Hermitian lattice
• PT-symmetric optical superlattices
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• E2-quasi-exact solvability for non-Hermitian models
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type
• Non-Hermitian systems of Euclidean Lie algebraic type with real eigenvalue spectra
• Supersymmetric correspondence in spectra on a graph and its line graph: From circuit theory to spoof plasmons on metallic lattices
• Non-Hermitian invisibility in tight-binding lattices
• A new non-Hermitian E2-quasi-exactly solvable model
• Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{$\mathcal{P}\mathcal{T}$}{PT}-symmetric systems
• An attractor dynamics in a non-Hermitian two-level system
• Invisible surface defects in a tight-binding lattice
• Semi-localization transition driven by a single asymmetrical tunneling
• Coherent confinement and unidirectional dynamics of a wave packet induced by a non-Hermitian Su-Schrieffer-Heeger segment
• Exceptional spectrum and dynamic magnetization
• A unifying E2-quasi-exactly solvable model