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Isospectrally patterned lattices.

Peter Schmelcher1,2,3

  • 1Zentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany. peter.schmelcher@uni-hamburg.de.

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Summary
This summary is machine-generated.

We introduce novel patterned lattices with tunable phase gradients. These lattices exhibit distinct energy domains and control over localized versus delocalized states, offering new avenues for material design.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Photonics

Background:

  • Isospectrality in coupled systems is key to designing novel material properties.
  • Phase gradients can influence the behavior of coupled cells within a lattice.

Purpose of the Study:

  • To introduce and explore patterned lattices composed of coupled isospectral cells with designed phase gradients.
  • To analyze the resulting band structure and localization phenomena in these novel lattices.

Main Methods:

  • Designing isospectral cells with controllable phase characteristics.
  • Investigating lattices with a constant phase gradient over a finite phase interval.
  • Analyzing the band structure and eigenstates to understand localization mechanisms.

Main Results:

  • The band structure exhibits three distinct energy domains with crossover edges.
  • Localization length emerges from the interplay between phase gradient and inter-cell coupling.
  • The fraction of localized to delocalized states is tunable via the phase gradient.

Conclusions:

  • Patterned lattices with designed phase gradients offer a novel platform for controlling quantum states.
  • The interplay of local rotation and coupling dictates localization phenomena.
  • This work opens new perspectives for investigating isospectrally patterned lattices.