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Miniband and Gap Evolution in Gauss Chains.

D S Citrin1,2

  • 1School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA.

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|September 28, 2024
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Summary
This summary is machine-generated.

The study explores quasiperiodic Gauss chains, revealing how their miniband and gap structures become more complex with increasing parameters. Certain quadratic Gauss chains exhibit unique properties treatable by renormalization group methods, indicating hidden symmetries.

Keywords:
Gauss chainselectronic structurequasiperiodic latticereal-space renormalization group

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Area of Science:

  • Condensed Matter Physics
  • Solid State Physics
  • Materials Science

Background:

  • Quasiperiodic lattices exhibit complex electronic properties.
  • The Gauss chain, a specific quasiperiodic lattice, has sites defined by zj=jnd.
  • Understanding band structures in such systems is crucial for electronic applications.

Purpose of the Study:

  • To numerically investigate the miniband and gap hierarchy in Gauss chains as system size (N) increases.
  • To analyze the effect of the parameter 'n' on the fragmentation of the band structure.
  • To identify specific Gauss chains amenable to real-space renormalization group (RSRG) analysis.

Main Methods:

  • Numerical simulations using a Kronig-Penney model.
  • Analysis of the electronic band structure formation.
  • Application of a real-space renormalization group approach to specific Gauss chain models.

Main Results:

  • The miniband and gap structure becomes more fragmented as 'n' increases, consistent with prior research.
  • The Gauss chain with zj=j^2d and generalized forms like zj=(j^2±1/2j)d are solvable via RSRG.
  • These quadratic cases appear to be the only ones solvable by RSRG, suggesting underlying symmetries.

Conclusions:

  • The complexity of Gauss chain electronic structures increases with lattice parameters.
  • The RSRG method provides insights into specific, symmetric Gauss chain configurations.
  • The findings highlight the importance of lattice symmetry in determining analytical tractability.