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Exploring localization properties in a folded N x N network on a cylinder’s shape with diagonal disorder and long-range hopping

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  • Santos Junior, M.S.
  • de Moura, F.A.B.F.

Abstract

In this work, we employ the inverse power method (IPM), a well-established technique in linear algebra, to investigate the quantum dynamics of a one-electron Hamiltonian in a unique geometric setup. Specifically, we consider a two-dimensional N×N lattice folded into a cylindrical topology, incorporating diagonal disorder and long-range hopping with a power-law decay. Unlike conventional studies that consider two-dimensional planar lattices, our model explicitly incorporates the curvature of the cylindrical geometry, enabling us to examine its potential influence on electronic properties. By analyzing the interplay between disorder, long-range hopping, and the system’s intrinsic curvature, our results suggest that geometry may play a role in the localization and transport behavior of electrons. These findings provide insights into how geometric factors could affect quantum systems, with potential implications for materials science and nanostructures exhibiting curved geometries.

Suggested Citation

  • Santos Junior, M.S. & de Moura, F.A.B.F., 2025. "Exploring localization properties in a folded N x N network on a cylinder’s shape with diagonal disorder and long-range hopping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 668(C).
    • Handle: RePEc:eee:phsmap:v:668:y:2025:i:c:s0378437125001669
    DOI: 10.1016/j.physa.2025.130514
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    References listed on IDEAS

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    1. dos Santos, J.L.L. & Sales, M.O. & de Moura, F.A.B.F., 2014. "Absorption spectra and localization aspects of a one-dimensional model with stretched exponential correlated disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 31-41.
    2. da Silva, L.D. & Ranciaro Neto, A. & Sales, M.O. & Lyra, M.L. & de Moura, F.A.B.F., 2017. "Optical absorption and delocalization in a quaternary tight-binding chain with correlated disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 895-900.
    3. Cressoni, José C. & Lyra, Marcelo L., 1998. "The nature of electronic states in a disordered chain with long-ranged hopping amplitudes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 18-29.
    4. R. F. Dutra & M. S. Santos Junior & D. Messias & C. V. C. Mendes & M. O. Sales & F. A. B. F. de Moura, 2023. "Charge transport in two-dimensional disordered systems with an external electric field," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(08), pages 1-11, August.
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