{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T05:47:09Z","timestamp":1782539229224,"version":"3.54.5"},"reference-count":56,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:00:00Z","timestamp":1782172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schr\u00f6dinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel\u2013Duke ordering to obtain exact analytical solutions for the energy spectrum and wave functions. The interplay between the fractal parameter \u03b1, the effective lattice scale l0, and the harmonic confinement strength \u03c9 is explored. We perform a comprehensive analysis of the Shannon entropy, Fisher information, and Fisher\u2013Shannon complexity in both coordinate and momentum spaces. Our results demonstrate that these parameters directly control the localization\u2013delocalization transition and the informational architecture of the quantum states, while satisfying the entropic and Fisher uncertainty relations. Furthermore, we derive the exact partition function and the corresponding thermodynamic properties (free energy, internal energy, entropy, and specific heat) of the system. The analytical framework presented offers valuable insights into the spectral, information-theoretic, and thermodynamic behavior of quantum systems in fractal semiconductor-like environments.<\/jats:p>","DOI":"10.3390\/nano16130787","type":"journal-article","created":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T05:52:11Z","timestamp":1782453131000},"page":"787","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Spectral, Information-Theoretic and Thermodynamic Properties of a Fractal Position-Dependent Mass Schr\u00f6dinger System"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-2724-4822","authenticated-orcid":false,"given":"Q. R. D. S.","family":"Moreira","sequence":"first","affiliation":[{"name":"Departamento de Engenharia de Teleinform\u00e1tica, Universidade Federal do Cear\u00e1, Campus do Pici, Bloco 725, Fortaleza 60455-760, CE, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4193-565X","authenticated-orcid":false,"given":"L. F.","family":"Ximenes","sequence":"additional","affiliation":[{"name":"Secretaria da Educa\u00e7\u00e3o do Estado do Cear\u00e1 (SEDUC-CE), Coordenadoria Regional de Desenvolvimento da Educa\u00e7\u00e3o (CREDE 6), Sobral 62039-010, CE, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6535-493X","authenticated-orcid":false,"given":"A. R. P.","family":"Moreira","sequence":"additional","affiliation":[{"name":"Secretaria da Educa\u00e7\u00e3o do Estado do Cear\u00e1 (SEDUC-CE), Coordenadoria Regional de Desenvolvimento da Educa\u00e7\u00e3o (CREDE 9), Horizonte 62880-384, CE, Brazil"},{"name":"Postgraduate Program in Electrical and Computer Engineering, Federal University of Cear\u00e1, Sobral 62010-560, CE, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4464-7602","authenticated-orcid":false,"given":"D. M.","family":"Neves","sequence":"additional","affiliation":[{"name":"CTI Center for Information Technology Renato Archer, Campinas 13069-901, SP, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4004-0926","authenticated-orcid":false,"given":"J. B. R.","family":"Silva","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia de Teleinform\u00e1tica, Universidade Federal do Cear\u00e1, Campus do Pici, Bloco 725, Fortaleza 60455-760, CE, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4897-5750","authenticated-orcid":false,"given":"J. C.","family":"Nascimento","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia de Teleinform\u00e1tica, Universidade Federal do Cear\u00e1, Campus do Pici, Bloco 725, Fortaleza 60455-760, CE, Brazil"},{"name":"Postgraduate Program in Electrical and Computer Engineering, Federal University of Cear\u00e1, Sobral 62010-560, CE, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116478","DOI":"10.1016\/j.physe.2026.116478","article-title":"Quantum information and thermodynamic features in position-dependent mass semiconductor heterostructures","volume":"178","author":"Moreira","year":"2026","journal-title":"Physica E"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.chemphys.2016.05.010","article-title":"Noise-driven diamagnetic susceptibility of impurity doped quantum dots: Role of anisotropy, position-dependent effective mass and position-dependent dielectric screening function","volume":"474","author":"Bera","year":"2016","journal-title":"Chem. 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