Accuracy of classical conductivity theory at atomic scales for free fermions in disordered media

Autor(es)

Aza, N. J. B. ^{[1, 2]} ; Bru, J-B ^{[3, 4, 5]} ; de Siqueira Pedra, W. ^[1] ; Ratsimanetrimanana, A. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Fis, Dept Fis Matemat, CP 66318, BR-05314970 Sao Paulo, SP - Brazil

^[2] Univ Andes, Fac Ciencias, Dept Fis, Carrera 1 18A-10, AA 4976-12340 Bloque Ip, Bogota - Colombia

^[3] BCAM, Mazarredo 14, Bilbao 48009 - Spain

^[4] Univ Basque Country, Fac Ciencia & Tecnol, Dept Matemat, Apartado 644, Bilbao 48080 - Spain

^[5] IKERBASQUE, Basque Fdn Sci, Bilbao 48011 - Spain

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 125, p. 209-246, MAY 2019.
• Citações Web of Science: 0

Resumo

The growing need for smaller electronic components has recently sparked the interest in the breakdown of the classical conductivity theory near the atomic scale, at which quantum effects should dominate. In 2012, experimental measurements of electric resistance of nanowires in Si doped with phosphorus atoms demonstrate that quantum effects on charge transport almost disappear for nanowires of lengths larger than a few nanometers, even at very low temperature (4.2 K). We mathematically prove, for non-interacting lattice fermions with disorder, that quantum uncertainty of microscopic electric current density around their (classical) macroscopic values is suppressed, exponentially fast with respect to the volume of the region of the lattice where an external electric field is applied. This is in accordance with the above experimental observation. Disorder is modeled by a random external potential along with random, complex-valued, hopping amplitudes. The celebrated tight-binding Anderson model is one particular example of the general case considered here. Our mathematical analysis is based on Combes-Thomas estimates, the Akcoglu-Krengel ergodic theorem, and the large deviation formalism, in particular the Gartner-Ellis theorem. (C) 2019 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 16/02503-8 - Comportamento macroscópico de sistemas de férmions não relativísticos interagentes
• Beneficiário: Walter Alberto de Siqueira Pedra
• Linha de fomento: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 17/22340-9 - Métodos construtivos para férmions interagentes com aplicações a teoria microscópica da condutividade e supercondutividade
• Beneficiário: Walter Alberto de Siqueira Pedra
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional