najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1177Research ArticleMATHEMATICSМАТЕМАТИКАLandau-Zener effect for a quasi-2D periodic sandwichBagraevN.

St. Petersburg

bagraev@mail.ioffe.ruMartinG.

Professor, NZ Institute for Advanced study

g.j.martin@massey.ac.nzPavlovB. S.

Professor, DSc., NZ Institute for Advanced study; V. Fock Institute for Physics at Physical Faculty

Saint Petersburg

pavlovenator@gmail.comYafyasovA.

Professor, DScV, Fock Institute for Physics at Physical Faculty

Saint Petersburg

yafyasov@desse.phys.spbu.ruA. F. Ioffe Physico-Technical Institute, Russian Academy of SciencesRussian FederationMassey University, Albany CampusNew ZealandMassey University, Albany Campus; St. Petersburg UniversityRussian FederationSt. Petersburg UniversityRussian Federation201118082025243250Copyright © Bagraev N., Martin G., Pavlov B.S., Yafyasov A., 20252025Bagraev N., Martin G., Pavlov B.S., Yafyasov A.Bagraev N., Martin G., Pavlov B.S., Yafyasov A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1177

Bloch-waves in 1D periodic lattices are typically constructed based on the transfer-matrix approach, with a complete system of solutions of the Cauchy problem on a period. This approach fails for the multi-dimensional Schr¨odinger equations on periodic lattices, because the Cauchy problem is ill-posed for the associated elliptic partial differential equations. In our previous work [8] we suggested a different procedure for the calculation of the Bloch functions for the 2D Schr¨odinger equation based on the Dirichlet-to-Neumann map substituted for the transfer -matrix. In this paper we suggest a method of calculation of the dispersion function and Bloch waves of quasi-2D periodic lattices, in particular of a quasi-2D sandwich, based on construction of a fitted solvable model. 

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The authors declare that there are no conflicts of interest present.