Model majhnega polarona - sklopitev elektronov z bozoni s trdo sredico

Kovač, Klemen (author), Bonča, Janez (mentor)

Elektron elektrostatsko interagira z okoliškimi gradniki kristalne rešetke polarizabilnega kristala. Kot posledica interakcije se okoli elektrona deformira rešetka in se tvori polaronski kompleks. Lastnosti polarona, kvazidelca elektron-fononske sklopitve, so precej drugačne od lastnosti prostega elektrona. Fizikalne lastnosti sistema, v katerem je omenjena interakcija prisotna, so lahko torej povsem drugačne kot lastnosti sistema, kjer je ta sklopitev zanemarljiva. Že kar nekaj časa je znano, da interakcija elektronov s fononi omogoča nastanek nizkotemperaturne superprevodnosti. Ni pa še povsem jasno, ali elektron-fononska sklopitev igra ključno vlogo tudi pri mehanizmu visokotemperaturnih superprevodnikov in pri kolosalni magnetoupornosti feromagnetnih oksidov. Magistrsko delo se posveča modelu majhnega polarona. Standardni Holstein-Hubbardov model omejimo z zamenjavo fononov z bozoni s trdo sredico (HCB). HCB model apliciramo na enodimenzionalni sistem enega oziroma dveh elektronov. Analiziramo statične lastnosti sistemov kot so energijska disperzija najnižjih stanj, pričakovano število bozonov v teh stanjih, kinetična energija, kvazidelčna teža in efektivna masa polarona, ter spektralno funkcijo. Obnašanje modela se zaradi omejitve trde sredice precej razlikuje od napovedi standardnega Holstein-Hubbardovega modela. Kljub temu pa je model še kako relavanten, saj se njegove prostostne stopnje ujemajo s prostostnimi stopnjami verige spinov-1/2 in posledično omogoča opis spinskih polaronov. V zaključku omenimo nekaj potencialnih smeri nadaljnega dela.

• Language: Slovenian
• Keywords: polaroni, elektron-fononska sklopitev, Holstein-Hubbardov model, bozoni s trdo sredico, spektralna funkcija
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-138759
• COBISS.SI-ID: 120201475
• Publication date in RUL: 16.08.2022

KOVAČ, Klemen, 2022, Model majhnega polarona - sklopitev elektronov z bozoni s trdo sredico [online]. Master’s thesis. [Accessed 14 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=138759

Secondary language

• Language: English
• Title: Small polaron model - electrons coupled to hard-core bosons

Abstract

An electron interacts electrostatically with the surrounding building blocks of a polarisable crystal lattice. The consequence of the interaction is a deformation formed around the electron. This complex is called a polaron, a quasiparticle of the electron-phonon interaction. Polaron properties are a lot different than the properties of a free electron. Physical properties of the system, in which such interaction is present, can, consequently, also be a lot different from the properties of a system, in which this interaction is negligible. It has been known for quite some time already that the interaction of electrons with phonons enables low-temperature superconductivity. However, it is still not certain whether it also plays an important role in the mechanism of the high-temperature superconductors and colossal magnetoresistance in ferromagnetic oxides. This work is dedicated to the small polaron model. We restrict the standard Holstein-Hubbard model by replacing phonons with hard-core bosons (HCB). We apply the HCB model to the one-dimensional one-electron and two-electron systems. We analyze the static properties such as the energy dispersion of the lowest-lying states, the expected number of bosons in these states, the kinetic energy, the quasiparticle weight, the polaron's effective mass, and also the spectral function. The behavior of the model is a lot different than the prediction of the standard Holstein-Hubbard model due to the restriction. Nevertheless, the model is quite relevant because its degrees of freedom match the degrees of freedom of the spin-1/2 system. In conclusion, we mention some of the potential directions for further work.

• Keywords: polarons, electron-phonon coupling, Holstein-Hubbard model, hard-core bosons, spectral function