Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina

master's thesis

• Title (english): The influence of magnetic field on the one-electron spectrum of two-dimensional electron gas
• Author: Kristina Tomić
• Mentor: Danko Radić (mentor)
• Committee member: Danko Radić (predsjednik povjerenstva)
• Committee member: Gorjana Jerbić-Zorc (član povjerenstva)
• Committee member: Draginja Mrvoš-Sermek (član povjerenstva)
• Committee member: Tomica Hrenar (član povjerenstva)
• Committee member: Ana Sušac (član povjerenstva)
• Committee member: Tajana Preočanin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2016-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom diplomskom radu promatrali smo utjecaj magnetskog polja na dvodimenzionalni plin slobodnih elektrona, na elektron na dvodimenzionalnoj kristalnoj rešetci te na elektron na kvazi - jednodimenzionalnoj kristalnoj rešetci. Uveli smo magnetsko polje u sustav načelom minimalne supstitucije te opisali neke klasične aspekte polja poput magnetovodljivosti u okviru Sommerfeldovog modela metala. Proučavane su kvazi-klasične veličine poput elektronskih orbita u faznom prostoru i ciklotronske mase. U smislu kvantnomehaničkog opisa riješena je Schrödingerova jednadžba za elektron u magnetskom polju u tri karakteristične geometrije: slobodni elektron, elektron na pravokutnoj kristalnoj rešetci u okviru aproksimacije čvrste veze i elektron u kvazi-jednodimenzionalnoj geometriji te je izračunat pripadni jednoelektronski spektar i valne funkcije. Pokazano je da magnetsko polje ima fundamentalni učinak "jednodimenzionalizacije" elektronskog spektra, a na pravokutnoj rešetci vodi na pojavu iznimno kompleksnog spektra fraktalne strukture (tzv. "Hofstadterov leptir“). Također, iz sadržaja diplomskog rada, odabrana je prikladna tema koja je prilagođena za nastavni sat iz predmeta Fizika u prirodoslovnoj gimnaziji.

Abstract (english)

In this diploma thesis we considered the influence of the magnetic field on two-dimensional electron gas, the electrons on a two-dimensional lattice and the electrons in a quasi – one - dimensional lattice. We introduced the magnetic field in the system using the principle of minimal substitution and described some aspects of classical fields like magneto – conductance within the Sommerfeld model of metals. We have also studied the quasi-classical traits of the electron gas in the magnetic field like electronic orbits in the phase space and the cyclotron mass. In terms of quantum-mechanical description we solved the Schrödinger equation for the electron in the magnetic field in three characteristic geometries: free electron, electron on a rectangular lattice within the tight – binding approximation, and an electron in a quasi-one-dimensional geometry and calculated the corresponding one-electron energy spectrum and wave functions. We showed that the magnetic field has a fundamental effect of “one - dimensioning” the electronic spectrum, while the rectangular lattice leads to the occurrence of a highly complex spectrum with fractal structure (so-called "Hofstadter's butterfly"). Furthermore, we selected a suitable topic from the contents of this diploma thesis and adapted it to form a Physics lesson in the high school.

• Keywords: dvodimenzionalni elektronski plin; jednoelektronski spektar
• Keywords (english): two-dimensional electron gas; one-electron spectrum
• Language: croatian
• URN:NBN: urn:nbn:hr:217:193438
• Study programme: Title: Physics and Chemistry; specializations in: Education; Course: Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra edukacije fizike i kemije (magistar/magistra edukacije fizike i kemije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-03-05 12:45:43