Optička vodljivost dvodimenzionalnih izolatora s inverzijom valentnih vrpci

master's thesis

• Title (english): Optical conductivity of a two-dimensional insulator with valence band inversion
• Author: Karla Lemac
• Mentor: Zoran Rukelj (mentor)
• Committee member: Zoran Rukelj (predsjednik povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Committee member: Željko Skoko (član povjerenstva)
• Committee member: Mario Novak (član povjerenstva)
• Committee member: Denis Sunko (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Na temelju izmjerenih transportnih veličina, poput električne vodljivosti, možemo dobiti nekoliko informacija o elektronskim vrpcama. U ovom radu razmatramo obrnuti proces: polazeći od mikroskopskog modela dvodimenzionalnog materijala s inverzijom valentnih vrpci računamo odzivne funkcije poput istosmjerne i optičke vodljivosti. Pod materijalima s inverzijom valentnih vrpci smatramo posebnu klasu dvodimenzionalnih polumetala čije valentne vrpce posjeduju elektron-šupljina simetriju i oblikom podsjećaju na meksički šešir. Da bismo pobliže proučili transportna svojstva takvih materijala, definirali smo minimalni elektronski efektivni hamiltonijan s dvama slobodnim parametrima. Dijagonalizacijom takvog hamiltonijana dobivene su vrpce oblika meksičkog šešira i mogućnost opisa dviju različitih osnovnih elektronskih faza. To su faza s energetskim procijepom i faza čvorne petlje. Cijeli je rad usmjeren k tom da na temelju općeg oblika tenzora vodljivosti, kojeg smo izveli u formalizmu jednadžbi gibanja za neravnotežnu Landauovu funkciju distribucije, te kojeg smo podijelili na unutarvpčane i međuvrpčane doprinose, pokažemo jedinstveni otisak dviju navedenih elektronskih faza; u istosmjernom i optičkom odzivu. U istosmjernoj vodljivosti, u kojoj glavni doprinosi dolaze od unutarvrpčanih procesa na temelju ovisnosti efektivne koncentracije elektrona o dopiranju, moguće je utvrditi razliku između faze s procijepom i faze čvorne petlje. Ta je razlika među fazama očita i na primjeru gustoće elektronskih stanja, koja za slučaj faze s procijepom ima korijenski singularitet, dok je gustoća stanja u fazi čvorne petlje konstantna funkcija energije. Konačna potvrda u identifikaciji faza dolazi iz međuvrpcane tj. optičke vodljivosti jer je pokazano da optički odziv faze s čvorinom petljom iščezava.

Abstract (english)

Based on the measured transport quantities, such as electrical conductivity, we can obtain some information about electronic bands. In this paper, we consider the reverse process, starting from a microscopic model of a two-dimensional material with inversed valence bands, we calculate response functions such as DC (direct current) and optical conductivity. Under the inversion of the valence bands we consider a special class of two-dimensional semimetals valence bands that have electron-hole symmetry and are shaped like a Mexican hat. In order to study the transport properties of such materials in more detail, we defined minimal electronic effective Hamiltonian with two free parameters. Diagonalization of such a Hamiltonian, Mexican hat-shaped bands were obtained and the possibility to describe two different basic electronic phases. These are the gapped phase and the nodal surface semimetal phase. The entire paper is aimed at the fact that, based on the general form of the conductivity tensor, which we derived in the formalism the equations of motion for the non-equilibrium Landau distribution function, and which we have divided into intraband and interband excitation, we will show the unique footprint of the two mentioned electronic phases; in DC and optical response. In DC conduction, where the main excitations come from intraband processes based on the dependence of the effective electron concentration on doping, it is possible to determine the difference between the gapped phase and the nodal surface phase. This difference between phases can also be seen in the example of the density of electronic states, which for the case of a gapped phase has a root singularity, while the density of states in the nodal surface phase is a constant function of energy. The final confirmation in the identification of phases comes from interband, i.e. optical conductivity because it was shown that the optical response of the phase with the nodal surface vanishes.

• Keywords: dvodimenzionalni polumetali; dvovrpcani hamiltonijan; opticka vodljivost; istosmjerna vodljivost
• Keywords (english): two-dimensional semimetals; two-band Hamiltonian; optical conductivity; DC conductivity
• Language: croatian
• URN:NBN: urn:nbn:hr:217:641678
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2024-09-22
• Created on: 2023-01-16 13:56:01