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Author:Ijäs, Mari
Title:Modeling the electronic and transport properties of graphene nanostrutures
Grafeenin nanorakenteiden elektronitilojen ja kuljetusominaisuuksien mallinnus
Publication type:Master's thesis
Publication year:2010
Pages:vi + 70      Language:   eng
Department/School:Kemian laitos
Main subject:Fysiikka (laskennallinen fysiikka)   (Tfy-105)
Supervisor:Nieminen, Risto
Instructor:Harju, Ari
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto  3521   | Archive
Keywords:graphene
quantum transport
grafeeni
kvanttikuljetus
Abstract (eng): Graphene is a versatile material suggested for nanoelectronics applications.
The purpose of this thesis is to provide deeper understanding in the properties of the possible circuit elements and the effect of interactions.
The energetics of graphene nanoflakes were studied within the Hubbard model using both exact diagonalization and approximate methods for solving the ground state.
To improve the treatment of the interactions, maintaining the computational cost low at the same time, a lattice density functional theory method was developed for the flakes.

The densities of states and charge densities were calculated for arbitrarily-shaped large graphene structures within the tight-binding picture.
Localized single-electron states due to structural confinement were found.

The conductance of one-dimensional nanostructures, consisting of a few-site gated nanodot weakly coupled to the leads, was studied using within linear response using the Kubo formula.
Analytical expressions for the conductance due to external bias voltage were derived and using them resonance structure in the conductance were located.
The results were confirmed using another method, based on magnetic flux-induced persistent currents in a ring-shaped structure.
Also quasi-one-dimensional structures resembling narrow graphene nanoribbons were studied using the second method.
The effect of interactions was also studied and splitting of the resonances was observed.
This effect was explained in terms of an energetic competition between the Hubbard repulsion and the gate voltage applied on the dot.
Abstract (fin): Tässä diplomityössä tutkitaan grafeenin nanorakenteiden elektronisia- ja kuljetusominaisuuksia.
Grafeenihiutaleita mallinnettiin Hubbardin hamiltonilaisella.
Hiutaleiden perustua määritettiin sekä täydellä diagonalisoinnilla, että likimääräisesti keskeiskenttäapproksimaatiolla, perturhaatioteorialla ja myös rajoittamalla kantaa, jossa diagonalisointi suoritettiin.
Vuorovaikutusten johdosta tarkka ratkaisu on laskennallisesti raskas, kun taas laskennallisesti nopealla keskeiskenttäapproksimaatiolla saadut tulokset poikkeavat tarkasta ratkaisusta.
Jotta vuorovaikutukset voitaisiin huomioida paremmin pitäen samalla laskenta-aika kohtuullisena, hiutaleille muotoiltin hilatiheysfunktionaaliteoria, joka paransi hiutaleiden kuvausta vuorovaikutuksen ollessa kohtalaisen heikko.

Suurista grafeenisysteemeistä laskettiin tilatiheys sekä yhden elektronin tilojen varaustiheyksiä hyödyntäen harvojen matriisien laskentamenetelmiä.
Laskut suoritettiin tiukan sidoksen menetelmällä ilman vuorovaikutusten huomioimista.

Kvanttipisteestä ja siihen heikosti kytketyistä johteista koostuvan systeemin johtavuutta tutkittiin Kubon kaavan avulla ilman vuorovaikutuksia.
Kvanttipisteelle asetettiin ulkoinen potentiaali ja johtavuuspiikkejä havaittiin kvanttipisteen ominaisenergioita vastaavilla ulkoisen potentiaalin voimakkuuksilla.
Vastaavia vuorovaikuttavia systeemejä tutkittiin tarkastelemalla virtaa rengasmaisissa rakenteissa.
Ilman vuorovaikutusta menetelmät tuottivat yhteneviä tuloksia ja vuorovaikuttavassa systeemissä diagonalisointia verrattiin keskeiskenttämenetelmään.
Resonanssipiikkien havaittu kahtiajakautuminen selittiin systeemin energiatermien välisellä kilpailulla.
ED:2010-06-02
INSSI record number: 39700
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