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[{"key": "dc.contributor.advisor", "value": "Heikkil\u00e4, Tero", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Ojaj\u00e4rvi, Risto", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2017-05-22T10:11:38Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2017-05-22T10:11:38Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2017", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1702141", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/54058", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Parhaiten tunnettu suprajohtavuuden syntymekanismi perustuu fononien v\u00e4litt\u00e4m\u00e4\u00e4n vetovoimaan elektronien v\u00e4lill\u00e4. T\u00e4ss\u00e4 tutkielmassa tutkin fononien v\u00e4litt\u00e4m\u00e4\u00e4 suprajohtavuutta systeemeiss\u00e4, jossa elektronivy\u00f6t ovat tasomaisia. Tasovy\u00f6ll\u00e4 elektronien dispersio on eritt\u00e4in heikko, jolloin tilatiheys on tavanomaista suurempi. T\u00e4m\u00e4n takia suprajohtavuus tasovy\u00f6ll\u00e4 on tavanomaista voimakkaampi silloin kun elektronien v\u00e4linen vetovoima on heikko.\r\nEliashbergin teoria on elektroni\u2013fononi-suprajohtavuuden teoria, joka ottaa luonnollisella tavalla fononien \u00e4\u00e4rellisen nopeuden huomioon elektronien v\u00e4lisess\u00e4 vuorovaikutuksessa. Pohjustuksena tasovy\u00f6suprajohtavuuteen perehdyn Eliashbergin teoriaan ensin Fermi-pinnalla. Tarkastelen my\u00f6s Coulombin vuorovaikutuksen sek\u00e4 fononispektrin vaikutusta Fermi-pinnan suprajohtavuuteen. Ratkon Eliashbergin teorian integraaliyht\u00e4l\u00f6ryhm\u00e4\u00e4 eri tapauksissa numeerisesti.\r\nTutkielmassa sovellan Eliashbergin teoriaa tasovy\u00f6mallille ja johdan uusia tuloksia t\u00e4ss\u00e4 mallissa. Redusoimalla Eliashbergin teorian staattisen vuorovaikutuksen rajalle saan selville tasovy\u00f6n BCS-vuorovaikutusparametrin mikroskooppisten suureiden avulla ilmaistuna. Huomaan kriittisen l\u00e4mp\u00f6tilan olevan heikolla kytkenn\u00e4ll\u00e4 kytkinvakion suhteen lineaarinen, mik\u00e4 vastaa aiempaa BCS-teorian ennustetta. T\u00e4m\u00e4 lineaarisuus s\u00e4ilyy my\u00f6s \u00e4\u00e4rellisen litteill\u00e4 dispersioilla. Tarkastelen my\u00f6s tasovy\u00f6ll\u00e4 fononispektrin ja Coulombin vuorovaikutuksen vaikutusta suprajohtavuuteen.\r\nKonkreettisena esimerkkin\u00e4 tasovy\u00f6systeemist\u00e4 tutkin romboedrisen grafiitin pintatiloja. Romboedrisen grafiitin elektronista rakennetta tarkastelen matalan energian rajalla ja esittelen pintatilojen matemaattisen johdon. Muotoilen Eliashbergin teorian itsekonsistenssiyht\u00e4l\u00f6t romboedriselle grafiitille matriisimuodossa, mik\u00e4 on my\u00f6s uusi tulos.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "The best-known mechanism for superconductivity is the phonon-mediated attractive interaction between electrons. In this thesis, I study phonon-mediated superconductivity in systems containing flat electronic bands. In the flat band, the electronic dispersion is very weak, which corresponds to a high density of states. For this reason, superconductivity in the flat band is stronger than in the Fermi surface when the attractive interaction is weak.\r\nThe Eliashberg theory is a rigorous theoretical framework of electron-phonon superconductivity, which takes naturally into account the finite speed of the phonons in the interaction between the electrons. As a preparation for the study of the flat band superconductivity, I review the Eliashberg theory for the Fermi surface. I also consider the effects of the Coulomb interaction and of different phonon spectra to superconductivity in the Fermi surface. I solve the self-consistency equations of the Eliashberg theory numerically.\r\nI apply the Eliashberg theory to a flat band model, in which I obtain novel results. By reducing the Eliashberg theory to a limit of a static interaction, I find the flat-band BCS interaction constant in terms of microscopic parameters. I also find the critical temperature to be linear with respect to the interaction constant, which agrees with the earlier results based on the BCS theory. I examine the effects of the different phonon spectra and the Coulomb interaction on superconductivity also in the flat band.\r\nAs a concrete example of a flat band system I study the surface states of rhombohedral graphite. I present the electronic structure of rhombohedral graphite within the lowenergy approximation and contruct the surface states. I obtain some new results by formulating the self-consistency equations of the Eliashberg theory for the rhombohedral graphite in an matrix form.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Risto Ojaj\u00e4rvi (rimamaoj) on 2017-05-22 10:11:37.624271. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2017-05-22T10:11:38Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201705222445.pdf: 1390125 bytes, checksum: aab0bdd27f523bcb26f461c62c7bd79b (MD5)\r\nlicense.html: 4818 bytes, checksum: 95166154e378330cf0d7c520e36fe2c1 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2017-05-22T10:11:38Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201705222445.pdf: 1390125 bytes, checksum: aab0bdd27f523bcb26f461c62c7bd79b (MD5)\r\nlicense.html: 4818 bytes, checksum: 95166154e378330cf0d7c520e36fe2c1 (MD5)\r\n Previous issue date: 2017", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (71 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "suprajohtavuus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "elektroni-fononi-vuorovaikutus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Eliashbergin teoria", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "tasovy\u00f6", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "romboedrinen grafiitti", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "pintatilat", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "superconductivity", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "electron-phonon interaction", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Eliashberg theory", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "flat band", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "rombohedral graphite", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "surface states", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Electron-phonon interaction in flat-band superconductivity", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201705222445", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": 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