پديد آورنده :
مزروعي، مهري
عنوان :
محاسبه ي فاز زاك يك مدل توپولوژيك يك بعدي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده فيزيك
صفحه شمار :
هشت، 51ص.: مصور، نمودار
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
فرهاد شهبازي
استاد مشاور :
پيمان صاحب سرا
توصيفگر ها :
عايق هاي توپولوژيك , اثر كوانتومي هال , عدد چرن , فاز بري
تاريخ نمايه سازي :
94/2/13
استاد داور :
فرهاد فضيله، مجتبي اعلايي
تاريخ ورود اطلاعات :
1396/09/26
چكيده انگليسي :
AbstractMu of condensed ma er physics is concerned with understanding how di erent kindsof order emerge from interactions between a large number of simple constituent In or dered phase su as crystals magnets and super uids the ordering is aracterisedthrough the symmetry breaking me anism in terms of a local order parameter Start ing around 1982 new mathematical ideas of quantum geometry and topology ideas havepenetrated into condensed ma er theory and led to new insights and ways of lookingat condensed ma er Recently they led to the discovery of the topological insulators anew exciting class of materials that sho ed material scientists who had studied thesematerials without noticing these properties Geometric order is preserved in Topologi cal insulators is order is a result of the time reversal symmetry In this thesis one ofsu models are studied In the mathematical expression kno ed forms have nontrivialtopology and knotless forms have trivial topology In quantum me anics the topologyof a quantum state does not ange as long as there is no energy gap Time reversal in variance is conserved in gapless nodes and kramers degeneration occurs in these points Time reversal symmetry is one of the most important symmetries in nature e interiorside of a topological insulators is gapped while the gapless edge state of these materi als cause conduction at the boundaries In this thesis we introduce two models in oneand two dimensions and investigate its topological aracteristics by calculating thetopological indices One of the wellknown indices is the ern number In 1998 Hal dane proposed a model that had a non trivial topology In the Haldane model there isa quantum Hall e ect is happened without magnetic eld and time reversal symme try breaking e model whi is proposed by Haldane is known as a ern insulator Topological index in one dimension is called zak phase Whi is also determined ex perimentally For this purpose a diatomic ain of rubidium is investigated whi isdescribed by the Rice Mele Hamiltonian We study dependance of topological invari ant to the hopping integrals We also determine the condition of existance of the edgestates and obtaine Keywords Topological insulators antum Hall efect Chern number Zak phase Berry phase
استاد راهنما :
فرهاد شهبازي
استاد مشاور :
پيمان صاحب سرا
استاد داور :
فرهاد فضيله، مجتبي اعلايي
