20.500.12556/RUL-181865 Teoretična obravnava transportnih in optičnih lastnosti elektronskih kristalov Theoretical analysis of transport and optical properties of electronic crystals V projektu obravnavamo transportne in optične lastnosti šibko dopiranih Wignerjevih kristalov. Za namen konkretnosti smo omejeni na efektivni dvodimenzionalni model tesne vezi na trikotni mreži s senčenim Coulombovim potencialom in fermioni brez internih prostostnih stopenj. Po zgledu materiala $1T-TaS_2$ smo osredotočeni na povprečne zasedenosti pri eni trinajstini atomske orbitale ter šibka dopiranja z elektroni ali vrzeli. Stanje sistema je opisano z nehomogeno teorijo Hartree-Focka, optične in transportne lastnosti pa smo preračunali z uporabo teorije linearnega odziva. Poleg tega smo upoštevali vpliva temperaturnih fluktuacij in netrivialnih konfiguracij z uporabo Metropolis-Hastingsovega algoritma. Uspelo nam je potrditi prisotnost faznega prehoda prvega reda pri končni temperaturi med fazama z in brez reda dolgega dosega. Poleg tega imata dopiranje in prisotnost domenskih sten netrivialni učinek na transportne in optične lastnosti snovi. In this project, we examine the transport and optical properties of weakly doped Wigner crystals. For concreteness, we restrict ourselves to an effective two-dimensional tight-binding model on a triangular lattice with a screened Coulomb potential and fermions without internal degrees of freedom. Following the example of the material $1T-TaS_2$, we focus on average fillings of one thirteenth of an atomic orbital, as well as weak electron or hole doping. The state of the system is described using an inhomogeneous Hartree–Fock theory, while the optical and transport properties are calculated using linear response theory. In addition, we take into account the effects of thermal fluctuations and non-trivial configurations using the Metropolis–Hastings algorithm. We confirm the presence of a first-order phase transition at finite temperature between phases with and without long-range order. Furthermore, doping and the presence of domain walls have a non-trivial effect on the transport and optical properties of the material. elektronski kristali teorija Hartree-Focka opti"cni odziv electronic crystals Hartree-Fock theory optical response true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-04-17 08:15:04 2026-04-17 08:15:10 2026-04-18 04:56:04 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 159655 275627523 21377.pdf 21377.pdf 1 1AE4293AAC20E81533749FDC6F6687F4 1185bacf5147363a6317e4e2529d5d8622572bda293d3ad7c867d9a3b1d1796a 8eff101f-3a24-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=232617 Fakulteta za matematiko in fiziko 0 0 0