20.500.12556/RUL-173113 Termoelektrični pojav v ekscitonskih izolatorjih Thermoelectric effect in excitonic insulators Ekscitonski izolatorji so polkovine, v katerih pri nizkih temperaturah pod vplivom Coulombske interakcije nastane kondenzat ekscitonov, vezanih stanj elektronov in vrzeli. Posledično se v disperziji odpre energijska reža in pojavijo se posebne transportne lastnosti. To stanje snovi je bilo teoretično napovedano v 60. letih prejšnjega stoletja in eksperimentalno potrjeno v 90. letih v posebnem režimu kvantnega Hallovega pojava v heterostrukturah. Nedvoumno potrditev tega stanja v kristalni snovi pa še pričakujemo. Nedavno so se pojavili kandidati za ekscitonske izolatorje, npr. Ta$_2$NiSe$_5$, vendar mehanizem njihovega faznega prehoda v izolatorsko fazo ni docela jasen. Pogost pristop k razrešitvi tovrstnih vprašanj so meritve transportnih lastnosti, ki odražajo odziv sistema na zunanje motnje. V magistrskem delu nas zanima teorija termoelektričnega transporta. Osredotočimo se na Seebeckov koeficient, ki pove, kolikšna napetost se inducira med koncema vzorca zaradi temperaturnega gradienta. V prvem delu naloge opišemo splošno teorijo transporta elektronov v kristalih, ki semiklasično sloni na Boltzmannovi teoriji, kvantno pa na Kubovi formuli linearnega odziva. V drugem delu v okviru približka povprečnega polja študiramo minimalni model ekscitonskega faznega prehoda v enodimenzionalnem elektronskem plinu ter njegov Seebeckov koeficient. Ugotovimo, da se kondenzacija ekscitonov lahko izraža v kvalitativno različnih oblikah disperzije in temperaturne odvisnosti Seebeckovega koeficienta. Pomemben rezultat je, da sipanje močno spremeni termoelektrični transport pri nizkih temperaturah, zato semiklasični opis ne zadošča. V tretjem delu opišemo Ta$_2$NiSe$_5$ s približkom tesne vezi in približkom povprečnega polja ter numerično izračunamo Seebeckov koeficient, tako v okviru Boltzmannove kot tudi Kubove teorije. Rezultat primerjamo z eksperimentalnimi meritvami in ugotovimo kvalitativno dobro ujemanje pri nizkih temperaturah. Prepoznamo tudi neskladja in predlagamo, kako bi jih lahko v prihodnosti razrešili. Excitonic insulators are semi-metals in which excitons, electron-hole pairs bound by the Coulomb interaction, condense at low temperatures. Consequently, the energy gap opens in the band structure and unusual transport properties arise. This state of matter was theoretically predicted in the 1960s. Exciton condensation was experimentally confirmed in the 1990s in a special quantum Hall regime in heterostructures, but an unambiguous confirmation of this state in bulk materials is still missing. Recently, candidate materials for excitonic insulators were proposed, e.g. Ta$_2$NiSe$_5$; however, the mechanism of their phase transition to the insulating phase is unclear. Commonly, such questions are addressed by measuring transport properties, which convey the system's response to external perturbations. In the master thesis, we are interested in thermoelectric transport and, specifically, the Seebeck coefficient. It expresses the voltage induced between ends of a sample due to a temperature gradient. In the first part, we describe a general theory of electronic transport in crystals. Semi-classically, the description is formulated within Boltzmann's theory, while quantum-mechanically, the main tool is Kubo's linear response theory. In the second part, we study a minimal model of the excitonic phase transition in a one-dimensional electron gas within the mean-field approximation, and its Seebeck coefficient. We find that the condensation of excitons can give rise to qualitatively different band structures and temperature dependence of the Seebeck coefficient. An important result is that scattering notably alters thermoelectric transport at low temperatures, which is why the semi-classical description is incomplete. In the third part, we study Ta$_2$NiSe$_5$ within the tight-binding approximation and the mean-field approximation, and numerically evaluate its Seebeck coefficient using both Boltzmann's and Kubo's theory. We compare our results to experimental data and find qualitative agreement at low temperatures. We also identify inconsistencies and propose how they could be resolved in future work. ekscitonski izolator Ta$_2$NiSe$_5$ termoelektrični transport Boltzmannova teorija Kubova teorija linearnega odziva Seebeckov koeficient excitonic insulator Ta$_2$NiSe$_5$ thermoelectric transport Boltzmann's theory Kubo's linear response theory Seebeck coefficient true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-09-13 08:15:04 2025-09-13 08:15:17 2025-11-04 03:53:25 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 153371 248960515 18966.pdf 18966.pdf 1 D9724D45E981D2DD12AB1B3DB9064527 de23e2cb2cea9a9f805609e00c3469976a6fa4e52aef5167abd6154f1c736a83 dae22f00-9068-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=217282 Fakulteta za matematiko in fiziko 0 0 0