20.500.12556/RUL-167690 Prestavljalni tok v Rice-Melejevem modelu in Kronig-Penneyjevem modelu Shift current in the Rice-Mele model and the Kronig-Penney model Prestavljalni tok je nelinearni optični odziv drugega reda, ki se pojavi le v materialih brez simetrije inverzije. Nanaša se na enosmerni tok, ki nastane pri vzbuditvi elektronov s fotoni iz nižjega v višji energijski pas. V magistrskem delu študiramo prestavljalni tok v enodimenzionalnem kristalu. Najprej obravnavamo Rice-Melejev model, za katerega izračunamo prestavljalni tok analitično. Od prej poznano analitično rešitev za prestavljalni tok razširimo za primer poljubnih položajev atomov znotraj osnovne celice. Električno polje opišemo z uporabo Peierlsove substitucije in prestavljalni tok izračunamo tudi numerično. Numerični rezultat se z analitičnim dobro ujema. V nadaljevanju nas zanima vpliv oblike atomskih orbital. Kristal opišemo s Kronig-Penneyjevim modelom, ki ga obravnavamo v približku tesne vezi. S pomočjo Löwdinove ortogonalizacije zagotovimo ortogonalnost baze. Tok izračunamo tako direktno, kot prek preslikave na Rice-Melejev model. Rešitvi se dobro ujemata, kar kaže, da je vpliv oblike atomskih orbital majhen. Shift current is a second-order nonlinear optical effect that occurs only in materials lacking inversion symmetry. It refers to a direct current generated by photons exciting electrons from a lower to a higher energy band. In this master's thesis, we study the shift current in a one-dimensional crystal. First, we describe the crystal within Rice-Mele model and analytically calculate the shift current. We extend the previously known analytical solution for the shift current to account for arbitrary atomic positions within the unit cell. The electric field is described using the Peierls substitution. We also compute the shift current numerically. The numerical results show good agreement with the analytical solution. Next, we investigate the influence of atomic orbital shapes on the shift current. To achieve this, we describe the crystal using the Kronig-Penney model, which we analyze within the tight-binding approximation. We ensure the orthogonality of the basis functions using Löwdin’s orthogonalization. The current is computed both directly and through mapping onto the Rice-Mele model. The two approaches yield consistent results, indicating that the influence of atomic orbital shapes on the shift current is negligible. prestavljalni tok prestavljalni vektor Rice-Melejev model Kronig-Penneyjev model Peierlsova substitucija Löwdinova ortogonalizacija približek tesne vezi atomske orbitale shift current shift vector Rice-Mele model Kronig-Penney model Peierls substitution Löwdin orthogonalization tight-binding approximation atomic orbitals true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-03-07 08:15:06 2025-03-07 08:15:14 2025-03-10 14:39:42 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 150054 228076291 16694.pdf 16694.pdf 1 2F489AEE9CED330F486E515D1FE3857B a2b901af89853c085706938645a84ce14aa9f0cfb72ddbc88a955d48750a8f1e fb3fe192-fb22-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=200407 Fakulteta za matematiko in fiziko 0 0 0