GRADUATE SCHOOL OF ENGINEERING AND SCIENCE
\nPHYSICS GRADUATE PROGRAM<\/p>\n
PhD Thesis Defense
\nMehmet Akif Keskiner
\nAdvisor: Prof. Dr. Mehmet \u00d6zg\u00fcr Oktel<\/p>\n
Title: Geometry, Topology, and Emergent Quantum Phases: Quasicrystals, Moir\u2019e Magnets, and Spin Liquids<\/p>\n
Abstract: This thesis explores how quasiperiodic geometry, moir\u00b4e superlattice, and fraction-lized spin excitations generate novel electronic and magnetic behavior. Through four theoretical studies, it examines: (i) strictly localized states in the Socolar dodecagonal quasicrystal; (ii) magnetic textures in a twisted moir\u00b4e superlattice; (iii) Kitaev-type spin liquids on the dual Ammann-Beenker quasicrystal; and (iv) magnetic order induced by Kondo coupling to quantum spin liquids. Localized states: In the Socolar dodecagonal lattice (SDL), a quasicrystal with twelvefold symmetry, we identify 18 distinct types of strictly localized states(LS), accounting for approximately 7.58% of the Hilbert space, closely matching numerical estimates of 7.61%. Through perpendicular space analysis, we demon-strate that at least 3.9% of sites are forbidden from hosting LS due to local connectivity constraints\u2014revealing behavior intermediate between Penrose and Ammann-Beenker quasicrystals. Moir\u00b4e magnetism: In twisted heterostructures composed of a Mott insulator and a semimetal, we study the emergence of spatially modulated magnetic order arising from nonuniform RKKY interactions. Our Monte Carlo simulations re-veal a rich phase structure: AA-stacked regions exhibit antiferromagnetic (AFM)order, AB stacked regions favor ferromagnetic (FM) alignment, and the inter-vening regions host ferromagnetic chains coupled antiferromagnetically (FMC). The spatial extent and coexistence of these domains are governed by the inverse decay length, \u03b1, of the Kondo interaction\u2014where small \u03b1 favors extended FMC regions, while larger \u03b1 leads to the coexistence of FM, AFM, and FMC textures across the moir\u00b4e unit cell. Quasicrystalline spin liquid: We formulate an exactly solvable Kitaev-type model on the dual Ammann\u2013Beenker lattice (dABL), exploiting its fourfold co-ordination and partite bond structure. Our comprehensive study uncovers a rich variety of phases, including both gapless and gapped quantum spin liquids with chiral and abelian characteristics, analyzed via Monte Carlo methods and varia- tional techniques. Additionally, incorporating an onsite perturbation refines the ground state selection to 21 unique vison configurations while preserving integra-bility. This work highlights the complex relationship between quasiperiodicity and emergent quantum magnetic phases. Spin-liquid-mediated magnetism: We investigate how magnetic order emerges among localized spins that interact exclusively via their coupling to a Kitaev-type spin liquid. Studying Kitaev, Yao-Lee, and square-lattice general- ization models, we derive effective spin interactions mediated by fractionalized Majorana fermions. Short-range couplings stabilize the spin liquid in the Kitaev model, while the Yao-Lee model exhibits long-range RKKY-like antiferromagnetic order and partial Majorana gap formation. The square lattice model shows com-peting anisotropic interactions, leading to dimerized quantum paramagnetism or Ising antiferromagnetism depending on parameters. These results reveal the rich magnetic phases enabled by Kitaev-type spin liquids.<\/p>\n
Date: August 20, Wednesday
\nTime: 16:00
\nPlace: Department of Physics seminar room SA-240<\/p>\n","protected":false},"excerpt":{"rendered":"
GRADUATE SCHOOL OF ENGINEERING AND SCIENCE PHYSICS GRADUATE PROGRAM PhD Thesis Defense Mehmet Akif Keskiner Advisor: Prof. Dr. Mehmet \u00d6zg\u00fcr Oktel Title: Geometry, Topology, and Emergent Quantum Phases: Quasicrystals, Moir\u2019e Magnets, and Spin Liquids Abstract: This thesis explores how quasiperiodic geometry, moir\u00b4e superlattice, and fraction-lized spin excitations generate novel electronic [\u2026] <\/p>\n