GRADUATE SCHOOL OF ENGINEERING AND SCIENCE
PHYSICS GRADUATE PROGRAM
PhD Thesis Defense
Mehmet Akif Keskiner
Advisor: Prof. Dr. Mehmet Özgür Oktel
Title: Geometry, Topology, and Emergent Quantum Phases: Quasicrystals, Moir’e Magnets, and Spin Liquids
Abstract: This thesis explores how quasiperiodic geometry, moir´e 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´e 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—revealing behavior intermediate between Penrose and Ammann-Beenker quasicrystals. Moir´e 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, α, of the Kondo interaction—where small α favors extended FMC regions, while larger α leads to the coexistence of FM, AFM, and FMC textures across the moir´e unit cell. Quasicrystalline spin liquid: We formulate an exactly solvable Kitaev-type model on the dual Ammann–Beenker 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.
Date: August 20, Wednesday
Time: 16:00
Place: Department of Physics seminar room SA-240