Alev Devrim Güçlü

Artificially engineered lattices provide a flexible platform for reproducing and extending theelectronic behavior of atomic-scale materials. Artificial graphene systems, in particular, mimicgraphene-like linear dispersion with tunable Dirac cones and offer a route to realizing more exoticband structures. Here we examine the emergence of quartic energy dispersion in artificial grapheneheterostructures using analytical modeling and numerical solutions of the effective Hamiltonian.We identify three distinct quartic band types—Mexican-hat-shaped (MHS), purely quartic, andnon-MHS quartic bands—and determine the conditions under which each arises. We find that astaggered honeycomb lattice supports all three classes of quartic dispersion, whereas its planar counterpartyields only purely quartic and non-MHS forms. These results demonstrate the feasibility ofengineering quartic band edges in artificial lattices and clarify how lattice geometry can be used totailor their characteristics.

We present the emergence of Nagaoka ferromagnetism in semiconductor-based artificial graphene with realistic Coulomb interaction using high-precision variational and diffusion Monte Carlo methods, complemented by exact diagonalization calculations of the generalized Hubbard model. We analyze models of armchair hexagonal geometries nanopatterned on GaAs quantum wells. Our results reveal a distinct magnetic phase transition driven by the absence/addition of a single electron at half-filling. This form of itinerant magnetism, predicted rigorously for the Hubbard model, remained unascertained in large scale realistic systems. We demonstrate that Coulomb scattering terms play a crucial role in stabilizing Nagaoka ferromagnetism, enabling the observation of the phase transition for system parameters near U / t ≈ 60 .

We investigate the effects of coupling between the two zigzag edges of graphene nanoribbons on the Wigner crystallization of electrons and holes using a combination of tight-binding, mean-field Hubbard and many-body configuration interaction methods. We show that the thickness of the nanoribbon plays a crucial role in the formation of Wigner crystal. For ribbon widths smaller than 16 Å, increased kinetic energy overcomes the long-range Coulomb repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38 Å wide, strong Wigner localization is observed for an even number of electrons, revealing an even-odd effect also found in the Coulomb-blockade addition spectrum. Interedge correlations are found to be strong enough to allow simultaneous crystallization on both edges, although an applied electric field can decouple the two edges. Finally, we show that Wigner crystallization can also occur for holes, albeit weaker than for electrons.

We theoretically investigate the effects of long-range disorder and electron-electron interactions on the optical properties of hexagonal armchair graphene quantum dots consisting of up to 10 806 atoms. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard, and configuration interaction methods. Imperfections in the graphene quantum dots are modeled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, the tight-binding method gives a poor description of the low-energy absorption spectra compared to mean-field and configuration interaction calculation results. As the size of the graphene quantum dot is increased, the universal optical conductivity limit can be observed in the absorption spectrum. When disorder is present, the calculated absorption spectrum approaches the experimental results for isolated monolayers of graphene sheets.