arXiv subjects

A. D. Güçlü

Publications and source records attributed to A. D. Güçlü.

15 recordsLinked to original sources

arXiv2025

Nagaoka ferromagnetism in semiconductor artificial graphene

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 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 $U/t \approx 60$.

cond-mat.mes-hall↗

arXiv2025

Quantum Monte Carlo study of artificial triangular graphene quantum dots

We investigate the magnetic phases of triangular graphene quantum dots (TGQDs) with zigzag edges using variational and quantum Monte Carlo methods. These systems serve as quantum simulators for bipartite lattices with broken sublattice symmetry, providing a platform to study the extended Hubbard model's emergent magnetic phenomena, including Lieb's magnetism at half-filling, edge depolarization upon single-electron addition, and Nagaoka ferromagnetism. Our non-perturbative quantum Monte Carlo simulations, performed for lattices of up to 61 sites, reveal that TGQDs transition from metallic to insulating regimes as a function of site radius size, while retaining edge-polarized ground states at half-filling. Notably, edge depolarization occurs upon single-electron doping in both metallic and insulating phases, contrasting with the Nagaoka ferromagnetism observed in hexagonal armchair geometries.

cond-mat.mes-hall↗

arXiv2023

Quantum Monte Carlo Study of Semiconductor Artificial Graphene Nanostructures

Semiconductor artificial graphene nanostructures where Hubbard model parameter $U/t$ can be of the order of 100, provide a highly controllable platform to study strongly correlated quantum many-particle phases. We use accurate variational and diffusion Monte Carlo methods to demonstrate a transition from antiferromagnetic to metallic phases for experimentally accessible lattice constant $a=50$ nm in terms of lattice site radius $ρ$, for finite sized artificial honeycomb structures nanopatterned on GaAs quantum wells containing up to 114 electrons. By analysing spin-spin correlation functions for hexagonal flakes with armchair edges and triangular flakes with zigzag edges, we show that edge type, geometry and charge nonuniformity affect the steepness and the crossover $ρ$ value of the phase transition. For triangular structures, the metal-insulator transition is accompanied with a smoother edge polarization transition.

cond-mat.mes-hall↗

arXiv2020

Atomic Collapse in Disordered Graphene Quantum Dots

In this paper, we numerically study a Coulomb impurity problem for interacting Dirac fermions restricted in disordered graphene quantum dots. In the presence of randomly distributed lattice defects and spatial potential fluctuations, the response of the critical coupling constant for atomic collapse is mainly investigated by local density of states calculations within the extended mean-field Hubbard model. We find that both types of disorder cause an amplification of the critical threshold. As a result, up to thirty-four percent increase in the critical coupling constant is reported. This numerical result may explain why the Coulomb impurities remain subcritical in experiments, even if they are supercritical in theory. Our results also point to the possibility that atomic collapse can be observed in defect-rich samples such as Ar$^{+}$ ion bombarded, He$^{+}$ ion irradiated, and hydrogenated graphene.

cond-mat.mes-hall↗

arXiv2020

Electronic and magnetic properties of graphene quantum dots with two charged vacancies

Electronic and magnetic properties of a system of two charged vacancies in hexagonal shaped graphene quantum dots are investigated using a mean-field Hubbard model as a function of the Coulomb potential strength $β$ of the charge impurities and the distance R between them. For $β=0$, the magnetic properties of the vacancies are dictated by Lieb's rules where the opposite (same) sub-lattice vacancies are coupled antiferromagnetically (ferromagnetically) and exhibit Fermi oscillations. Here, we demonstrate the emergence of a non-magnetic regime within the subcritical region: as the Coulomb potential strength is increased to $β\sim 0.1$ , before reaching the frustrated atomic collapse regime, the magnetization is strongly suppressed and the ground state total spin is given by $S_{z}=0$ both for opposite and same sublattice vacancy configurations. When long-range electron-electronz in-teractions are included within extended mean-field Hubbard model, the critical value for the frustrated collapse increases from $β_{cf} \sim 0.28$ to $β_{cf} \sim 0.36$ for $R < 27 \ Å $ .

cond-mat.mes-hall↗

arXiv2020

Collapse of the vacuum in hexagonal graphene quantum dots: a comparative study between the tight-binding and the mean-field Hubbard models

In this paper, we perform a systematic study on the electronic, magnetic, and transport properties of the hexagonal graphene quantum dots (GQDs) with armchair edges in the presence of a charged impurity using two different configurations: (1) a central Coulomb potential and (2) a positively charged carbon vacancy. The tight binding (TB) and the half-filled extended Hubbard models are numerically solved and compared with each other in order to reveal the effect of electron interactions and system sizes. Numerical results point out that off-site Coulomb repulsion leads to an increase in the critical coupling constant to $β_{\text{c}}$ = 0.6 for a central Coulomb potential. This critical value of the $β$ is found to be independent of GQD size, reflecting its universality even in the presence of electron-electron interactions. In addition, a sudden downshift in the transmission peaks shows a clear signature of the transition from subcritical $β$ $<$ $β_{\text{c}}$ to supercritical $β$ $>$ $β_{\text{c}}$ regime. On the other hand, for a positively charged vacancy, the collapse of the lowest bound state occurs at $β_{\text{c}}$ = 0.7 for the interacting case. Interestingly, the local magnetic moment, induced by a bare carbon vacancy, is totally quenched when the vacancy is subcritically charged, whereas the valley splittings in electron and hole channels continue to exist in both regimes.

cond-mat.mes-hall↗

arXiv2018

Defect induced Anderson localization and magnetization in graphene quantum dots

We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an extended mean-field Hubbard model. We observe that randomly distributed defects with concentrations between 1-5\% of the total number of atoms leads to localization alongside magnetic puddle-like structures. We show that localization lenght is not affected by magnetization if there is an even distribution of defects between the two sublattices of the honeycomb lattice. However, for an uneven distributions, localization is found to be significantly enhanced.

cond-mat.mes-hall↗

arXiv2018

Effects of random atomic disorder on the magnetic stability of graphene nanoribbons with zigzag edges

We investigate the effects of randomly distributed atomic defects on the magnetic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. For a balanced defect distribution among the sublattices of the honeycomb lattice in the bulk region of the ribbon, the ground state antiferromagnetism of the edge states remains unaffected. By analyzing the excitation spectrum, we show that while the antiferromagnetic ground state is susceptible to single spin flip excitations from edge states to magnetic defect states at low defect concentrations, it's overall stability is enhanced with respect to the ferromagnetic phase.

cond-mat.mes-hall↗

arXiv2017

Effects of interedge scattering on the Wigner crystallization in graphene nanoribbons

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 \mboxÅ, increased kinetic energy overcomes the long-range Coulomb repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38 \mboxÅ wide, strong Wigner localization is observed for even number of electrons, revealing an even-odd effect also found in 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 occurs for holes, albeit weaker than for electrons.

cond-mat.str-el↗

arXiv2017

Effects of long-range disorder and electronic interactions on the optical properties of graphene quantum dots

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 10806 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 modelled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy absorption spectra compared to meanfield 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, calculated absorption spectrum approaches the experimental results for isolated monolayer of graphene sheet.

cond-mat.mes-hall↗

arXiv2016

Magnetic Phases of Graphene Nanoribbons under Potential Fluctuations

We investigate the effects of long-range potential fluctuations and electron-electron interactions on electronic and magnetic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. We show that electron-electron interactions make the edge states robust against potential fluctuations. When the disorder is strong enough, the presence of electron-hole puddles induces a magnetic phase transition from antiferromagnetically coupled edge states to ferromagnetic coupling, in agreement with recent experimental results.

cond-mat.mes-hall↗

arXiv2015

Wigner crystallization at graphene edges

Using many-body configuration interaction techniques we show that Wigner crystallization occurs at the zigzag edges of graphene at surprisingly high electronic densities up to $0.8$ $\mbox{nm}^{-1}$. In contrast with one-dimensional electron gas, the flat-band structure of the edge states makes the system interaction dominated, facilitating the electronic localization. The resulting Wigner crystal manifests itself in pair-correlation functions, and evolves smoothly as the edge electron density is lowered. We also show that the crystallization affects the magnetization of the edges. While the edges are fully polarized when the system is charge neutral (i.e. high density), above the critical density, the spin-spin correlations between neighboring electrons go through a smooth transition from antiferromagnetic to magnetic coupling as the electronic density is lowered.

cond-mat.mes-hall↗

arXiv2010

Spin and electronic correlations in gated graphene quantum rings

We present a theory of graphene quantum rings designed to produce degenerate shells of single particle states close to the Fermi level. We show that populating these shells with carriers using a gate leads to correlated ground states with finite total electronic spin. Using a combination of tight-binding and configuration interaction methods we predict ground state and total spin of the system as a function of the filling of the shell. We show that for smaller quantum rings, the spin polarization of the ground state at half filling depends strongly on the size of the system, but reaches a maximum value after reaching a critical size.

cond-mat.mtrl-sci↗

arXiv2009

Zero-energy states in triangular and trapezoidal graphene structures

We derive analytical solutions for the zero-energy states of degenerate shell obtained as a singular eigenevalue problem found in tight-binding (TB) Hamiltonian of triangular graphene quantum dots with zigzag edges. These analytical solutions are in agreement with previous TB and density functional theory (DFT) results for small graphene triangles and extend to arbitrary size. We also generalize these solutions to trapezoidal structure which allow us to study bowtie graphene devices.

cond-mat.mtrl-sci↗

arXiv2005

The maximum density droplet to lower density droplet transition in quantum dots

We show that, Landau level mixing in two-dimensional quantum dot wave functions can be taken into account very effectively by multiplying the exact lowest Landau level wave functions by a Jastrow factor which is optimized by variance minimization. The comparison between exact diagonalization and fixed phase diffusion Monte Carlo results suggests that the phase of the many-body wave functions are not affected much by Landau level mixing. We apply these wave functions to study the transition from the maximum density droplet state (incipient integer quantum Hall state with angular momentum L=N(N-1)/2) to lower density droplet states (L>N(N-1)/2).

cond-mat.mes-hall↗