A. D. Guclu

Izmir Institute of Technology · Department of Physics

Semiconductor artificial graphene nanostructures where the 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 a...

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 exp...

We investigate finite size and external magnetic field effects on the atomic collapse due to a Coulomb impurity placed at the center of a hexagonal graphene quantum dot within tight binding and mean-field Hubbard approaches. For large quantum dots, the atomic collapse effect persists when the magnetic field is present, characterized by a series of...

In this thesis, electronic, magnetic, and transport properties of armchair edged hexagonal and zigzag edged triangular graphene quantum dots (GQDs) are investigated in the presence of charged impurities. In this manner, a special attention has been paid to the Coulomb impurity problem in these structures. The collapse of the wave functions starting...

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...

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...

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...

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 $\beta$ of the charge impurities and the distance R between them. For $\beta=0$, the magnetic properties of the vacancies are dictated by...

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 and the half-fil...

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 hal...

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...

We present the Wigner crystallization on partially filled topological flat bands. We identify the Wigner crystals by analyzing the cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength measured by the magnitude of the Fourier peaks, in...

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...

We computationally analyze the optical conductance of clean and disordered graphene quantum dots (GQD) consisting of up to 10806 atoms . The calculations are performed within tight binding, mean field Hubbard and configuration interaction approximations where the imperfections in the GQD are modeled using a random potential landscape. The optical c...

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 crysta...

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. Imperfectio...

We investigate the Wigner crystallization of electrons and holes at the zigzag edges of graphene nanoribbons using a combination of tight-binding, mean field Hubbard and many-body configuration interaction methods. The long-range electron-electrons interaction causes the electronic localization at the zigzag edge of graphene nanoribbon and formatio...

No abstract is available for this article.

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 st...

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 ele...

magnified image We present here a theory of the optical properties of graphene quantum dots (GQDs) with tunable band gaps by lateral size confinement, from UV to THz. Starting from the Hartree–Fock ground state, we construct the correlated many‐body ground and excited states of GQDs as a linear combination of a finite number of electron–hole pair e...

magnified image When a Dirac electron is confined to a triangular graphene quantum dot with zigzag edges, its low‐energy spectrum collapses to a shell of degenerate states at the Fermi level leading to a magnetized edge. The shell degeneracy and the total magnetization are proportional to the edge size and can be made macroscopic. In this review, w...

We present a theory of the effect of spin-orbit coupling on optical properties of triangular graphene quantum dots (TGQD). TGQDs with zigzag edges exhibit a degenerate band of states at the Fermi level. For the charge neutral TGQD, the shell is expected to be half-filled by spin polarised electrons leading to finite magnetisation. Using four-band t...

We study the interaction between two magnetic adatom impurities in graphene using the Anderson model. The two-impurity Anderson Hamiltonian is solved numerically by using the quantum Monte Carlo technique. We find that the inter-impurity spin susceptibility is strongly enhanced at low temperatures, significantly diverging from the well-known Ruderm...

After a brief review of the history of research on carbon materials, this chapter describes fabrication methods, mechanical properties and electronic band structure of bulk graphene, including the tight-binding model, effective mass model of Dirac Fermions, Berry’s phase, chirality and absence of backscattering, and the effect of interlayer couplin...

In this chapter we describe magnetic properties of graphene quantum dots and rings with broken sublattice symmetry using the TB+HF+CI methodology. The broken sublattice symmetry leads to the existence of a shell of degenerate levels at the Fermi level. We discuss how the electronic and magnetic properties of GQDs depend on the filling of the shell...

This chapter describes the size, shape and edge dependence of the electronic properties of graphene quantum dots obtained using the empirical tight-binding model. The effective mass extension of the TB model is discussed, including the effect of the magnetic field. The one-band TB model is extended to the \(sp^2\) TB model and spin-orbit coupling i...

This chapter describes the optical properties of graphene quantum dots. It discusses the size, shape and edge dependence of the energy gap, optical joint density of states, excitons, charged excitons, optical spin blockade and optical control of the magnetic moment in triangular graphene quantum dots with zigzag edges. The electronic and optical pr...

This chapter describes the fabrication methods and experiments on graphene nanostructures and quantum dots, with focus on the role of edges and size quantization effects.

This chapter introduces the problem of electron–electron interactions, briefly describes several methods and their application to graphene quantum dots. The Hubbard model, the mean-field Hartree-Fock method, the Density Functional Theory and the configuration interaction (CI) method are introduced and applied to graphene quantum dots.

We present a microscopic theory of electronic and optical properties of colloidal graphene quantum dots (CGQDs). The single-particle properties are described in the tight-binding model based on the pz carbon orbitals. Electron-electron screened Coulomb direct, exchange, and scattering matrix elements are calculated using Slater pz orbitals. The man...

This chapter introduces and motivates the subject of the monograph, the rapidly growing field of research on the electronic, optical and magnetic properties of graphene quantum dots.

Single particle properties of graphene quantum dots.- Electron-electron interaction in gated graphene nanostructures.- Magnetic properties of gated graphene nanostructures.- Optical properties of graphene nanostructures.

To create carbon-based nanoscale integrated electronic, photonic, and spintronic circuit one must demonstrate the three functionalities in a single material, graphene quantum dots (GQDs), by engineering lateral size, shape, edges, number of layers and carrier density. We show theoretically that spatial confinement in GQDs opens an energy gap tunabl...

We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a shell of degenerate states at the Fermi level. We derive a semi-analytical form for zero-energy states...

We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in Möbius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the Möbius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigza...

We show that the magnetization of triangular graphene quantum dots with zigzag edges can be manipulated optically. When the system is charge neutral, the magnetic moment can be first erased by addition of a single electron spin with a gate, then restored by absorption of a photon. The conversion of a single photon to a magnetic moment results in a...

We present a theory of electronic properties of gated triangular graphene quantum dots with zigzag edges as a function of size and carrier density. We focus on electronic correlations, spin and geometrical effects using a combination of atomistic tight-binding, Hartree-Fock and configuration interaction methods (TB+HF+CI) including long range Coulo...

We demonstrate that in triangular graphene quantum dots with zigzag edges (TGQD), robust optical transitions occur simultaneously in the THz, visible and UV spectral ranges. Optical properties are determined by strong electron‐electron and excitonic interactions. Using a combination of tight‐binding, Hartree‐Fock and configuration interaction app...

Our recent work on the electronic and optical properties of semiconductor and graphene quantum dots is reviewed. For strained self-assembled InAs quantum dots on GaAs or InP substrate atomic positions and strain distribution are described using valence-force field approach and continuous elasticity theory. The strain is coupled with the effective m...

Electronic and magnetic properties of triangular graphene rings potentially fabricated using carbon nanotubes as masks are described as a function of their size and width. The electronic properties of the charge neutral system are calculated using tight-binding method and interactions are treated using the mean-field Hubbard model. We show that for...

We present theoretical results based on mean-field and exact many-body approaches showing that in bilayer triangular graphene quantum dots with zigzag edges the magnetism can be controlled by an external vertical electric-field. We demonstrate that without electric field the spins of the two layers of the quantum dot interact ferromagnetically. At...

We present the results of ab initio calculations of the effect of reconstruction and passivation of zigzag edges on the electronic and magnetic properties of triangular graphene quantum dots. We find that, similarly to nanoribbons, hydrogen-passivated ideal zigzag edges are energetically favored over the pentagon-heptagon zigzag. However, the recon...

We present a theory of optical, magnetic and electronic properties of graphene quantum dots. We demonstrate that there exists a class of triangular graphene quantum dots with zigzag edges [1-8] which combines magnetic, optical and transport properties in a single-material structure. These dots exhibit robust magnetic moment and optical transitions...

We use Quantum Monte Carlo (QMC) techniques to investigate the behavior of electrons in an inhomogeneous quasi-one-dimensional wire as a model of quantum point contact geometries. Previous QMC work by Guclu et al. demonstrated that electrons can be strongly localized in quantum point contacts, and this result was reproduced by Welander et al. using...

We present the results of ab-initio density functional theory based calculations of the stability and reconstruction of zigzag edges in triangular graphene quantum dots. We show that, while the reconstructed pentagon-heptagon zigzag edge structure is more stable in the absence of hydrogen, ideal zigzag edges are energetically favored by hydrogen pa...

We present a theory of excitonic processes in gate controlled graphene quantum dots. The dependence of the energy gap on shape, size and edge for graphene quantum dots with up to a million atoms is predicted. Using a combination of tight-binding, Hartree-Fock and configuration interaction methods, we show that triangular graphene quantum dots with...

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 pre...

We study electronic and magnetic properties of triangular graphene dots with zig-zag edges. Such structures have recently attracted attention due to the existance of a shell of degenerate states at the Fermi level, with half-filled shell exhibiting a magnetic moment[1,2,3]. In this work, we present new results demonstrating the important role of el...

We show that the ground state and magnetization of the macroscopically degenerate shell of electronic states in triangular gated graphene quantum dots depends on the filling fraction of the shell. The effect of degeneracy, finite size, and electron-electron interactions are treated nonperturbatively using a combination of density functional theory,...

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system — a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low-density region, where localization of electrons occurs. The nature of the transition fro...

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...

We present results of tight binding calculations demonstrating existence of degenerate electronic shells of Dirac Fermions in narrow, charge neutral graphene quantum rings. We predict removal of degeneracy with finite magnetic field. We show, using a combination of tight binding and configuration interaction methods, that by filling a graphene ring...

We study electronic properties of Graphene quantum dots in magnetic fields. Graphene quantum dots are atomically thick nanometer-scale islands constructed by connecting benzene molecules. Quantum dots with triangular and hexagonal shape have shown to have different edge properties [1,2], and triangular zig-zag structures have recently attracted att...

We use Quantum Monte Carlo techniques to map out the phase diagram of interacting electrons in a quantum wire. Interacting quasi-one-dimensional systems provide excellent examples of quantum phase transitions that are tractable. Previous work gave a qualitative description of the phase diagram of a quasi-one-dimensional system [Meyer, Matveev, and...

We investigate the electronic properties of a narrow constriction (quantum point contact) in a quantum ring using variational and diffusion Monte Carlo methods. Quantum point contacts are basic building blocks of nanoscale devices. The experimental control over their width allowed the observation of conductance quantization in integer steps of G0=2...

We argue that Coulomb blockade phenomena are a useful probe of the cross-over to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to r_s ~ 55), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by com...

We investigate the electronic properties of quantum dots in the low density regime up to rs˜60 using variational and diffusion quantum Monte Carlo methods. Quantum dots are highly tunable systems that allow the study of the physics of strongly correlated electrons. With decreasing electronic density, interactions become stronger and electrons are e...

We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than...

We propose a new scheme for an approximate solution of the Schroedinger equation for a many-body interacting system, based on the use of pairs of walkers. Trial wavefunctions for these pairs are combinations of standard symmetric and antisymmetric wavefunctions. The method consists in applying a fixed-node restriction in the enlarged space, and com...

Physical properties of the electron gas, which describes conduction electrons interacting via Coulomb forces, change dramatically depending on the balance between the strength of the kinetic energy and the Coulomb repulsion. For weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the s...

The maximum-density droplet of quantum dots is a finite-size realization of the state at filling factor one. For a sufficiently small number of electrons, it becomes unstable to the creation of a central hole as the magnetic field is increased or the strength of the confinement potential reduced. The simplest model for the hole is a vortex at the c...

Properties of the "electron gas" - in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected - change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood. For very weak interactions (high density), the system behaves as a Fermi liquid, with del...

The maximum-density droplet of quantum dots in a high magnetic field, which is a finite-size realization of the state at filling factor 1, becomes unstable to the creation of a central hole (provided it contains a small number of electrons) as the magnetic field is increased or the strength of the confinement potential reduced. The simplest model f...

Composite fermion wave functions projected onto the lowest Landau level, provide an accurate description of two-dimensional quantum dots in the limit of strong magnetic fields. We show that the range of validity of these wave functions can be extended to smaller magnetic fields by incorporating Landau level mixing effects with the variational and d...

Composite-fermion wave functions, projected onto the lowest Landau level, provide accurate wave functions for quantum dots in the limit of strong magnetic fields. We show that the range of validity of these wave functions can be greatly extended to smaller magnetic fields by incorporating Landau level mixing effects by multiplying them with a Jastr...

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 th...

this paper to report our investigation of geometrical factors in QD's under an external uniform magnetic field. Using an exact diagonalization technique in a continuous potential landscape, with up to five confined electrons. An exact calculation on the energetics of interaction, magnetic field, and geometry is very valuable for elucidating many-bo...

For filling factors 1/(2n+1) (n an integer) corresponding to angular momenta L = (2n+1)N(N-1)/2, where N is the number of electrons, the Laughlin wavefunction is both compact and accurate. By performing variational and diffusion Monte Carlo calculations we show that it can be improved by multiplying it by a Jastrow factor that puts in the correct e...

We report a theoretical investigation of the Kondo effect in a quantum dot (QD) molecule, where a larger QD supports multiple transmission channels and a smaller side-coupled QD acts as the Kondo impurity. The conductance can be completely suppressed by Kondo scattering when there is only one transport channel; but for multiple channels the conduct...

We report diffusion quantum Monte Carlo (DQMC) calculations of disordered quantum dots in the presence of an external magnetic field. The addition spectra, spin configuration, Hund’s rule, and many-body densities are investigated up to 13 electrons. The data from DQMC is in excellent agreement with exact diagonalization for disorder-free quantum do...

We report exact diagonalization studies of quantum dots in which energetics due to electron-electron interaction, magnetic field, and geometrical factors compete and induce interesting ground-state electron configurations. The geometrical effect is generated by a confining potential in the form of a ring with a quantum dot in the middle. Due to the...

Carrier transport and recombination in a strained InGaAsP/InP multiple-quantum-well structure emitting at 1.55 μm are investigated experimentally and theoretically using both time-resolved photoluminescence and Monte Carlo simulations. A method for including carrier recombination in a Monte Carlo simulation is described. The calculated spectra are...

The most widespread approaches to semiconductor device simulation are the drift-diffusion equations, momentum/energy balance equations, and the Monte Carlo method. In this article, the first comparison between results of a Monte Carlo simulation of a multiple-quantum-well structure and those obtained using a classical drift-diffusion simulator is p...

Many-body addition spectra of a circularly shaped quantum dot having two potential minima is studied by exact diagonalization. Such a potenial landscape generates interesting energetic competition between direct Coulomb interaction, exchange, external magnetic field, and the geometrical factor. Due to a spatial separation of electrons in the dot, a...