Electrons scattering in the monolayer graphene with the short-range impurities

Scattering problem for electrons in monolayer graphene with short-range perturbations of the types “local chemical potential” and “local gap” has been solved. Zero gap and non-zero gap kinds of graphene are considered. The determined S-matrix can be used for calculation of such observables as conductance and optical absorption.     

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking(symmetry of sublattices).We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for "local chemical potential" and "local gap".The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states(BSs) has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~+(r),g_m~+(r),and f_m~-(r),g_m~-(r),can be established by SO(2) group.     

Bound states in disclinated graphene with Coulomb impurities in the presence of a uniform magnetic field

In this contribution, we study the effects caused by an impurity on the quantum dynamics of massive excitations in a disclinated graphene in the presence of an external magnetic field. Within a continuum approach, the problem is mathematically modeled by the definition of a special vector potential containing all the information about the topology and the interacting fields. The presence of disclination is introduced by a term in the Dirac equation that translates the appearance of a phase associated with the transport of the spinor around the apex of the cone. We solve exactly the Dirac equation for this problem and the eigenvalues are obtained. We observe the influence of the disclination on the spectrum of energy and the allowed values of magnetic field.     

The role of the Rashba coupling in spin-current of monolayer gapped graphene

In the current work, based on a semiclassical Boltzmann approach, we have investigatedthe influence of the Rashba spin-orbit coupling on spin-current of a single layer gappedgraphene. It was shown that the Rashba coupling plays a considerable role in thegeneration of the spin-current of vertical spins in mono-layer graphene. The behavior ofthe spin-current is determined by the density of impurities. It was also shown that thespin-current of the system could increase by increasing the Rashba coupling strength andband-gap of the graphene and the sign of the spin-current could be controlled by thedirection of the current-driving electric field.     

Optical properties of gapped graphene structure driven by electron electron interaction

We analyze the effects of on-site electronic coulomb repulsion U on the optical absorption and density of states of a graphene like structure with two different sublattice on-site energies in the context of Hubbard model. Mean field approximation has been implemented in order to find excitation spectrum of electronic system. Antiferromagnetic long range ordering has been considered as the ground state of model Hamiltonian. We find that the band gap in both optical conductivity and density of states decreases with strength of coulombic interaction. The absorption spectra of the graphene like structure as a nanoscale system exhibit the prominent peaks, mainly owing to the divergent density of states and excitonic effects.     

Bound states and equation of state for nondegenerate quantum systems with short-range interactions

The influence of bound states on the second virial coefficient for systems with short-range interactions is investigated, and the equation of state is determined by different methods. The dissociation equilibrium between bound and free particles is discussed.     

Domain walls in gapped graphene

The electronic properties of a particular class of domain walls in gapped graphene are investigated. We show that they can support midgap states which are localized in the vicinity of the domain wall and propagate along its length. With a finite density of domain walls, these states can alter the electronic properties of gapped graphene significantly. If the midgap band is partially filled, the domain wall can behave like a one-dimensional metal embedded in a semiconductor and could potentially be used as a single-channel quantum wire.     

Acoustic analog of monolayer graphene and edge states

Acoustic analog of monolayer graphene has been designed by using silicone rubber spheres of honeycomb lattices embedded in water. The dispersion of the structure has been studied theoretically using the rigorous multiple-scattering method. The energy spectra with the Dirac point have been verified and zigzag edge states have been found in ribbons of the structure, which are analogous to the electronic ones in graphene nanoribbons. The guided modes along the zigzag edge excited by a point source have been numerically demonstrated. The open cavity and “Z” type edge waveguide with 60° corners have also been realized by using such edge states.     

Design of electron wave filters in monolayer graphene with velocity modulations

We compare the transport properties of electrons in monolayer graphene by modulating the Fermi velocity inside the barrier. A critical transmission angle is found only when the Fermi velocity in the barriers is larger than the one outside the barriers. It is shown that the transmission exhibits periodicity with the incident angle below the critical transmission angle, and attenuates exponentially in the opposite situation. For both situations, peak splitting occurs in the transmission as the number of the velocity barriers increases, and the characteristics of the transmission suggest an interesting application of an excellent band-pass filter. The dependence of the conductance on the Fermi energy through an identical velocity- modulation structure differs wildly with different Fermi velocities of the barrier. The counterpart of the peak splitting is the sharp oscillations in the conductance profile. Furthermore, some oscillations for the multiple barriers are so sharp that the structure may be used as an excellent sensor.     

Nonlinear optical response in gapped graphene

We present a formulation for the nonlinear optical response in gapped graphene, where the low-energy single-particle spectrum is modeled by massive Dirac theory. As a representative example of the formulation presented here, we obtain a closed form formula for the third harmonic generation in gapped graphene. It turns out that the covariant form of the low-energy theory gives rise to peculiar logarithmic singularities in the nonlinear optical spectra. The universal functional dependence of the response function on dimensionless quantities indicates that the optical nonlinearity can be largely enhanced by tuning the gap to smaller values.     

Edge states at the interface between monolayer and bilayer graphene

The electronic properties for monolayer-bilayer hybrid graphene with zigzag interface are studied by both the Dirac equation and numerical calculation in zero field and in a magnetic field. Basically there are two types of zigzag interface dependent on the way of lattice stacking at the edge. Our study shows they have different locations of the localized edge states. Accordingly, the energy-momentum dispersion and local density of states behave quit differently along the interface near the Fermi energy EF=0.     

NMR parameters in gapped graphene systems

We calculate the nuclear spin-lattice relaxation time and the Knight shift for the case of gapped graphene systems. Our calculations consider both the massive and massless gap scenarios. Both the spin-lattice relaxation time and the Knight shift depend on temperature, chemical potential, and the value of the electronic energy gap. In particular, at the Dirac point, the electronic energy gap has stronger effects on the system nuclear magnetic resonance parameters in the case of the massless gap scenario. Differently, at large values of the chemical potential, both gap scenarios behave in a similar way and the gapped graphene system approaches a Fermi gas from the nuclear magnetic resonance parameters point of view. Our results are important for nuclear magnetic resonance measurements that target the ¹³C active nuclei in graphene samples.     

Field-induced disorder in a gapped spin system with nonmagnetic impurities

We study the combined effect of doping and an external magnetic field on S = 1/2 dimers which are weakly coupled by three-dimensional antiferromagnetic interactions J'. We show that application of an external magnetic field H opposes the long-range Ne el order which is known to result from doping with nonmagnetic impurities and drives the system back to the disordered phase if 3D interactions J' are not too large. We discuss the zero temperature phase diagram in the (H,J') plane and suggest that the reentrant behavior can be experimentally observed.     

Bound states of two surface phonons at a crystal surface with an adsorbed monolayer

We obtain the Bethe-Salpeter equation for the Green's function describing the propagation of two surface phonons interacting via cubic and quartic anharmonicity. We solve that equation by keeping only the latter contribution to its kernel. The two-dimensional nature of the problem is reflected in the existence of a bound state of two high-frequency surface phonons associated with the presence of an overlayer of light atoms, for all values of the coupling strength. This is illustrated with the detailed solution of a simple model.     

含带隙石墨烯纳米带的自旋筛选输运

利用Landauer-Büttiker公式和非平衡格林函数方法,研究了在电荷和自旋偏压共同作用下的扶手椅型石墨烯纳米带的自旋相关的电子输运性质. 当系统存在两种偏压时,不用自旋的电子具有不同的偏压窗口. 同时,含带隙石墨烯纳米带具有与自旋无关的导电电压阈值. 通过设置适当的两种偏压值,系统可以产生易于调节的单一自旋的电流.     

Analytic conditions for the existence of localized electron states in linear chains with two impurities

The negative eigenvalue theorem is used to obtain an analytic result for the integrated density of electron states in several types of low-dimensional lattices with two impurities in the tight binding approximation. From this expression, analytic conditions for the existence of localized electronic states are obtained. The result is directly applicable to the problem of surface states and that of chemisorption on a linear chain.The author would like to thank Prof. Dr. L.Valenta for suggesting the problem and for constant encouragement.     

Bound states of a photon and optical reflectivity in a monolayer of dielectric spheres

In a monolayer of arrayed macroscopic spheres of dielectric, it is shown that the localized states of photons appear as sharp peaks in the line shape of reflectivity of light. They are confirmed as such by calculating the integrated density of states of photons and the dependence of the reflectivity on the radius of spheres. The condition for their existence and the possibility of their detection are also discussed.     

Spontaneously gapped ground state in suspended bilayer graphene

Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.     

Ultrashort pulses in graphene with Coulomb impurities

We have investigated the propagation of an electromagnetic field in graphene with impurities, including the two-dimensional case. The spectrum of electrons for the graphene subsystem is taken from a model that takes into account Coulomb impurities. Based on Maxwell’s equations, we have obtained an effective equation for the vector potential of the electromagnetic field. It has been revealed that the pulse shape depends on free parameters.