Impurities in a biased graphene bilayer

We study the problem of impurities and midgap states in a biased graphene bilayer. We show that the properties of the bound states, such as localization lengths and binding energies, can be controlled externally by an electric field effect. Moreover, the band gap is renormalized and impurity bands are created at finite impurity concentrations. Using the coherent potential approximation, we calculate the electronic density of states and its dependence on the applied bias voltage.     

Particle-hole bound states of dipolar molecules in an optical lattice

We investigate the particle-hole pair excitations of dipolar molecules in an optical lattice, which can be described with an extended Bose-Hubbard model. For strong enough dipole-dipole interaction, the particle-hole pair excitations can form bound states in one and two dimensions. With decreasing dipole-dipole interaction, the energies of the bound states increase and merge into the particle-hole continuous spectrum gradually. The existence regions, the energy spectra and the wave functions of the bound states are carefully studied and the symmetries of the bound states are analyzed with group theory. For a given dipole-dipole interaction, the number of bound states varies in momentum space and a number distribution of the bound states is illustrated. We also discuss how to observe these bound states in future experiments.     

Coulombic bound states in semiconductor quantum wells

Recent theoretical works on Coulombic bound states in semiconductor quantum wells (Q.W.) are reviewed. Due to carrier confinement along the growth axis the bound impurity or exciton states display enhanced binding energies over the bulk values. The presence of free carriers in modulation-doped quantum wells decreases the impurity binding energies. However the quasi-bidimensionality of the carrier motion prevents a complete vanishing of impurity bound states. The photoluminescence line of high-quality quantum well is often Stokes-shifted with respect to the absorption or excitation spectra. This Stokes shift can be correlated with interface defects in a qualitative fashion.     

Massless Electronic Excitations in Graphene Near Coulomb Impurities

Journal of Experimental and Theoretical Physics - We study low-energy massless electronic excitations in a graphene monolayer near a pointlike Coulomb impurity. We assume that such excitations are...     

The emergence of bound states in a superconducting gap at the topological insulator edge

We consider the edge of a superconducting topological insulator with the impurity in the presence of the Zeeman field. We analytically prove that in the trivial phase two Andreev bound states (ABSs) arise with energies moving from the superconducting gap edges to zero forming two Majorana-like bound states, as the impurity strength varies from 0 to ±2. When the Zeeman field is locally perturbed, ABSs arise both in the trivial and topological phases, but in the topological phase ABSs with energy near the gap edges cannot transform into Majorana bound states and vice versa.     

Visualization of nano-plasmons in graphene

We study localized plasmons at the nanoscale (nano-plasmons) in graphene. The collective excitations of induced charge density modulations in graphene are drastically changed in the vicinity of a single impurity compared to graphene's bulk behavior. The dispersion of nano-plasmons depends on the number of electrons and the sign, strength and size of the impurity potential. Due to this rich parameter space the calculated dispersions are intrinsically multidimensional requiring an advanced visualization tool for their efficient analysis, which can be achieved with parallel rendering. To overcome the problem of analyzing thousands of very complex spatial patterns of nano-plasmonic modes, we take a combined visual and quantitative approach to investigate the excitations on the two-dimensional graphene lattice. Our visual and quantitative analysis shows that impurities trigger the formation of localized plasmonic excitations of various symmetries. We visually identify dipolar, quadrupolar and radial modes, and quantify the spatial distributions of induced charges.     

Klein Paradox of Two-Dimensional Dirac Electrons in Circular Well Potential

We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.     

Marginal Fermi liquid resonance induced by a quantum magnetic impurity in d-wave superconductors

We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.     

Substitutional impurity in the graphene quantum dots

The process of formation of the localized defect states due to substitutional impurity in sp²-bonded graphene quantum dot is considered using a simple tight-binding-type calculation. We took into account the interaction of the quantum dot atoms surrounding the substitutional impurity from the second row of elements. To saturate the external dangling sp² orbitals of the carbon additionally 18 hydrogen atoms were introduced. The chemical formula of the quantum dot is H₁₈C₅₁X, where X is the symbol of substitutional atom. The position of the localized levels is determined relative to the host-atoms (C) ε_p energies. We focused on the effect of substitutional doping by the B, N and O on the eigenstate energies and on the total energy change of the graphene dots including for O the effect of lattice distorsion. We conclude that B, N, and O can form stable substitutional defects in graphene quantum dot.     

Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields

The present paper discusses magnetic confinement of the Dirac excitations in graphene in the presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to 1/r is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in the presence of the 1/r (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cutoff Coulomb potential to dictate the excitation spectra of graphene. The spectrum of the graphene excitations in the presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.     

High magnetic field effects on shallow and deep impurities in semiconductors

It is shown that high magnetic fields provide an efficient means to distinguish strongly localized impurity states from shallow, effective-mass-like states, irrespective of the binding energies of these states. The ground and excited states of a simple model Hamiltonian for shallow and deep impurities are analyzed for arbitrary magnetic field strengths.     

Coulomb Center in a Transition Metal Dichalcogenide Monolayer

JETP Letters - Electronic processes involving a charged impurity in a transition metal dichalcogenide monolayer and in gapped graphene have been theoretically studied. The spectrum of bound states,...     

Unconventional quasiparticle lifetime in graphene

We address the question of how large can the lifetime of electronic states be at low energies in graphene, below the scale of the optical phonon modes. For this purpose, we study the many-body effects at the K point of the spectrum, which induce a strong coupling between electron-hole pairs and out-of-plane phonons. We show the existence of a soft branch of hybrid states below the electron-hole continuum when graphene is close to the charge neutrality point, leading to an inverse lifetime proportional to the cube of the quasiparticle energy. This implies that a crossover should be observed in transport properties, from such a slow decay rate to the lower bound given at very low energies by the decay into acoustic phonons.     

Local density of states of one-dimensional Mott insulators and charge-density wave states with a boundary

We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.     

Local polariton states in polar crystals with impurities

We show that an impurity embedded in an ionic crystal can give rise to a novel kind of local states. These states exist within a polariton gap of a material and are a mix of excitations of the crystal, such as phonons or excitons, and the transverse electromagnetic field. Electromagnetic components of the states along with the corresponding excitations of the material are localized in the vicinity of an impurity.     

Transition in a Luttinger liquid with two-level impurities to the fermi-liquid state

The mechanisms leading to instability of the non-Fermi-liquid state of a Luttinger liquid with two-level impurities are proposed. Since exchange scattering in 1D systems is two-channel scattering in a certain range of parameters, several types of non-Fermi-liquid excitations with different quantum numbers exist in the vicinity of the Fermi level. These excitations include, first, charge density fluctuations in the Luttinger liquid and, second, many-particle excitations due to two-channel exchange interaction, which are associated with band-type as well as impurity fermion states. It is shown that mutual scattering of many-particle excitations of various types leads to the emergence of an additional Fermi-liquid singularity in the vicinity of the Fermi level. The conditions under which the Fermi-liquid state with a new energy scale (which is much smaller than the Kondo temperature) is the ground state of the system are formulated.     

Screening of Local Magnetic Moment by Electrons of Disordered Graphene

Based on the Anderson impurity model and self-consistent approach, we investigate the condition for the screening of a local magnetic moment by electrons in graphene and the influence of the moment on electronic properties of the system. The results of numerical calculations carried out on a finite sheet of graphene show that when the Fermi energy is above the single occupancy energy and below the double occupancy energy of the local impurity, a magnetic state is possible. A phase diagram in a parameter space spanned by the Coulomb energy U and the Fermi energy is obtained to distinguish the parameter regions for the magnetic and nonmagnetic states of the impurity. We find that the combined effect of the impurity and finite size effect results in a large charge density near the edges of the finite graphene sheet. The density of states exhibits a peak at the Dirac point which is caused by the appearance of the edge states localized at the zigzag edges of the sheet.     

Effect of a single localized impurity on the local density of States in monolayer and bilayer graphene

We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in monolayer and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.     

Current carriers in a Hubbard antiferromagnet

The possible types of single-particle excitations of a Hubbard antiferromagnetic semiconductor are investigated, starting from the self-consistent-field approximation. Unlike the preceding studies, the excitation is described in the general case by a superposition of states of a freely propagating electron, an uncoupled electron-spin wave pair, and a coupled electron-spin wave pair. It is shown in this case that in a finite interval of problem parameter values there exists an isolated low-lying band, corresponding to low-mobility excitations with substantial large-radius impurity quasioscillators. It is also shown that in the strong interaction limit the excitation bandwidth remains finite due to the contribution of bound states.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 50–56, September, 1988.The author is grateful to M. I. Katsnel'son and V. Yu. Irkhin for the statement of the problem and for useful discussions, as well as M. S. Svirskii for discussing the results of this study.     

Study of shallow impurity states in compound semiconductors using high resolution photoluminescence spectroscopy

In this paper we review briefly the use of high resolution photoluminescence to study the behavior of shallow impurity states in compound semiconductors. As an illustration we focus our review on GaAs. The binding energies of the ground state and of several low-lying excited states of the impurity centers are determined by studying the radiative transitions associated with excitons bound to neutral donors or acceptors. The difference between the binding energies of different donors in GaAs is rather small. Thus to resolve transitions associated with different chemical donors a magnetic field is used. This has the effect of sharpening the transitions as well as increasing the separation between them. One can identify donors in samples with total impurity concentrations as high as 5X10¹⁵/cm³. The binding energies of different chemical acceptors in GaAs are much higher. Thus the radiative transitions associated with excitons bound to neutral acceptors can be resolved in zero magnetic field. Energy levels of shallow donors and acceptors in GaAs are reviewed.