Attractive Impurity Research Articles

Few-boson processes in the presence of an attractive impurity under one-dimensional confinement

We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with $\delta$-functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths are all calculated in terms of two parameters, namely the mass ratio: $m_{\text{L}}/m_{\text{H}}$, and ratio $g_{\text{HH}}/g_{\text{HL}}$ of the $\delta$-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic process become energetically allowed. In the Tonks-Girardeau limit ($g_{\text{HH}}\rightarrow \infty$), our results are relevant to experiments involving trapped fermions with an impurity atom.

On the possibility of the observation of the resonance interaction between kinks of the sine-Gordon equation and localized waves in real physical systems

The resonance dynamics of kinks of the sine-Gordon equation in a system with a single point impurity with allowance for the generation of localized waves in the presence of an external force and dissipation has been studied. Equations of motion for the coordinate of the kink center and the amplitude of the impurity mode have been found. The analysis of solutions of these equations and results of the numerical simulation of the modified sine-Gordon equation have showed that damping and the external force act against the appearance of the resonance reflection of the kink from the attractive impurity. However, the resonance energy exchange between solitons causing it still takes place.

Confinement effects on an ultra-cold matter wave-packet by a square well impurity near the de-localization threshold: analytic solutions, scaling, and width properties

The determination of the maximum number of atoms and the density profile of an ultra-cold wave-packet, under confinement conditions by an attractive impurity near the de-localization threshold, have been an open problem in ultra-cold atom physics. In this work, we study the effect of a wave-guide impurity on an ultra-cold matter wave-packet at the threshold of de-localization. The impurity is modeled by a 1-D square well potential with depth V 0 and length 2R 0. Coupling of the square well potential to a contact impurity of strength β at the center is also considered. The time-independent non-linear Schrodinger equation describing a Bose-Einstein condensate at the delocalization threshold is exactly solved. The density profile, maximum non-linear coupling constant, g max, and maximum number of atoms, N max, prompt to be localized by the defect potential in the ground and first excited states are also reported. It is shown that g max and the density profiles become only functions of the reduced impurity size ξ = √V 0 R 0. It is also found that the first excited state at the threshold of de-localization exists only for ξ ≥ π/(2√2), always holding a lower number of atoms than the corresponding ground state for the same reduced impurity size. Also, the addition of a repulsive contact impurity leads to a non-linear coupling constant at the de-localization threshold lower than that of the square well potential. In spite of the non-linear character of the Gross-Pitaevskii equation, it is found that a general scaling-law holds for defects with the same ξ, related with the same g max, having the same reduced density profile in the quasi-free direction. We report the full width at half maximum for the wave-function and density profile, finding a large spread for small reduced confining conditions. Implications of these results for the determination of the wave-packet properties under confinement in atom chip and Bose-Einstein condensates are presented with the aim to motivate further experimental work.

Soliton-impurity interaction in two Ablowitz-Ladik chains with different coupling

The interaction of solitons with point defects in a system of coupled Ablowitz- Ladik (AL) chains is studied numerically. The system is a discrete analog of coupled nonlinear Schrodinger equations. Two types of interchain coupling are investigated: one which admits reduction of the system to the standard integrable AL model (dispersive coupling) and one which couples opposite sites of the chains and does not admit reduction to the AL model (nondispersive coupling). The action of the two coupling types is additive and they can compensate each other in some cases. We have obtained that the single-peak bound soliton-defect solution (attractive impurity) is stable against perturbations, while the double-peak bound soliton-defect solution (repulsive impurity) is unstable and can be easily destroyed. Linear point defects do not influence the period of energy transfer and it is close to the period for the homogeneous case.

One-dimensional dark solitons in lattices with higher-order nonlinearities

The existence of dark solitons in the discrete nonlinear Schrödinger equation with third- and fifth-order nonlinearities is investigated. Effects of discreteness for the homogeneous case are analyzed. Exact analytical solutions are found for wide static dark solitons in the presence of impurities. The bound soliton-defect formations can have a single minimum for attractive impurities or two minima for repulsive impurities. In contrast to the standard cubic nonlinear case, where the positions of the minima do not depend on the nonlinearity, now they are strongly influenced by the quintic nonlinearity. The model plays an important role in numerous physical systems with complicated nonlinear interactions.

Fermi-edge transmission resonance in graphene driven by a single Coulomb impurity.

The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude ≈e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.

Impurity spectra of graphene under electric and magnetic fields

Using the coupled series expansion method developed in this paper, we have investigated the quantum behavior of Coulomb impurity states under external electric and magnetic fields in graphene. Under magnetic field, we have obtained an accurate full spectrum of the attractive and repulsive Coulomb impurities for both massless and massive Dirac electrons and have found that bound states can be tuned between in and out of the gap by Coulomb impurities and a magnetic field. When a linear radial electric field in combination with a magnetic field are applied, the energy levels of Coulomb impurity states experience intercrossing, and they disappear because of Klein tunneling as the electric field exceeds the magnetic field. The results are helpful in controlling Coulomb impurity states by external fields in graphene and the method proves to be an efficient way to obtain accurate solutions of the Dirac equation with various fields.

Fractionally charged impurity states of a fractional quantum Hall system

The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In contrast to the noninteracting case, where only a single bound state below the lowest Landau level forms, electron–electron interactions strongly renormalize the impurity potential, effectively giving it a finite range, which can support many quasi-bound states (long-lived resonances). Averaging the spectral weights of the quasi-bound states and extrapolating to the thermodynamic limit, for filling factor ν = 1/3 we find evidence consistent with localized fractionally charged e/3 quasi-particles. For ν = 2/5, the results are slightly more ambiguous, due to finite size effects and possible bunching of Laughlin-quasi-particles.

Impurity-induced subgap bound states in alkali-doped iron chalcogenide superconductors

Measurements of the local density of states near impurities can be useful for identifying the superconducting gap structure in alkali doped iron chalcogenide superconductors K_xFe_{2-y}Se_2. Here, we study the effects of nonmagnetic and magnetic impurities within a nearest neighbor d-wave and next-nearest neighbor s-wave superconducting state. For both repulsive and attractive nonmagnetic impurities, it is shown that sub-gap bound states exist only for d-wave superconductors with the positions of these bound states depending rather sensitively on the electron doping level. Further, for such disorder Coulomb interactions can lead to local impurity-induced magnetism in the case of d-wave superconductivity. For magnetic impurities, both s-wave and d-wave superconducting states support sub-gap bound states. The above results can be explained by a simple analytic model that provides a semi-quantitative understanding of the variation of the impurity bound states energies as a function of impurity potential and chemical doping level.

Binding carriers to a nonmagnetic impurity in a two-dimensional square Ising antiferromagnet

A hole in a two-dimensional Ising antiferromagnet was believed to be infinitely heavy due to the string of wrongly oriented spins it creates as it moves, which should trap it near its original location. Trugman showed that, in fact, the hole acquires a finite effective mass due to contributions from so-called Trugman loop processes, where the hole goes nearly twice around closed loops, first creating and then removing wrongly oriented spins, and ending up at a different lattice site. This generates effective second- and third-nearest-neighbor hopping terms which keep the quasiparticle on the sublattice it was created on. Here, we investigate the trapping of the quasiparticle near a single attractive nonmagnetic impurity placed at one lattice site. We consider the two cases with the quasiparticle and impurity being on the same versus on different sublattices. The main result is that even though the quasiparticle can not see the bare disorder in the latter case, the coupling to magnons generates an effective renormalized disorder on its own sublattice which is strong enough to lead to bound states, which however have a very different spectrum than when the quasiparticle and impurity are on the same sublattice.

Single nonmagnetic impurity resonance in FeSe-based 122-type superconductors as a probe for pairing symmetry

We study the effect of a single nonmagnetic impurity in AyFe2−xSe2 (A = K, Rb, or Cs) superconductors by considering various pairing states based on a three-orbital model consistent with the photoemission experiments. The local density of states on and near the impurity site has been calculated by solving the Bogoliubov-de Gennes equations self-consistently. The impurity-induced in-gap bound states are found only for attractive impurity scattering potential, as in the cases of doping of Co or Ni, which is characterized by the strong particle-hole asymmetry, in the nodeless dx2−y2 wave pairing state. This property may be used to probe the pairing symmetry of FeSe-based 122-type superconductors.

Bound states in the one-dimensional two-particle Hubbard model with an impurity

We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive ($V>0$) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion (H${}^{\ensuremath{-}}$) problem. There are several different types of bound states in this system, each of which appears in a specific region. For given $V$, there exists a (positive) critical value ${U}_{c1}$ of $U$ (the on-site atom-atom interaction), below which the ground state is a bound state. Interestingly, close to the critical value ($U\ensuremath{\lesssim}{U}_{c1}$), the ground state can be described by the Chandrasekhar-type variational wave function, which was initially proposed for H${}^{\ensuremath{-}}$. For $U>{U}_{c1}$, the ground state is no longer a bound state. However, there exists a second (larger) critical value ${U}_{c2}$ of $U$, above which a molecule-type bound state is established and stabilized by the repulsion. We have also tried to solve for the eigenstates of the model using the Bethe ansatz. The model possesses a global ${\mathbb{Z}}_{2}$ symmetry (parity) which allows classification of all eigenstates into even and odd states. It is found that all states with odd parity have the Bethe form, but none of the states in the even-parity sector. This allows us to identify analytically two odd-parity bound states, which appear in the parameter regions $\ensuremath{-}2V<U<\ensuremath{-}V$ and $\ensuremath{-}V<U<0$, respectively. Remarkably, the latter one can be embedded in the continuum spectrum with appropriate parameters. Moreover, in part of these regions, there exists an even-parity bound state accompanying the corresponding odd-parity bound state with almost the same energy.

Extrinsic spin Nernst effect in two-dimensional electron systems

The spin accumulation due to the spin current induced by the perpendicular temperature gradient (the spin Nernst effect) is studied in a two-dimensional electron system (2DES) with spin-orbit interaction by employing the Boltzmann equation. The considered 2DES is confined within a symmetric quantum well with $\ensuremath{\delta}$ doping at the center of the well. A symmetry consideration leads to the spin-orbit interaction which is diagonal in the spin component perpendicular to the 2DES. As origins of the spin current, the skew scattering and the side jump are considered at each impurity on the center plane of the well. It is shown that, for repulsive impurity potentials, the spin-Nernst coefficient changes its sign at the impurity density where contributions from the skew scattering and the side jump cancel each other out. This is in contrast to the spin Hall effect in which the sign change of the coefficient occurs for attractive impurity potentials.

Kinetic Monte Carlo Simulation of Impurity Effects on Nucleation and Growth of SiC Clusters on Si(100)

The influence of attractive and repulsive impurities on the nucleation process of the SiC clusters on Si(100) surface was investigated. Kinetic Monte Carlo simulations of the SiC clusters growth show that that increase of the impurity concentration (both attractive and repulsive) leads to decrease of the mean cluster size and rise of the nucleation density of the clusters.

Light Doping Effect on System Energy in Conjugated Polymers

Based on a tight binding model, we investigate impurity effect upon the stability of neutral and negatively or positively charged 1D conjugated polymer chains. Impurities are introduced by an attractive or a repulsive potential located at the lattice sites. The offsets of system energy due to light doping are calculated within adiabatic approximation. We show that doping position has significant impact upon system stability. A general picture of impurity distribution along the stretch direction of the polymer chain is obtained for both attractive and repulsive impurity potentials in neutral as well as in charged conjugated polymers. A polymer chain can generally be divided into edge, center and transition regions in terms of impurity distribution. It is found the static impurity distribution within a polymer is dominated by the strength and the sign of the impurity potential as well as whether the polymer chain is neutral or charged. Impurity distribution within the edge and the transition region is characterized by cluster and that within the center region by separation.

Numerical study of laser-assisted transmission and reflection coefficients of a wave packet by an attractive impurity

We study the transmission and reflection probabilities for a wave packet that collides with an attractive impurity (e.g. a quantum dot, a perturbation on a waveguide, etc.) in the presence of an intense, ultra-fast Gaussian laser pulse with intensity in the range I=1012–1014 W/cm2, wavelength of 780 nm and FWHM of 10 fs. The study is based on a numerical solution to the time-dependent Schrödinger equation by means of a finite difference approach. The attractive impurity is modeled by different 1-D potential shape (square, harmonic, triangular, circular, and double harmonic) wells. We find a strong effect of the laser intensity on the reflection and transmission coefficients as a function of energy of the incoming wave-packet, with the strongest effect in the low collisions energy range and high laser intensity. Furthermore, we find that contrary to the laser-free case where there is no trapping probability by the impurity, in the presence of the laser pulse appears a trapping probability for low collision energies. The probability of trapping increases as the laser intensity increases. We present different scenarios where these results can be of interest.

Evidence for nonlinear screening and enhancement of scattering by a single Coulomb impurity for dielectrically confined electrons in InAs nanowires

The conductance due to scattering by a single repulsive Coulomb impurity is measured as a function of gate voltage in backgated InAs nanowires by analysis of random telegraph noise. Comparison with a quantum mechanical theory for carrier response and scattering reveals that the large dielectric mismatch between the nanowire and its surroundings enhances the Coulomb interaction, produces a nonlinear screening process that weakens dielectric response, and enhances the self-consistent Coulomb-impurity barrier of a single repulsive impurity, as nanowire diameter is reduced. Consequently, the scattering rate by such an impurity is enhanced by nearly two orders magnitude for 30 nm diameter InAs nanowires. A dramatic asymmetry of scattering by repulsive and attractive impurities, where the latter produce majority carriers, explain how a single repulsive impurity can control the conductance of a 1 $\ensuremath{\mu}$m long InAs nanowire. Relevance to proposed nanoelectronic and sensing devices is discussed.

The influence of magnetic impurities in the vortex core dynamics in magnetic nano-disks

In this work we have used spin dynamics simulations to study the gyrotropic frequency behavior in nano-disks of Permalloy with magnetic impurities. We consider the effect of attractive impurity and repulsive impurity placed near the vortex core gyrotropic trajectory. We observed that the gyrotropic frequency is affected by the presence of impurity. The gyrotropic frequency shift depends on the relative position between the impurity and the vortex core gyrotropic trajectory and if impurity is attractive or repulsive. Our results agree with the analytical model and with experimental behavior for the gyrotropic frequency shown in the literature.

Statics and dynamics of atomic dark-bright solitons in the presence of impurities

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counter-intuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscil- lations of solitons are found to be in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

Effect of a localized impurity on soliton dynamics in the Bose—Einstein condensates

By using a multiple-scale method, we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates. It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity, while at the position of the localized impurity the soliton can be quasitrapped by the impurity. Additionally, we find that the strength of the localized impurity has an important effect on the dark soliton dynamics. With increasing strength of the localized impurity, the amplitude of the dark soliton becomes bigger, while its width is narrower, and the soliton propagates slower.