On-site Impurity Research Articles

Structure of the impurity band in heavily doped nonmagnetic semiconductors

We study the properties of the impurity band in heavily doped nonmagnetic semiconductors using the Jacobi-Davidson algorithm and the supervised deep learning method. The disorder averaged inverse participation ratio and Thouless number calculation show us the rich structure inside the impurity band. A convolutional neural network model, which is trained to distinguish the extended/localized phase of the Anderson model with high accuracy, shows us the results in good agreement with the conventional approach. Together, we find that there are three mobility edges in the impurity band for a specific on-site impurity potential, which means the presence of the extended states while filling the impurity band.

Sensitivity of superconducting states to the impurity location in layered materials

The family of multi-layered superconductors derived from the doped topological insulator Bi$_2$Se$_3$ has been found to be unusually robust against non-magnetic disorder. Recent experimental studies have highlighted the fact that the location of impurities could play a critical role for this puzzling robustness. Here we investigate the effects of four different types of impurities, on-site, interstitial, intercalated and polar, on the superconducting critical temperature. We find that different components of the scattering potential are active depending on the impurity configuration and choice of orbitals for the effective low-energy description of the normal state. For the specific case of Bi$_2$Se$_3$-based superconductors, we find that only the symmetric share of impurity configurations contribute to scattering, such that polar impurities are completely inactive. We also find that a more dominant mass-imbalance term in the normal-state Hamiltonian can make the superconducting state more robust to intercalated impurities, in contrast to the case of on-site or interstitial impurities.

A Lieb–Robinson bound for quantum spin chains with strong on-site impurities

We consider a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. We prove commutator bounds for its Heisenberg dynamics which incorporate the coupling strengths of the impurities. The impurities are assumed to satisfy a minimum spacing, and each impurity has a non-degenerate spectrum. Our results are proven in a broadly applicable setting, both in finite volume and in thermodynamic limit. We apply our results to improve Lieb–Robinson bounds for the Heisenberg spin chain with a random, sparse transverse field drawn from a heavy-tailed distribution.

Effects of disorder in the Fibonacci quasicrystal

We study the properties of the one-dimensional Fibonacci chain, subjected to the placement of on-site impurities. The resulting disruption of quasiperiodicity can be classified in terms of the renormalization path of the site at which the impurity is placed, which greatly reduces the possible amount of disordered behavior that impurities can induce. Moreover, it is found that, to some extent, the addition of multiple, weak impurities can be treated by superposing the individual contributions together and ignoring nonlinear effects. This means that a transition regime between quasiperiodic order and disorder exists, in which some parts of the system still exhibit quasiperiodicity, while other parts start to be characterized by different localisation behaviours of the wavefunctions. This is manifested through a symmetry in the wavefunction amplitude map, expressed in terms of conumbers, and through the inverse participation ratio. For the latter, we find that its average of states can also be grouped in terms of the renormalization path of the site at which the impurity has been placed.

Probing Majorana zero modes by measuring transport through an interacting magnetic impurity

Motivated by recent experiments we consider transport across an interacting magnetic impurity coupled to the Majorana zero mode (MZM) observed at the boundary of a topological superconductor (SC). In the presence of a finite tunneling amplitude we observe hybridization of the MZM with the quantum dot, which is manifested by a half-integer zero-bias conductance $G_0=e^2/2h$ measured on the metallic contacts. The low-energy feature in the conductance drops abruptly by crossing the transition line from the topological to the non-topological superconducting regime. Differently from the in-gap Yu-Shiba-Rosinov-like bound states, which are strongly affected by the on-site impurity Coulomb repulsion, we show that the MZM signature in the conductance is robust and persists even at large values of the interaction. Interestingly, the topological regime is characterized by a vanishing Fano factor, $F=0$, induced by the MZM. Combined measurements of the conductance and the shot noise in the experimental set-up presented in the manuscript allow to detect the topological properties of the superconducting wire and to distinguish the low-energy contribution of a MZM from other possible sources of zero-bias anomaly. Despite being interacting the model is exactly solvable, which allows to have an exact characterization of the charge transport properties of the junction.

Effect of an external electric field on local magnetic moments in silicene

In this work we analyze the effects of the application of an external electric field in the formation of a local magnetic moment in silicene. By adding an impurity in a top site in the host lattice and computing the real and imaginary part of the self-energy of the impurity energy level, the polarized density of states is used in order to obtain the occupation number of the up and down spin formation in the impurity considering the mean field approximation. Unequal occupation numbers is the precursor of a formation of a local magnetic moment and this depends critically on the Hubbard parameter, the on-site energy of the impurity, the spin-orbit interaction in silicene and the electric field applied. In particular, it is shown that in the absence of electric field, the boundary between the magnetic and non-magnetic phases increases with the spin-orbit interaction with respect to graphene with a top site impurity and shrinks and narrows it when the electric field is turned on. The electric field effect is studied for negative and positive on-site impurity energies generalizing the results obtained in the literature for graphene.

Superconductivity and Jahn–Teller effect in bilayer cuprate superconductors

We have proposed a model Hamiltonian describing the interlayer tunnelling in d-wave bilayer cuprate superconductors in the coexistence of superconductivity and Jahn–Teller effect with the on-site non-magnetic impurity. The Hamiltonian is solved for the quasi-particle energy bands, the superconducting and the Jahn–Teller gap parameters by using Zubarev’s technique of double time electron Green’s functions. The effects of interlayer tunnelling and the strength of non-magnetic potential are studied for superconducting and Jahn–Teller gap parameters. The density of states for both the layers of the bi-layer system is studied and the results are compared with others.

Lévy Flights due to Anisotropic Disorder in Graphene.

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed backscattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in the stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities, which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent T-matrix approximation.

Persistent quantum resonance transition in spin Hall transport

We propose an H-shaped two-dimensional topological insulator (2DTI) as a persistent quantum resonance device. The helical edge states of 2DTI are robust against a nonmagnetic field. However, the helical edge states interfere with bound states created by a nonmagnetic impurity. Transmissions between leads shows two kinds of quantum resonance in this device, the Breit-Wigner resonance and a Fano-like resonance. These resonances can be realized in the device through modulating the on-site impurity potential. Resonances in 2DTI are persistent because the helical state has no backscattering that is protected by time-reversal-symmetry conservation. The finite-size effect in 2DTI leads to the phase transition between the Fano and the Breit-Wigner resonances through modulating the thickness of the 2DTI leads.

Dynamics of the impurity screening cloud following quantum quenches of the resonant level model

.We present a detailed analysis of the evolution of the impurity screening cloud in the resonant level model (RLM) followed by quenches of system parameters. The considered quenches are either local or found to be effectively local. The screening cloud is characterized by impurity-bath correlators and by the entanglement of a block centered around the impurity with the rest of the system. We consider several local quench protocols, such as, quenches from initially decoupled to coupled impurity, quenches between different finite couplings of the impurity, and ‘detuning quenches’ involving changing the onsite impurity potential away from or to the chemical potential of the bath. The relevant correlators and the entanglement display versions of the ‘light-cone’ effect, since the information about the quench travels through the bath at finite speed. At long times (‘inside’ the light cone), the impurity screening cloud relaxes exponentially to the final equilibrium structure, with the relaxation rate given by the emergent energy scale of impurity screening. Also, snapshots of the time-evolving spatial profile of impurity-bath correlators show exponential dependences on space, with the length scale given by the screening length.

Valley properties of doped graphene in a magnetic field

The aim of this work is to describe the electronic properties of graphene in a constant magnetic field in the long wavelength approximation with random binary disorder, by solving the Soven equation self-consistently. Density of state contributions for different valleys in each sublattice sites are obtained for different values of magnetic field strength showing remarkable differences between K and K' valleys. A band gap is obtained by an asymmetric on-site impurity concentration and the graphene electrons acquire an anomalous magnetic moment, which is opposite in different valleys, which depend highly in the interplay between the impurity band, the band edges and the broadening of the Landau levels. In turn, magnetization as a function of B for different on-site random impurities is computed showing that by decreasing the on-site impurity energy values, maximum magnetization is shifted towards higher values of B which can be used to create and manipulate polarized valley currents. Finally, conductivity and local vertex function are obtained as a function of energy showing that scattering contributions from A and B sublattices differ significantly. Effective medium local two-irreducible vertex is computed showing that scattering from sublattices A and B do not contribute equally, which can be related to weak anti-localization. From these results, it could be possible to explore how the valley pseudospin can be used to create polarized currents by populating asymmetrically the sublattice sites, where the population can be tuned with the applied magnetic field strength.

Quantum plateau of Andreev reflection induced by spin-orbit coupling

In this work we uncover an interesting quantum plateau behavior for the Andreev reflection between a one-dimensional quantum wire and superconductor. The quantum plateau is achieved by properly tuning the interplay of the spin-orbit coupling within the quantum wire and its tunnel coupling to the superconductor. This plateau behavior is justified to be unique by excluding possible existences in the cases associated with multi-channel quantum wire, the Blonder-Tinkham-Klapwijk continuous model with a barrier, and lattice system with on-site impurity at the interface.

Indirect Coupling Between Localized Magnetic Moments in Zero-Dimensional Graphene Nanostructures (Quantum Dots)

The indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling between on-site magnetic impurities is studied for two kinds of graphene nanoflakes consisting of approximately 100 carbon atoms, posessing either zigzag or armchair edge. The tight-binding Hamiltonian with Hubbard term is used in non-perturbative calculations of coupling between the impurities placed at the edge of the structure. In general, for zigzag-edged nanoflakes a pronounced coupling robust against charge doping is found, while for armchair-edged structures the interaction is weaker and much more sensitive to charge doping. Also the distance dependence of indirect exchange differs significantly for both edge forms.

Nonperturbative expression for the transmission through a leaky chiral edge mode

Chiral edge modes of topological insulators and Hall states exhibit nontrivial behavior of conductance in the presence of impurities or additional channels. We present a simple formula for the conductance through a chiral edge mode coupled to a disordered bulk. For a given coupling matrix between the chiral mode and bulk modes, and a Green's function matrix of bulk modes in real space, the renormalized Green's function of the chiral mode is expressed in closed form as a ratio of determinants. We demonstrate the usage of the formula in two systems: (i) a 1d wire with random on-site impurity potentials for which we found that the disorder averaging is made simpler with the formula, and (ii) a quantum Hall fluid with impurities in the bulk for which the phase picked up by the chiral mode due to the scattering with the impurities can be conveniently estimated.

Topologically protected mid-gap states induced by impurity in one-dimensional superlattices

Based on the discovery of the nontrivial topological properties of one-dimensional superlattices, we show that mid-gap states emerge in such systems induced by a single on-site impurity. Besides the trivial bound state located at the impurity site, these mid-gap states are localized at the adjacent sites of the impurity in the limit of a strongly attractive/repulsive impurity potential, behaving as edge states under open boundary conditions and thus carrying the information of topological properties. This feature makes it possible to reveal the topological properties of superlattices via the impurity effect and to realize the adiabatic pumping between the opposite sides of the impurity in setups of one-dimensional optical lattices or photonic crystals.

Effect of realistic finite-size impurities onTcin Fe-based superconductors based on the five-orbital tight-binding model

We present a systematic study of the impurity effect on Tc in Fe-based superconductors, assuming that the sign-reversal s-wave state due to inter-pocket repulsion ($s_\pm$-wave state) is realized. For this purpose, we introduce several realistic impurity models with non-local modifications of potentials and hopping integrals around the impurity site. When we use the impurity model parameters for 3d- and 4d-impurity atoms derived from the recent first principle study by Nakamura et al., we find that the $s_\pm$-wave state is very fragile against impurities: The superconductivity with $T_{c0}=30K$ is destroyed by introducing small residual resistivity $\rho_0^{cr} = 5z^{-1} ~ 10z^{-1} [\mu\Omega cm]$ ($z^{-1} = m^*/m$ being the mass-enhancement factor), consistently with the previous theoretical study for the on-site impurity model by Onari and Kontani. This result is essentially unchanged for different non-local impurity models with realistic parameters. We also discuss the effect of the impurity-induced non-local orbital order on the superconducting state.

A solvable model for electronic transport of a nanowire in the presence of effective impurities

We propose an analytical model to describe the electronic transport properties of a uniform chain including one or two on-site impurities located at arbitrary sites by using Green’s function technique within the tight-binding approach. We reduce some quasi one-dimensional periodic quantum wires to uniform chains including one or two effective on-site impurities with help of the renormalization procedure. Then, we employ the formalism to drive their electronic conductance analytically. For some interesting configurations, we provide a list for on-site energies of effective impurities and all needed quantities. Some defects in a conjugated polymer can also be described by the effective on-site impurities when the system is reduced into a uniform chain.

Indirect RKKY interaction between localized magnetic moments in armchair graphene nanoribbons

A form of indirect Ruderman–Kittel–Kasuya–Yosida (RKKY)-like coupling between magnetic on-site impurities in armchair graphene nanoribbons is studied theoretically. The calculations are based on a tight-binding model for a finite nanoribbon system with periodic boundary conditions. A pronounced Friedel-oscillation-like dependence of the coupling magnitude on the impurity position within the nanoribbon resulting from quantum size effects is found and investigated. In particular, the distance dependence of coupling is analysed. For semiconducting nanoribbons, this dependence is exponential-like, resembling the Bloembergen–Rowland interaction. For metallic nanoribbons, interesting behaviour is found for finite length systems, in which zero-energy states make an important contribution to the interaction. In such situations, the coupling decay with distance can then be substantially slower.

Indirect coupling between localized magnetic moments in triangular graphene nanoflakes

The indirect, charge-carrier mediated coupling between localized magnetic moments is studied for graphene nanoflakes of triangular shape and zigzag edge. The characteristic feature of such nanoflakes is the presence of a shell of zero-energy states in the electronic spectrum. The tight-binding Hamiltonian supplemented with a Hubbard term is used for electronic structure calculations. The indirect RKKY (Ruderman–Kittel–Kasuya–Yosida) coupling energy is derived from the total electronic energy of the system in a non-perturbative way. The attention is focused on the on-site and plaquette impurities situated along the edge. The charge doping is also taken into account. It is found that the zero-energy states may give rise to a coupling mechanism which is describable by a first-order perturbation calculus and can yield robust indirect coupling of both ferro- and antiferromagnetic character, which dominates over the usual RKKY mechanism. The numerical results obtained emphasize the importance of the Hubbard term and the effect of the charge doping on the coupling.

Impurity Bound States and Disorder-Induced Orbital and Magnetic Order in the s ± State of Fe-Based Superconductors

We study the presence of impurity bound states within a five-band Hubbard model relevant to iron-based superconductors. In agreement with earlier studies, we find that in the absence of Coulomb correlations there exists a range of repulsive impurity potentials where in-gap states are generated. In the presence of weak correlations, these states are generally pushed to the edges of the gap, whereas for larger correlations the onsite impurity potential induces a local magnetic region which reintroduces the low-energy bound states into the gap.