Resonant Impurity Research Articles

Quasiparticle interference and impurity resonances on WTe2

Using scanning tunneling microscopy/spectroscopy (STM/STS), we examine quasiparticle scattering and interference properties at the surface of WTe2. WTe2, layered transition metal dichalcogenide, is predicted to be a type-II Weyl semimetal. The Weyl fermion states in WTe2 emerge as topologically protected touching points of electron and hole pockets, and Fermi arcs connecting them can be visible in the spectral function on the surface. To probe the properties of surface states, we have conducted low-temperature STM/STS (at 2.7 K) on the surfaces of WTe2 single crystals. We visualize the surface states of WTe2 with atomic scale resolution. Clear surface states emerging from the bulk electron pocket have been identified and their connection with the bulk electronic states shows good agreement with calculations. We show the interesting double resonance peaks in the local density of states appearing at localized impurities. The low-energy resonant peak occurs near the Weyl point above the Fermi energy and it may be mixed with the surface state of Weyl points, which makes it difficult to observe the topological nature of the Weyl semimetal WTe2.

Band dispersion of graphene with structural defects

We study the band dispersion of graphene with randomly distributed structural defects using two complementary methods, exact diagonalization of the tight-binding Hamiltonian and implementing a self-consistent T matrix approximation. We identify three distinct types of impurities resulting in qualitatively different spectra in the vicinity of the Dirac point. First, resonant impurities, such as vacancies or 585 defects, lead to stretching of the spectrum at the Dirac point with a finite density of localized states. This type of spectrum has been observed in epitaxial graphene by photoemission spectroscopy and discussed extensively in the literature. Second, nonresonant (weak) impurities, such as paired vacancies or Stone-Wales defects, do not stretch the spectrum but provide a line broadening that increases with energy. Finally, disorder that breaks sublattice symmetry, such as vacancies placed in only one sublattice, open a gap around the Dirac point and create an impurity band in the middle of this gap. We find good agreement between the results of the two methods and also with the experimentally measured spectra.

Dissipation without resistance: Imaging impurities at quantum Hall edges

Motivated by the recent experiment by Marguerite et al. [1] on imaging in graphene samples, we investigate theoretically the dissipation induced by resonant impurities in the quantum Hall regime. The impurity induced forward scattering of electrons at quantum Hall edges leads to an enhanced phonon emission, which reaches its maximum when the impurity state is tuned to resonance by a scanning tip voltage. Our analysis of the effect of the tip potential on the dissipation reveals peculiar thermal rings around the impurities, in consistency with experimental observations. Remarkably, this impurity-induced dissipation reveals non-trivial features that are unique for chiral 1D systems such as quantum Hall edges. First, the dissipation is not accompanied by the generation of resistance. Second, this type of dissipation is highly nonlocal: a single impurity induces heat transfer to phonons along the whole edge.

Local spectra at impurity and neighboring sites in graphene: Resonance manifestation

The electronic spectrum of graphene with a single point impurity is considered. Local densities of states at the impurity site and its nearest neighbors are calculated analytically. Their evolution with increasing the impurity potential is examined. It is shown that in the domain of the well-defined impurity resonance the local density of states at the first-nearest neighbor of the impurity site is approximately a scaled-up copy of the local density of states at the impurity site. The corresponding factor is found to be proportional to the squared impurity potential.

Defect and Dopant Mediated Thermoelectric Power Factor Tuning in β‐Zn4Sb3

AbstractThe presence of defects in thermoelectric materials plays a significant role in the modification their properties by influencing the behavior of electrons and phonons. Dopants with a unique f‐orbital can directly cause distortions in electronic density of states (eDOS) and phonon transport mechanism by intentionally inducing defects in their lattice. The theoretical and experimental outcomes of engineered vacancy defects are investigated by intentional doping of f‐block rare earth elements in β‐Zn4Sb3. Thermoelectric behavior breaks down the inverse relation and results in a parallel increase in Seebeck coefficient and electrical conductivity for β‐(Zn0.997Ce0.003)4Sb3 and β‐(Zn0.997Er0.003)4Sb3. This synergistic response triples the power factor of a thermoelectric β‐Zn4Sb3 system realized by the impurity induced resonant distortion in eDOS. From first principle GGA + U calculations, the above‐mentioned unconventional properties are attributed to the effect of doping induced vacancy formation and the formation of resonant impurity levels. Hence, it is postulated that defect engineering can be a broad strategy to improve the power factor of the system and can be extended to other thermoelectric materials.

The investigation of hydrostatic pressure dependent optoelectronic properties of GaAsNBi spherical quantum dot

The electronic band structure of GaAsNBi spherical quantum dot (QDs) have been calculated under hydrostatically induced pressure using 16 band k.p model and considering the band anticrossing (BAC) interaction between the valence band (VB) of the host material with the N and Bi related resonant impurity level. It has a linear variation in bandgap with different Bi concentration and non-linear in bandgap with varying pressure, for 2.3%N in both the cases. However, small differences are observed in valance band offset (VBO), whereas more considerable changes can be seen in the conduction band offset (CBO) with an increasing hydrostatic pressure, which implies a stronger confinement of charge carriers. Finally, we also studied the percentage of strain distribution and its related properties of GaAsNBi spherical QDs along the radial direction, lattice misfit under biaxial and hydrostatic strain. These QDs are also being used in many applications, including selective frequency operation for optoelectronic devices by tuning distinct mole fraction and pressure.

Electronic properties of graphene with point defects (Review Article)

This review is an attempt to consistently examine the electronic spectrum of graphene containing defects (such as adsorbed atoms, substitutional atoms, vacancies) that can be adequately described using the Lifshitz model. Therefore, the known Hamiltonian of this model is chosen for the case of two-dimensional relativistic electrons, and the criteria for the appearance of an impurity resonance near the Dirac point are provided. The theory of concentration band structure transformation in graphene is outlined, from which it follows that a transport gap opens in the vicinity of the impurity resonance energy when a specific value of the impurity concentration is reached. Along the way, the question of whether or not it is possible (or impossible) for Dirac quasiparticles to become localized in such a spatially disordered system is analyzed. Based on this, it is feasible to explain and describe the recently observed in impure graphene phenomenon of metal-insulator transition, which turns out to be a direct consequence of the system’s Fermi energy falling into the domain of the transport gap. The concept of local spectrum rearrangement, which can also unfold as the defect concentration increases, is introduced and justified for graphene. We formulate the physical reasons why the minimum of graphene’s low-temperature conductivity dependence on the Fermi energy of electrons does correspond to the impurity resonance energy, and not the Dirac point, as it has been claimed in a number of theoretical and experimental studies. Furthermore, the mentioned minimum value proves to be not universal, but is dependent, instead, on the concentration of defects. The analytical considerations of the impurity effects are accompanied by numerical simulations of the examined system, and a complete correspondence between these two approaches is established as a result. In particular, the general scenarios of spectrum rearrangement, electron state localization, as well as of effects having a local nature, are confirmed.

Impurity-induced resonant states in topological nodal-line semimetals

Nodal-line semimetals are characterized by a kind of topologically nontrivial bulk-band crossing, giving rise to almost flat surface states. Yet, a direct evidence of the surface states is still lacking. Here we study theoretically impurity effects in topological nodal-line semimetals based on the T-matrix method. It is found that for a bulk impurity, some in-gap states may be induced near the impurity site, while the visible resonant impurity state can only exist for certain strength of the impurity potentials. For a surface impurity, robust resonant impurity states exist in a wide range of impurity potentials. Such robust resonant states stem from the topological protected weak dispersive surface states, which can be probed by scanning tunneling microscopy, providing a strong signature of the topological surface states in the nodal-line semimetals.

Time-dependent potential impurity in a topological insulator

We consider periodically driven potential impurities coupled to the surface states of a two-dimensional topological insulator. The problem is addressed by means of two models, out which the first model is an effective continuum Hamiltonian for the surface states, whereas the Kane-Mele lattice model is our second approach. While both models result in drastic changes in the local density of electron states with increasing amplitude and frequency of the driving field, the linearly low energy local density of electron states remains in the continuum model, however, with an increased Fermi velocity. The spectrum of the continuum model remains gapless under the emergence of new impurity resonances near the Fermi energy. The Kane-Mele lattice model represents a finite size system, with edge states appearing at the boundary of the system. We, thus, consider the impurity at two different positions, one at the boundary and one at the center of the lattice. In the former case, a reduction and broadening of the low energy local density of electron states result with increasing amplitude of the driving field. On the other hand, there are no new resonances emerging in the spectrum. In the latter case, the spectrum is gapped both in the absence of the impurity as well as for weak amplitudes of the driving field, while the gap tends to fill up with impurity states with increasing amplitude.

Spin relaxation in fluorinated single and bilayer graphene

We present a joint experiment-theory study on the role of fluorine adatoms in spin and momentum scattering of charge carriers in dilute fluorinated graphene and bilayer graphene. The experimental spin-flip and momentum scattering rates and their dependence on the density of fluorine and carrier doping are obtained through weak localization and conductivity measurements, respectively, and suggest the role of fluorine as resonant magnetic impurities. For the estimated fluorine concentration of a few 100 ppm, the observed spin lifetimes are in the range of 1-10\,ps. Theoretically, we established tight-binding electronic structures of fluorinated graphene and bilayer graphene by fitting to density functional supercell calculations and performed a comprehensive analysis of the spin-flip and momentum scattering rates within the same devices, aiming to develop a consistent description of both scattering channels. We find that resonant scattering in graphene is very sensitive to the precise position of the resonance level, as well as to the magnitude of the exchange coupling between itinerant carriers and localized spins. The experimental data point to the presence of weak spin-flip scatterers that, at the same time, relax the electron momentum strongly, nearly preserving the electron-hole symmetry. Such scatterers would exhibit resonance energies much closer to the neutrality point than what density functional theory predicts in the dilute limit. The inclusion of a magnetic moment on fluorine adatoms allowed us to qualitatively capture the carrier density dependence of the experimental rates but predicts a greater (weaker) spin (momentum) relaxation rate than the measurements. We discuss possible scenarios that may be responsible for the discrepancies. Our systematic study exposes the complexities involved in accurately capturing the behavior of adatoms on graphene.

Propagation of chirped optical similaritons in inhomogeneous tapered centrosymmetric nonlinear waveguides doped with resonant impurities

We investigate the existence and propagation properties of linearly chirped self-similar solitons in an inhomogeneous tapered centrosymmetric nonlinear waveguide doped with resonant impurities under diffraction and nonlinearity management. The exact self-similar bright and dark soliton solutions are presented by employing an improved homogeneous balance principle and an F-expansion method. It is found that these chirped self-similar beams possess a strictly linear chirp that leads to efficient compression or amplification. The dynamical behaviors of these self-similar structures in a periodic distributed amplification waveguide system and an exponential diffraction decreasing waveguide are respectively studied for different choices of tapered index profile. The results show that the soliton shape and propagation behavior can be effectively controlled by selecting the diffraction, quintic nonlinearity, tapering, and gain or loss.

Effect of resonant impurity scattering of carriers on the Drude-peak broadening in uniaxially strained graphene

An explanation is proposed for the recently observed in optical spectra of monolayer graphene giant increase in the Drude peak width under applied uniaxial strain. We argue that the underlying mechanism of this increase can be based on resonant scattering of carriers from inevitably present impurities such as adsorbed atoms that can be described by the Fano-Anderson model. We demonstrate that the often neglected scalar deformation potential plays the essential role in this process. The conditions necessary for the maximum effect of the giant Drude peak broadening are determined. It is stressed that the effect is strongly enhanced when the Fermi level gets closer to the Dirac point. Our theoretical analysis provides guidelines for functionalizing graphene samples in a way that would allow to modulate efficiently the Drude peak width by the applied strain.

Large enhancement of the thermoelectric power factor in disordered materials through resonant scattering

In the search for more efficient thermoelectric materials, scientists have placed high hopes in the possibility of enhancing the power factor using resonant states. In this study, we investigate theoretically the effects of randomly distributed resonant impurities on the power factor. Using the Chebyshev Polynomial Green's Function method, we compute the electron transport properties for very large systems (10 million atoms) with an exact treatment of disorder. The introduction of resonant defects can lead to a large enhancement of the power factor together with a sign inversion in the Seebeck coefficient. This boost depends crucially on the position of the resonant peak, and on the interplay between elastic impurity scattering and inelastic processes. Strong electron-phonon or electron-electron scattering are found detrimental. Finally, the robustness of our results is examined in the case of anisotropic orbitals and two-dimensional confinement. Our findings are promising for the prospect of thermoelectric power generation.

Surface terminations and layer-resolved tunneling spectroscopy of the 122 iron pnictide superconductors

The surface terminations of 122-type alkaline earth metal iron pnictides AEFe2As2 (AE = Ca, Ba) are investigated with scanning tunneling microscopy/spectroscopy (STM/STS). Cleaving these crystals at a cryogenic temperature yields a large majority of terminations with atomically resolved square-root-two (rt2) or 1*2 lattice, as well as the very rare terminations with 1*1 symmetry. By means of lattice alignment and chemical marking, we identify these terminations as rt2-AE, 1*2-As, and rt2-Fe surfaces, respectively. Layer-resolved spectroscopy on these terminating surfaces reveals a well-defined superconducting gap on the As terminations, while the gap features become weaker and absent on AE and Fe terminations respectively. The local gap features are hardly affected by the surface reconstruction on As or AE surface, whereas a suppression of them along with the in-gap states can be induced by As vacancies. The emergence of two impurity resonance peaks at +-2 meV is consistent with the sign-reversal pairing symmetry. The definite identification of surface terminations and their spectroscopic signatures shall provide a more comprehensive understanding of the high-temperature superconductivity in multilayered iron pnictides.

Charge Transfer between Layers in a Bilayer Quasi-Two-Dimensional (BEDT-TTF)4CoBr4(C6H4Cl2) Organic Metal

Based on the analysis of the behavior of the magnetoresistance, the regime of interlayer charge transport in a bilayer quasi-two-dimensional (BEDT-TTF)4CoBr4(C6H4Cl2) organic metal is discussed. It is noted that a strongly incoherent mode is the most likely in the entire temperature range 1.5–300 K. The metallic type of the temperature dependence of the interlayer resistance at low temperatures is most likely associated with charge transfer through resonant impurities.

Specific Features of the Electron Spin Resonance of an Iron Impurity in HgSe Crystals

The electron-spin-resonance spectra of transition metal ions Fe in the HgSe matrix are analyzed. The spectra have an appearance typical of the Fe3+ ion, i.e., they consist of five fine-structure lines with a splitting that corresponds to a weak crystal field. The spectra are observed at temperatures of up to 50 K. The spectral lines are deformed and have a Dyson shape. An analysis of the temperature dependences of the line amplitudes shows that a transition from paramagnetic ordering to ferromagnetic ordering occurs with decreasing temperature, with the Curie temperature T ≈ 7 K.

Potential and spin-exchange interaction between Anderson impurities in graphene

The effective interaction between resonant magnetic Anderson impurities in graphene, mediated by conduction electrons, is studied as a function of the strength of the onsite energy level of the impurities and the amplitude of coupling to conduction electrons. The sign and character of the interaction depend on whether the impurities reside on the same or opposite sublattices. For the same (opposite) sublattice, the potential interaction is attractive (repulsive) in the weak coupling limit with $1/R^3$ dependence on the distance; the interaction reverses sign and becomes repulsive (attractive) in the strong coupling limit and displays $1/R$ behavior. The spin-exchange coupling is ferromagnetic (antiferromagnetic) at both large and small distances, but reverses sign and becomes anti-ferromagnetic (ferromagnetic) for intermediate distances. For opposite sublattices, the effective spin exchange coupling is resonantly enhanced at distances where the energy levels cross the Dirac points.

Magnetic impurity resonance states for different pairing symmetries in twisted bilayer graphene

In this work, we study the magnetic impurity resonance states in the superconducting phase of ‘magic’ angle twisted bilayer graphene for different pairing symmetries. Using a two-orbital model on the emergent honeycomb lattice, we find that the resonance states are dramatically different for -wave pairing and topological nontrivial pairings. When the magnetic impurity is located at one site of the emergent honeycomb lattice, i.e. the center of the AB spot of the moiré pattern, the spacial distributions of the resonance states will break both the threefold and twofold rotation symmetries of point group for pairing symmetries which belong to the irreducible representations of this point group. When the magnetic impurity is located at the center of the emergent honeycomb lattice i.e. the center of the AA spot of the moiré pattern, the appearance of resonance peak at the position close to the impurity can be considered as a strong evidence of non--wave pairing.

Evidence of Incoherent Carriers Associated with Resonant Impurity Levels and Their Influence on Superconductivity in the Anomalous Superconductor Pb_{1-x}Tl_{x}Te.

We present a combined experimental and theoretical study of the evolution of the Fermi surface of the anomalous superconductor Pb_{1-x}Tl_{x}Te as a function of thallium concentration, drawing on a combination of magnetotransport measurements (Shubnikov-de Haas oscillations and the Hall coefficient), angle resolved photoemission spectroscopy, and density functional theory calculations of the electronic structure. Our results indicate that for Tl concentrations beyond a critical value, the Fermi energy coincides with resonant impurity states in Pb_{1-x}Tl_{x}Te, and we rule out the presence of an additional valence band maximum at the Fermi energy. A comparison to nonsuperconducting Pb_{1-x}Na_{x}Te implies that the presence of these impurity states at the Fermi energy provides the enhanced pairing interaction and thus also the anomalously high temperature superconductivity in this material.

Electronic properties of graphene with point defects

This article attempts a point-by-point review of the electron spectrum of graphene containing defects (adsorbed atoms, substitutional atoms, vacancies) that can be adequately described within the Lifshitz model. In this regard, the known Hamiltonian for this model is calculated for the case of two-dimensional relativistic electrons, and the criteria for occurrence of an impurity resonance near a Dirac point are given. The theory of concentration band structure transformation of graphene is presented, from which it follows that a transport gap is opened upon reaching a strictly defined value of impurity concentration in the neighborhood of the energy of impurity resonance. At the same time, the question of the possibility (or impossibility) of localization in such a {spatially disordered system} of Dirac quasiparticles is analyzed. Based on this, it is possible to provide an explanation and present a description of a phenomenon recently observed in {impure graphene}, the metal-dielectric transition that appears as a direct consequence of the decrease of the Fermi energy of the system in the region of a transport gap. The concept of local spectrum rearrangement of graphene, which also occurs during the process of increased concentration of defects in it, is introduced and substantiated. Physical reasons are formulated, by which the position of the minimum of the low-temperature conductivity of graphene as a function of the Fermi energy of electrons corresponds to the impurity resonance energy rather than to the Dirac point, as has been validated in a number of theoretical and test studies. Here, it appears that the minimum value is not a universal magnitude, but depends on the concentration of defects. Analytical examination of impurity effects is accompanied by numerical modeling of the system under study, as a result of which complete correspondence has been established between these two approaches. In particular, the overall picture of spectrum rearrangement, localization of electron states, and also the effects having local nature are confirmed.