Impurity Wave Functions Research Articles

Lifshitz model in the presence of spin–orbit coupling

Wave function of a localized state created by a short-range impurity in two dimensions falls off with distance, r, from the impurity as 1r1/2exp(−ra), where a is the localization radius. With randomly positioned identical impurities with low concentration, n≪a−2, the level smears into a band due to the overlap of the impurity wave functions. This is the essence of the Lifshitz model. We demonstrate that, upon incorporation of the spin–orbit coupling, the impurity wave functions acquire oscillating factors which, subsequently, modify their overlap. As a result of such modification, the density of states develops singularities at certain energies.

Negative Magnetoresistance in Hopping Regime of Lightly Doped Thermoelectric SnSe

Semiconducting SnSe, an analog of black phosphorus, recently attracted great scientific interest due to a disputed report of a large thermoelectric figure of merit, which has not been reproduced subsequently. Here we concentrate on the low-temperature ground state. To gain a better understanding of the system, we present magneto-transport properties in high-quality single crystals of as-grown, lightly doped SnSe down to liquid helium temperatures. We show that SnSe behaves as a p-type doped semiconductor in the vicinity of a metal-insulator transition. Electronic transport at the lowest temperatures is dominated by the hopping mechanism. Negative magnetoresistance at low fields is well described by antilocalization, while positive magnetoresistance at higher fields is consistent with the shrinkage of localized impurity wavefunctions. At higher temperatures, a dilute metallic regime is realized where elusive T2 and B2 resistivity dependence is observed, posing a challenge to theoretical comprehension of the underlying physical mechanism.

Anisotropy of the Paramagnetic Susceptibility in the 3D Dirac Semimetal Cd-=SUB=-3-=/SUB=-As-=SUB=-2-=/SUB=- Caused by Chromium Impurity: the EPR on Cr-=SUP=-3+-=/SUP=- Ions

In the literature devoted to magnetic impurities in Dirac semimetals, the appearance of anisotropic and long-range non-oscillating contributions to the Ruderman--Kittel--Kasuya--Yosida interaction is predicted. These contributions are due to the hybridization of the wave functions of magnetic impurities with the wave functions of Dirac electrons, which have a linear dispersion law. We have studied electron paramagnetic resonance (EPR) in powder samples of topological 3D Dirac semimetal Cd3As2 with an admixture of chromium ions. Anisotropy of the magnetic susceptibility in the paramagnetic state was found from the behavior of the resonance field. The appearance of magnetic anisotropy in the paramagnetic state is associated with an increase in the contribution of the orbital moments of chromium ions Cr2+ and Cr3+ due to their interaction with the orbital moments of donor Dirac electrons, which have anomalously large values of g factors. Keywords: magnetic resonance, topological materials, magnetic impurities.

Анизотропия парамагнитной восприимчивости дираковского полуметалла Cd-=SUB=-3-=/SUB=-As-=SUB=-2-=/SUB=-, обусловленная примесью хрома: ЭПР на ионах Cr-=SUP=-3+-=/SUP=-

In the literature devoted to magnetic impurities in Dirac semimetals, the appearance of anisotropic and long-range non-oscillating contributions to the Ruderman–Kittel–Kasuya–Yosida interaction is predicted. These contributions are due to the hybridization of the wave functions of magnetic impurities with the wave functions of Dirac electrons, which have a linear dispersion law. We have studied electron paramagnetic resonance (EPR) in powder samples of topological 3D Dirac semimetal Cd3As2 with an admixture of chromium ions. Anisotropy of the magnetic susceptibility in the paramagnetic state was found from the behavior of the resonance field. The appearance of magnetic anisotropy in the paramagnetic state is associated with an increase in the contribution of the orbital moments of chromium ions Cr2+ and Cr3+ due to their interaction with the orbital moments of donor Dirac electrons, which have anomalously large values of g factors.

First-Principles Calculations of Shallow Acceptor-Carbon Complexes in Si : A Potential-Patching Method with a Hybrid-Functional Correction

Shallow impurities play critical roles in the applications of semiconductor materials, but their simulations through first-principles calculations are challenging due to the delocalized nature of the impurity wave function. The authors propose a first-principles approach to study shallow impurities, which allows simulations of extremely large supercells to obtain converged impurity levels and wave functions. The method is applied to acceptor-carbon complexes in silicon and yields good agreement with experiments. This work thus presents a feasible approach for accurate simulations of shallow impurities and can provide helpful insights to assist experimental dopant engineering.

Influence of Deformation on Pb1−xInxTe1−yIy and Pb1−x−ySnxInyTe Films

Herein, the original technique for transport measurements at one‐axis deformation is applied for the characterization of In‐doped n‐type Pb1−xSnxTe thin films on a mica substrate. The main advantage of the developed setup is the possibility of obtaining a significantly higher pressure compared with bulk samples. A systematic study of the transport properties as a function of pressure for In‐doped PbTe and PbSnTe films is conducted. A huge deformation of up to ≈6% without sample destruction is obtained within one‐axis deformation and an applied pressure of up to ≈30 kbar for Pb1−xInxTe1−yIy and Pb1−x−ySnxInyTe thin films. This allowed us to determine the position of the In resonance level in the band spectrum of the PbSnTe compound as a function of the pressure. The In impurity level is moving up with the application of pressure. Such a conclusion is confirmed by the Hall effect and electrical conductivity measurements for Pb1−xSnxTe films doped with In and can be explained by the fact that In impurity wave functions are strongly localized and interact weakly with Bloch states of PbSnTe and with each other.

Bose polaron in spherically symmetric trap potentials: Ground states with zero and lower angular momenta

Single-atomic impurities immersed in a dilute Bose gas in the spherically symmetric harmonic trap potentials are studied at zero temperature. In order to find the ground state of the polarons, we present a conditional variational method with fixed expectation values of the total angular momentum operators, $\hat{J}^2$ and $\hat{J}_z$, of the system, using a cranking gauge-transformation for bosons to move them in the frame co-rotating with the impurity. In the formulation, the expectation value $\langle \hat{J^2}\rangle$ is shown to be shared in impurity and bosons, but the value $\langle \hat{J}_z\rangle$ is carried by the impurity due to the rotational symmetry. We also analyze the ground-state properties numerically obtained in this variational method for the system of the attractive impurity-boson interaction, and find that excited boson distributions around the impurity overlap largely with impurity's wave function in their quantum-number spaces and also in the real space because of the attractive interaction employed.

Magnetoreflection and magnetophotoluminescence in the dilute magnetic semiconductor Zn1−xMnxTe

Magnetoreflection (MR) and magnetophotoluminescence (MPL) are studied in the diluted magnetic semiconductor ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$. The use of both methods in parallel allows us to follow features resulting from the mean-field exchange behavior as well as individual characteristics of ${\mathrm{Mn}}^{2+}$ paramagnetic ions. Resonance linewidths observed in MR are analyzed and shown to depend on spin-dependent scattering of excitons. A striking feature of the MPL spectrum is an enhancement of all spin-polarized luminescence structures in an external magnetic field. Relations between the Zeeman energy shift of exciton transitions due to exchange interaction of Mn ions with mobile carriers and circular polarization of MPL due to internal recombination in ${\mathrm{Mn}}^{2+}$ are revealed. Mixing of left and right circular light polarizations is demonstrated in excitonic and donor-acceptor pair (DAP) structures of MPL peaks. An enhancement of binding energy with increasing magnetic field for excitons localized by potential fluctuations is demonstrated and explained. It is observed that the energy of MPL peaks related to DAPs is only weakly sensitive to magnetic field. This relative stability is caused by a suppression of the mean-field Zeeman shift due to the two-component form of impurity wave functions. The simultaneous presence of paramagnetic ions and residual nonmagnetic impurities in our ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ samples provides for a rich physical picture.

Site-occupation embedding theory using Bethe ansatz local density approximations

Site-occupation embedding theory (SOET) is an alternative formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a non-interacting) one. It provides a rigorous framework for combining wavefunction (or Green function) based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wavefunction has been performed with the density matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

High-field magnetotransport in Cu2ZnGeS4 single crystals

The quaternary chalcogenides, attracting much attention in recent time as promising solar energy materials, permit an effective optimization of their composition by the Ge incorporation. In particular, this implies an interest to the Cu2ZnGeS4 compound, which utilization requires, however, a deeper understanding of its electronic properties in general. Here, we investigate magnetotransport of the p-type Cu2ZnGeS4 single crystals, including resistivity, ρ (T), magnetoresistance (MR) and Hall effect, in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping charge transfer has been established within a broad temperature interval of T between ∼100 and 200 K by investigations of ρ (T) in zero field. The positive and negative contributions to MR have been observed, attributing them to shrinkage of the impurity wave functions by the magnetic field and to the destructive interference of the hopping charge carriers, respectively. Observation of the negative Hall coefficient, RH (T), exhibiting the dependence close to that of ρ (T), gives a strong support to the Mott conduction mechanism in our p-type Cu2ZnGeS4 material. In addition, the conductivity, connected with thermal activation of holes on the mobility edge, Ec, has been identified both below and above the Mott conduction interval. Finally, the joint analysis of the ρ (T) and MR data has yielded a series of important microscopic parameters. These include such details of the hole spectrum in the acceptor band, as its semi-width, W, the density of localized states, g (μ), at the Fermi level, μ, the positions of μ and Ec, as well as values of the localization radius of holes, a, and of the acceptor concentration, NA.

High-field hopping magnetotransport in kesterites

Transport properties of the kesterite-like single crystals of Cu2ZnSnS4, Cu2ZnSnxGe1−xSe4 and Cu2ZnGeS4 are investigated in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping (VRH) conduction is established by investigations of the resistivity, ρ (T), in all the materials mentioned above within broad temperature intervals of ΔTv4 ∼ 50–150 K, 50–250 K and 100–200 K, respectively. In addition, the Shklovskii-Efros VRH conductivity below Tv2 ∼ 3–4 K, the nearest-neighbour hopping (NNH) charge transfer between T ∼ 250–320 K and the conductivity by activation of holes on the mobility threshold at temperatures outside ΔTv4, respectively, are observed in these materials. In Cu2ZnSnS4, magnetoresistance (MR) contains only a positive contribution, connected mainly to a shrinkage of impurity wave functions by the magnetic field. At the same time, a negative contribution to MR, attributable to interference effects in VRH, is observed in Cu2ZnSnxGe1−xSe4 and, especially, in Cu2ZnGeS4. The joint analysis of the MR and ρ (T) data has yielded important electronic parameters of the materials. This includes widths of the acceptor band W and of the Coulomb gap Δ, the NNH activation energy En, the localization radius a, the acceptor concentration NA and the density of the localized states at the Fermi level, g (μ). A dramatic increase of a in Cu2ZnSnS4 with decreasing T is observed, whereas in Cu2ZnSnxGe1−xSe4 all the parameter W, En, g (μ), a and NA are non-monotonic functions of x. Finally, in Cu2ZnGeS4 the Hall coefficient RH (T) is negative (despite of the p-type conduction), exhibiting the dependence close to that of ρ (T) in the Mott VRH interval.

Numerical study of localized impurity in a Bose-Einstein condensate

Motivated by recent experiments, we investigate a single $^{133}\text{Cs}$ impurity in the center of a trapped $^{87}\text{Rb}$ Bose-Einstein condensate. Within a zero-temperature mean-field description we provide a one-dimensional physical intuitive model which involves two coupled differential equations for the condensate and the impurity wave function, which we solve numerically. With this we determine within the equilibrium phase diagram spanned by the intra- and inter-species coupling strength, whether the impurity is localized at the trap center or expelled to the condensate border. In the former case we find that the impurity induces a bump or dip on the condensate for an attractive or a repulsive Rb-Cs interaction strength, respectively. Conversely, the condensate environment leads to an effective mass of the impurity which increases quadratically for small interspecies interaction strength. Afterwards, we investigate how the impurity imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the impurity-induced bump in the condensate wave function starts decaying marginally, whereas the dip decays with a characteristic time scale which decreases with increasing repulsive impurity-BEC interaction strength. Secondly, once the attractive or repulsive interspecies coupling constant is switched off, we find that white-shock waves or bi-solitons emerge which both oscillate within the harmonic confinement with a characteristic frequency.

Theoretical investigation of the heavily-doped semiconductor aspect of ultra-dilute GaAsN

The model of GaAs1−y N y (y = 0.001) as a heavily-doped semiconductor in the ultra-dilute region is attentively examined. The model enables GaAsN to be viewed as a disordered assembly of three-dimensional quantum dots (potential wells) caused by random potential fluctuations from nitrogen pairs in the system. Consequently, Feynman’s path-integration technique is applied in order to quantify the density of states (DOS) in the vicinity of the conduction band edge. The obtained DOS tail, even though overestimated, still clearly shows a much shorter tail than that the experimental result does. This shows that the heavily-doped semiconductor viewpoint is not proper for GaAsN, not even in the ultra-dilute region. Furthermore, this also suggests that the impurity wave function overlap is not a basic mechanism of band gap reduction.

Atomic-scale detection of magnetic impurity interactions in bulk semiconductors

We demonstrate on the basis of ab initio simulations how passivated semiconductor surfaces can be exploited to study bulklike interaction properties and wave functions of magnetic impurities on the atomic scale with conventional and spin-polarized scanning tunneling microscopy. By applying our approach to the case of $3d$ transition metal impurities close to the H/Si$(111)$ surface, we show exemplarily that their wave functions in Si are less extended than for Mn in GaAs, thus obstructing ferromagnetism in Si. Finally, we discuss possible applications of this method to other dilute magnetic semiconductors.

Impurity-related photoionization cross section in a pyramid-shaped quantum dot: Intense laser field and hydrostatic pressure effects

Within the effective mass approximation the binding energy and photoionization cross section of a donor impurity in a pyramid shaped quantum dot under simultaneous action of the hydrostatic pressure and high-frequency laser field have been investigated. We found that: (i) the variation of the binding energy reflects the spatial distribution of the impurity wave function, which is significantly modified by the laser radiation; (ii) the photoionization cross section and resonant peak magnitude depend on the donor position, laser field intensity and pressure. The localization of resonant peak maxima in the doping planes and their dependence on external perturbations are systematically investigated.

Binding energy of hydrogenic donor impurity in [formula omitted] concentric double quantum rings: Effects of geometry, hydrostatic pressure, temperature, and aluminum concentration

We consider the effects of hydrostatic pressure, temperature, aluminum concentration and impurity position on hydrogen-like donor binding energy in GaAs/Ga1−xAlxAs concentric double quantum rings. The ground state energy and the impurity wave function are calculated using the variational method. For the hydrostatic pressure effects the Γ−X crossover has been taken into account. The probability density of electron without electron-impurity interaction have been investigated for different values of the sizes of the structure. The dependencies of the binding energy on geometry of the structure, hydrostatic pressure, temperature, aluminum concentration and impurity positions have been also investigated. The results show that the binding energy is an increasing (decreasing) function of the hydrostatic pressure and aluminum concentration (temperature). Additionally we have found that when the impurity is placed within the inner ring, the binding energy behavior strongly depends on the widths of the outer ring and coupling barrier.

Ferromagnetic coupling in Mg‐doped passivated AlN nanowires: A first‐principles study

AbstractBased on density functional theory calculations, we have studied the electronic structures and magnetic properties of passivated AlN nanowires (NWs) with Mg dopants. The calculated results show that double Mg atom doped passivated AlN NWs display ferromagnetic properties, and the total magnetic moment is 1.80 µB per 96‐atom unit cell excluding the pseudohydrogen atoms. However, a couple of Mg atom doped bare AlN nanowire unit cells display anti‐ferromagnetic (AFM) properties. Unequal properties of magnetic coupling in different Mg‐doped AlN structures are due to the different localization and overlapping of impurity wave functions. It is also found that the ferromagnetic stability and Curie temperature of the passivated AlN NWs are much higher than those of bulk structures.

Theoretical intrinsic lifetime limit of shallow donor states in silicon

The intrinsic lifetime of the $2{p}_{0}$ shallow impurity state in silicon doped with P, As, Sb, or Bi has been computed by combining matrix elements of the electron-phonon coupling within the density-functional perturbation theory, with the envelope function approximation for the impurity wave functions. The theoretical lifetime due to the electronic interaction with intervalley phonons has been found to be 1.1 ns for P-doped silicon, and this theoretical limit is much longer than has been previously believed for the last five decades.

Impurity-Induced Bound States and Proximity Effect in a Bilayer Exciton Condensate

The effect of impurities which induce local interlayer tunneling in bilayer exciton condensates is discussed. We show that a localized single-fermion bound state emerges inside the gap for any strength of impurity scattering and calculate the dependence of the impurity state energy and wave function on the potential strength. We show that such an impurity-induced single-fermion state enhances the interlayer coherence around it, and is similar to the superconducting proximity effect. As a direct consequence of these single-impurity states, we predict that a finite concentration of such impurities will increase the critical temperature for exciton condensation.

Simultaneous effects of hydrostatic pressure and temperature on donor binding energy and photoionization cross section in Pöschl–Teller quantum well

We consider the effects of hydrostatic pressure and temperature on the binding energy and photoionization cross section of hydrogen-like impurity in Pöschl–Teller quantum well. The ground state energy and the impurity wave function are calculated using the variational method. The binding energy dependencies on the width of the quantum well, the hydrostatic pressure, the impurity position and the temperature are reported. The dependencies of the photoionization cross section on incident photon energy for two different polarizations of the light, different values of hydrostatic pressure and temperature have been also considered. The results show that the binding energy is an increasing (decreasing) function of the hydrostatic pressure (temperature) and that the binding energy can increase or decrease depending not only on the values of the confining potential parameters, but also on the impurity position. In the case of the photoionization cross section, the results show that by changing the polarization of the light, the behavior of the photoionization cross section dependence on photon energy changes dramatically. Associated with the increasing (decreasing) of the binding energy with the hydrostatic pressure (temperature) there is a redshift (blueshift) of the photoionization cross section as a function of the energy of the incident photon.