Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.

Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

Determination of electronic energy levels of molecules by 90° low energy electron scattering

A review of the theory of electron scattering indicates that low incident beam energies and large scattering angles are the favorable conditions for the observation of optically forbidden transitions in atoms and molecules.

An apparatus capable of yielding electron impact spectra at 90° with incident electron beam energies between 30 and 50 electron volts is described. The resolution of the instrument is about 1 electron volt.

Impact spectra of thirteen molecules have been obtained. Known forbidden transitions to the helium 2³S, the hydrogen b³Ʃ⁺_u, the nitrogen A³Ʃ⁺_u, B³π_g, a’π_g, and C³π_u, the carbon monoxide a³π, the ethylene ᾶ³B_1u, and the benzene ᾶ³B_1u states from the corresponding ground states have been observed.

In addition, singlet-triplet vertical transitions in acetylene, propyne, propadiene, norbornadiene and quadricyclene, peaking at 5.9, 5.9, 4.5, 3.8, and 4.0 ev (±0.2 ev), respectively, have been observed and assigned for the first time.

Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

Three-photon-excited upconversion luminescence of Ce3+: YAP crystal by femtosecond laser irradiation

Infrared to ultraviolet and visible upconversion luminescence was demonstrated in trivalent cerium doped YAlO3 crystal (Ce3+: YAP) under focused infrared femtosecond laser irradiation. The fluorescence spectra show that the upconverted luminescence comes from the 5d-4f transitions of trivalent cerium ions. The dependence of luminescence intensity of trivalent cerium on infrared pumping power reveals that the conversion of infrared radiation is dominated by three-photon excitation process. It is suggested that the simultaneous absorption of three infrared photons pumps the Ce3+ ion into upper 5d level, which quickly nonradiatively relax to lowest 5d level. Thereafter, the ions radiatively return to the ground states, leading to the characteristic emission of Ce3+. (c) 2005 Optical Society of America.

红外飞秒激光诱导Ce^3＋掺杂闪烁晶体的上转换发光研究

本文研究了红外飞秒激光照射下Ce^3＋ 掺杂的YAP和LSO两种闪烁晶体的上转换发光现象.实验发现在飞秒激光泵浦下,这两种晶体的荧光均来自于Ce^3＋离子的5d-4f跃迁.荧光强度与泵浦光功率之间的依赖关系揭示了Ce^3＋：YAP和Ce^3＋：LSO晶体的上转换过程皆由三光子吸收过程所主导.分析表明,Ce^3＋：YAP和Ce^3＋：LSO晶体中的三光子吸收是三光子同时吸收.

Resonant excitation and imaging of nonequilibrium exciton spins in single core-shell GaAs-AlGaAs nanowires.

Nonequilibrium spin distributions in single GaAs/AlGaAs core-shell nanowires are excited using resonant polarized excitation at 10 K. At all excitation energies, we observe strong photoluminescence polarization due to suppressed radiative recombination of excitons with dipoles aligned perpendicular to the nanowire. Excitation resonances are observed at 1- or 2-LO phonon energies above the exciton ground states. Using rate equation modeling, we show that, at the lowest energies, strongly nonequilibrium spin distributions are present and we estimate their spin relaxation rate.

Numerical analysis of gain saturation, noise figure, and carrier distribution for quantum-dot semiconductor-optical amplifiers

The gain saturation behaviors and noise figure are numerically analyzed for quantum-dot semiconductor optical amplifiers (QD-SOAs). The carrier and photon distributions in the longitudinal direction as well as the photon energy dependent facet reflectivity are accounted in the rate equations, which are solved with output amplified spontaneous emission spectrum as iterative variables. The longitudinal distributions of the occupation probabilities and spectral-hole burning are presented for electrons in the excited and ground states of quantum dots. The saturation output power 19.7 dBm and device gain 20.6 dB are obtained for a QD-SOA with the cavity length of 6 rum at the bias current of 500 mA. The influences of them electron intradot relaxation time and the QD capture time on the gain spectrum are simulated with the relaxation time of 1, 30, and 60 ps and capture time of 1, 5, and 10 ps. The noise figure as low as 3.5 dB is expected due to the strong polarization sensitive spontaneous emission. The characteristics of gain saturation and noise figure versus input signal power for QD-SOAs are similar to that of semiconductor. linear optical amplifiers with gain clamping by vertical laser fields.

Electronic structure and optical gain of wurtzite ZnO nanowires

The electronic structure and optical gain of wurtzite ZnO nanowires are investigated in the framework of effective-mass envelope-function theory. We found that as the elliptical aspect ratio e increases to be larger than a critical value, the hole ground states may change from optically dark to optically bright. The optical gain of ZnO nanowires increases as the hole density increases. For elliptical wire with large e, the y-polarized mode gain can be several thousand cm(-1), while the x-poiarized mode gain may be 26 times smaller than the former, so they can be used as ultraviolet linearly polarized lasers. (C) 2008 American Institute of Physics.

Highly anisotropic and electric field tunable Zeeman splittings in Mn-doped CdS nanowires

The electronic structure, Zeeman splitting, and g factor of Mn-doped CdS nanowires are studied using the k center dot p method and the mean field model. It is found that the Zeeman splittings of the hole ground states can be highly anisotropic, and so can their g factors. The hole ground states vary a lot with the radius. For thin wire, g(z) (g factor when B is along the z direction or the wire direction) is a little smaller than g(x). For thick wire, g(z) is mcuh larger than g(x) at small magnetic field, and the anisotropic factor g(z)/g(x) decreases as B increases. A small transverse electric field can change the Zeeman splitting dramatically, so tune the g(x) from nearly 0 to 70, in thick wire. The anisotropic factor decreases rapidly as the electric field increases. On the other hand, the Zeeman splittings of the electron ground states are always isotropic.

Quantum critical phenomena in the XY spin chain with the Dzyaloshinski-Moriya interaction (Retracted article. See vol 80, artn 019903, 2009)

We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.

Strain relaxation and band-gap tunability in ternary InxGa1-xN nanowires

The alloy formation enthalpy and band structure of InGaN nanowires were studied by a combined approach of the valence-force field model, Monte Carlo simulation, and density-functional theory (DFT). For both random and ground-state structures of the coherent InGaN alloy, the nanowire configuration was found to be more favorable for the strain relaxation than the bulk alloy. We proposed an analytical formula for computing the band gap of any InGaN nanowires based on the results from the screened exchange hybrid DFT calculations, which in turn reveals a better band-gap tunability in ternary InGaN nanowires than the bulk alloy.

Singlet-triplet transition in quantum dots confined by triangular and bowl-like potentials: the effect of electric fields

We theoretically investigate the energy spectra of two-electron two-dimensional (2e 2D) quantum dots (QDs) confined by triangular potentials and bowl-like potentials in a magnetic field by exact diagonalization in the framework of effective mass theory. An in-plane electric field is,found to contribute to the singlet-triplet transition of the ground state of the 2e 2D QDs confined by triangular or bowl-like potentials in a perpendicular magnetic field. The stronger the in-plane electric field, the smaller the magnetic field for the total spin of the ground states in the dot systems to change from S = 0 to S = 1. However, the influence of an in-plane electric field on the singlet-triplet transition of the ground state of two electrons in a triangular QD modulated by a perpendicular magnetic field is quite small because the triangular potential just deviates from the harmonic potential well slightly. We End that the strength of the perpendicular magnetic field needed for the spin singlet-triplet transition of the ground state of the QD confined by a bowl-like potential is reduced drastically by applying an in-plane electric field.

Interface-related in-plane optical anisotropy of quantum wells studied by reflectance-difference spectroscopy

The in-plane optical anisotropy of three groups of GaAs/AlGaAs quantum well structures has been studied by reflectance-difference spectroscopy (RDS). For GaAs/Al0.36Ga0.64As single QW structures, it is found that the optical anisotropy increases quickly as the well width is decreased. For an Al0.02Ga0.98As/AlAs multiple QW with a well width of 20nm, the optical anisotropy is observed not only for the transitions between ground states but also for those between the excited states with transition index n up to 5. An increase of the anisotropy with the transition energy, or equivalently the transition index n, is clearly observed. The detailed analysis shows that the observed anisotropy arises from the interface asymmetry of QWs, which is introduced by atomic segregation or anisotropic interface roughness formed during the growth of the structures. More, when the 1 ML InAs is inserted at one interface of GaAs/AlGaAs QW, the optical anisotropy of the QW can be increased by a factor of 8 due to the enhanced asymmetry of the QW. These results demonstrate clearly that the RDS is a sensitive and powerful tool for the characterization of semiconductor interfaces.