STM/STS measurements of two-dimensional electronic states trapped around surface defects in magnetic fields

The local density of states (LDOS) near point defects on a surface of highly oriented pyrolytic graphite (HOPG) was studied at very low temperatures in magnetic fields up to 6 T. We observed localized electronic states over a distance of the magnetic length around the defects in differential tunnel conductance images at the valley energies of the Landau levels (LLs) as well as relatively extended states at the peak ones of LLs. These states appear mainly at energies above the Fermi energy corresponding to the electron LL bands. The data suggest that the quantum Hall state is realized in the quasi two dimensional electron system in HOPG. At the peak energy associated with the n=0 (electron) and -1 (hole) LLs characteristic of the graphite structure, a reduced LDOS around the defects is observed. The spatial distribution is almost field independent, which indicates that it represents the potential shape produced by the defects.     

The linewidth of infrared light transitions between the Landau levels in graphene

We theoretically propose a structure that the population inversion between the Landau levels (LLs) of the graphene can be achieved by the electrical injection. This structure may be used for the Landau level-laser and related infrared and terahertz emitters. We mainly study the linewidth of the optical transitions between LLs in graphene due to the electron–acoustic phonon scattering. Within the Huang–Rhysʼs lattice relaxation model, we improve the effective single-phonon mode (ESM) for the acoustic phonon to calculate the linewidth of the optical transition and compare the obtained results with that of in the low and high-temperature limit. We find that the ESM provides a very good approximation for the temperature dependence of linewidth, which covers the dominating features of the low and high-temperature limit.     

Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Magneto-electronic properties of rhombohedral (ABC-stacked) trilayer graphene are investigated by the tight-binding (TB) model with all important interlayer interactions taken into account. A numerical strategy, band-like matrix, is applied to solve the huge Hamiltonian matrix and thus the eigenvalues and eigenvectors of Landau levels (LLs) are well defined. Based on the characteristics of the wave functions, the LLs are divided into three groups. These LLs are strongly affected by the stacking configuration and interlayer interactions. The LL spectra do reflect the main features of the zero-field subbands, i.e., the existence of three LL groups, specified onset energies of the three groups, and asymmetric electronic structure. In an ABC-stacked structure, the LL wave functions are each composed of six magnetic TB Bloch functions for six sublattices. Each magnetic TB Bloch function exhibits the spatial symmetry, localization feature, and oscillation modes. Three sets of effective quantum numbers are defined to index the LLs of the three groups based on the oscillation modes in specific sublattices. These effective quantum numbers are useful for defining the optical selection rules of the optical absorption spectra.     

Quantum Hall effect in back-gated InAs/GaSb heterostructures under a tilted magnetic field

We investigate the quantum Hall effect (QHE) in the InAs/GaSb hybridized electron–hole system grown on a conductive InAs substrate which act as a back-gate. In these samples, the electron density is constant and the hole density is controlled by the gate-voltage. Under a magnetic field perpendicular to the sample plane, the QHE appears along integer Landau-level (LL) filling factors of the net-carriers, where the net-carrier density is the difference between the electron and hole densities. In addition, longitudinal resistance maxima corresponding to the crossing of the extended states of the original electron and hole LLs make the QHE regions along integer-ν_net discontinuous. Under tilted magnetic fields, these R_xx maxima disappear in the high magnetic field region. The results show that the in-plane magnetic field component enhances the electron–hole hybridization and the formation of minigaps at LL crossings.     

Effects of electron correlation and the Breit interaction on one- and two-electron one-photon transitions in double K hole states of He-like ions(10 ≤ Z ≤ 47)

The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state 2s2p to the 1s2s and 1s^2 configurations of 11 selected He-like ions(10 ≤ Z ≤ 47) are calculated using the fully relativistic multi-configuration Dirac–Fock method(MCDF). An appropriate electron correlation model is constructed with the aid of the active space method, which allows the electron correlation effects to be studied efficiently. The contributions of the electron correlation and the Breit interaction to the transition properties are analyzed in detail. It is found that the two-electron one-photon(TEOP) transition is correlation sensitive. The Breit interaction and electron correlation both contribute significantly to the radiative transition properties of the double K hole state of the He-like ions. Good agreement between the present calculation and previous work is achieved. The calculated data will be helpful to future investigations on double K hole decay processes of He-like ions.     

Electron–hole transition in a spherical quantum dot confined at the center of a cylindrical nano-wire: Comparison of isotropic and anisotropic effective mass

Electronic structure of an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire is investigated. The Schrodinger equation within the effective mass approximation is solved and the energy eigenvalues and transition energies are calculated as a function of quantum dot and nano-wire radii using the finite element method. The two types of heavy holes, hhI and hhII, with isotropic and anisotropic effective masses are considered, respectively. The effect of spherical and nano-wire confining potentials, the size of the dot and the nano-wire on ground and first excited state energies of the electron, heavy hole I and heavy hole II are investigated. The results show that the electron and heavy holes energies decrease as the dot and the nano-wire radii increase. The emitted wavelength of transitions between el-hhI and el-hhII are also calculated and compared. The results show that the anisotropy of the effective mass has great effect on the emitted wavelength.     

Optical and magnetooptical properties of manganese-zinc ferrospinels

The use of optical methods for the investigation of the electronic structure of oxide ferrimagnets is complicated by the large variety of possible types of electron transitions whose energies are close to each other and lie in the near infrared, visible, and near ultraviolet regions of the spectrum. Therefore, for the correct identification of the transitions, it is desirable to apply traditional optical spectroscopy, which permits quantitative evaluation of the transition intensities (oscillator strength), in conjunction with magnetooptical (MO) methods providing information on weak intraconfigurational transitions which are not manifest in ordinary absorption or reflection spectra.     

Spin-dependent resistivity and quantum Hall ferromagnetism in two-dimensional electrons confined to AlAs quantum wells

We observe a strong dependence of the amplitude and field position of longitudinal resistivity (ρ_xx) peaks in the spin-resolved integer quantum Hall regime on the spin orientation of the Landau level (LL) in which the Fermi energy resides. The amplitude of a given peak is maximal when the partially filled LL has the same spin as the lowest LL, and amplitude changes as large as an order of magnitude are observed as the sample is tilted in field. In addition, the field position of both the ρ_xx peaks and plateau–plateau transitions in the Hall resistance shift depending on the spin orientation of the LLs. The spin dependence of the resistivity points to a new explanation for resistivity spikes, associated with first-order quantum Hall ferromagnetic transitions, that occur at the edges of quantum Hall states.     

Anomalous robustness of the ν=5/2 fractional quantum Hall state near a sharp phase boundary

We report magnetotransport measurements in wide GaAs quantum wells with a tunable density to probe the stability of the fractional quantum Hall effect at a filling factor of ν=5/2 in the vicinity of the crossing between Landau levels (LLs) belonging to the different (symmetric and antisymmetric) electric subbands. When the Fermi energy (E(F)) lies in the excited-state LL of the symmetric subband, the 5/2 quantum Hall state is surprisingly stable and gets even stronger near this crossing, and then suddenly disappears and turns into a metallic state once E(F) moves to the ground-state LL of the antisymmetric subband. The sharpness of this disappearance suggests a first-order transition.     

Intersubband,interband transitions,and optical properties of two vertically coupled hemispherical quantum dots with wetting layers

The electron and heavy hole energy levels of two vertically coupled In As hemispherical quantum dots/wetting layers embedded in a Ga As barrier are calculated numerically. As the radius increases, the electronic energies increase for the small base radii and decrease for the larger ones. The energies decrease as the dot height increases. The intersubband and interband transitions of the system are also studied. For both, a spectral peak position shift to lower energies is seen due to the vertical coupling of dots. The interband transition energy decreases as the dot size increases, decreases for the dot shapes with larger heights, and reaches a minimum for coupled semisphere dots.     

The electronic structures of the core and valence ion states of metal oxides

SCF-Xα SW MO calculations on metal core ion hole states and X-ray emission (XES) and X-ray photoelectron (XPS) transition states of the non- transition metal oxidic clusters MgO₆^10?, AlO₄^5? and SiO₄^4? show relative valence orbital energies to be virtually unaffected by the creation of valence orbital or metal core orbital holes. Accordingly, valence orbital energies derived from XPS and XES are directly comparable and may be correlated to generate empirical MO diagrams. In addition, charge relaxation about the metal core hole is small and valence orbital compositions are little changed in the core hole state. On the other hand, for the transition metal oxidic clusters FeO₆^10?, CrO₆^9? and TiO₆^8? relative valence orbital energies are sharply changed by a metal core orbital or crystal field orbital hole, the energy lowering of an orbital increasing with its degree of metal character. Consequently O 2p nonbonding → M 3d-O 2p antibonding (crystal field) energies are reduced, while M 3d bonding → O 2p nonbonding and M 3d-O 2p antibonding → M 4s,p-O 2p antibonding (conduction band) energies increase. Charge relaxation about the core hole is virtually complete in the transition metal oxides and substantial changes are observed in the composition of those valence orbitals with appreciable M 3d character. This change in composition is greater for e _g than for t_2g orbitals and increases as the separation of the e_g crystal field (CF) orbitals and the O 2p nonbonding orbital set decreases. Based on the hole state MO diagrams the higher energy XPS satellite in TiO₂ (at about 13 eV) is assigned to a valence → conduction band transition. The UV PES satellites at 8.2 eV in Cr₂O₃ and 9.3 eV in FeO are tentatively assigned to similar transitions to conduction band orbitals, although the closeness in energy of the crystal field and O 2p nonbonding orbitals in the valence orbital hole state prevents a definite assignment on energy criteria alone. However the calculations do clearly show that charge transfer transitions of the e_g bonding → e_g crystal field orbital type would generally occur at lower energy than is consistent with observed satellite structure.A core electron hole has little effect upon relative orbital energies and is only slightly neutralized by valence electron redistribution for MgO and SiO₂. For the transition metal oxides a core hole lowers the relative energies of M3d containing orbitals by large amounts, reducing O → M charge transfer and increasing M 3d crystal field → conduction band energies. Large and sometimes overcomplete neutralization of the core hole is observed, increasing from CrO₆^9? to FeO₆^10? to TiO₆^8?. as the O → M charge transfer energy declines.High energy XPS satellites in TiO₂ may be assigned to O 2p nonbonding → conduction band transitions while lower energy UV PES satellites in FeO and Cr₂O₃ arise from crystal field or O 2p nonbonding → conduction band excitations. Our “shake-up” assignment for FeO₆^10?, CrO₆^9? and TiO₆^8? are less than definitive because no procedure has yet been developed to calculate “shake-up” intensities resulting from transitions of the type described. However the results do allow a critical evaluation of earlier qualitative predictions of core and valence hole effects. First, we find that the comparison of hole or valence state ionic systems with equilibrium distance systems of higher nuclear and/or cation charge (e.g. the comparison of the FeO₆^10? Fe 2p core hole state to Co₃O₄) is dangerous. For example, larger MO distances in the ion states substantially reduce crystal field splittings. Second, core and CF orbital holes sharply reduce O → M charge transfer energies, giving 2e_g → 3e_g energy separations which are generally too small to match observed satellite energies. Third, highest occupied CF-conduction band energies are only about 4–5 eV in the ground states, but increase to about 7–11 eV in the core and valence hole states of the transition metal oxides studied. The energetic arguments presented thus support the idea of CF and/or O 2p nonbonding → conduction band excitations as assignments for “shake-up” satellites, at least in oxides of metals near the beginning of the transition series.     

Influences of strains on the formation of the quasi-Dirac cone and the Landau levels in black phosphorus

A tunable tight-binding (TB) Hamiltonian, which can be tuned continuously by applying the strains, is proposed based on the two tight-binding Hamiltonian models used to describle the pristine and compressed black phosphorus (BP). This tunable TB Hamiltonian should be of fundamental significance in two aspects: i) A general tunable TB Hamiltonian making it possible to study the BP more conveniently and deeply; ii) An extension of the study of the strain effect from the monolayer phosphorene to the multilayer phosphorene and even the bulk BP in the presence of both the in-plane and out-of-plane strains. Furthermore, based on the tunable TB Hamiltonian we can find the strain-induced quasi-Dirac cone, and clearly disclose how the strains affect the formation of the quasi-Dirac cone. Then we investigate the Landau levels (LLs) of BP under different magnetic fields, uncovering the linear, square-root, or complex dependence of the LLs on the LL number or the magnetic field. Moreover, the double-step and triple-step transitions of the LLs are found to be induced by the strains for the BP in the in-plane and out-of-plane magnetic fields. This research successfully incorporates the out-of-plane strain effect into the tunable TB Hamiltonian, enabling the comprehensive investigation of the strain-correlated effect in BP.     

Resonant electron exchange scattering in late transition metal monoxides

Intra-atomic d-d transitions in NiO(100) and CoO(100) have been investigated with angle-resolved electron energy loss spectroscopy (EELS) at primary energies close to the metal 3s excitation threshold. Electron exchange scattering was found to be resonantly enhanced at the 3s threshold due to the temporary formation of a negative ion core state and its subsequent decay via Auger-like transitions. In both oxides the threshold is lowered several eV due to a strong electron- core hole interaction. Angle-dependent studies reveal a different dependency of exchange processes on the scattering angle as compared with nonresonant measurements and reveal a different angle dependence for each specific d-d transition. It is suggested that in these oxides large-angle single-step inelastic scattering contributes significantly to the EELS measurements in reflection mode.     

InAs/AlSb/GaSb量子阱中的双色光吸收

为了降低噪声对InAs/GaSb量子阱作为双色电探测器性能的影响,设计性能优良的光电探测器,在InAs/GaSb量子阱中加入AlSb夹层,以减少电子和空穴在界面处的复合,从而抑制由于电子和空穴复合引起的噪声。首先应用转移矩阵方法求解薛定谔方程得到量子阱中电子和空穴的能级和波函数,研究AlSb夹层对电子和空穴波函数的影响。应用平衡方程方法求解外加光场条件下的玻尔兹曼方程,研究所有电子和空穴跃迁通道对光吸收系数的贡献,重点研究了AlSb夹层厚度对光吸收系数的影响。结果表明:基于In As/GaSb的量子阱体系可以实现双色光吸收,加入AlSb夹层可以有效抑制电子和空穴在界面处的隧穿,从而降低复合噪声,同时AlSb夹层的加入也对吸收峰有影响。AlSb夹层的厚度达到2 nm即可有效降低电子和空穴复合噪声,双色光吸收峰在中远红外波段,为该量子阱作为性能良好的中远红外光电探测器提供理论支撑。     

Density of states and zero Landau Level probed through capacitance of graphene

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels.     

Temperature scaling of quantum Hall plateau transition in bilayer systems

We have investigated the scaling behavior of the quantum Hall plateau transition in double quantum well systems with different interlayer tunneling strengths. The scaling behavior of the localization property is found to be similar between the case when the relevant Landau level (LL) is non-degenerate and the case when two LLs associated with the two layers are accidentally degenerate. In both cases, the scaling exponent κ0.4 close to the canonical value is obtained, and it is unaffected by the in-plane magnetic field which changes the interlayer tunneling strength.     

Electronic structures of GaAs/AlGaAs concentric double rings in applied electric and magnetic field

The electronic structures of GaAs/Al_0.35Ga_0.65As concentric double rings are calculated based on the effective mass envelope function theory, with and without the applied electric and magnetic field along the growth direction. The Hamiltonian matrix elements are determined through the Fourier transform method. As the heterostructure evolves from a single ring to the concentric double rings, our simulation is performed on the bound state energies of the electron and the hole. The results show that the energy levels undulate with the evolution of the ring. The applied magnetic field increases the ground state energies both of the electron and of the hole, as well as the transition energy between the first conduction subband and valence subband. However, the electric field decreases the electronic energies linearly.     

Collisional Lifetimes of Elementary Excitations in Two-Dimensional Systems in the Field of a Strong Electromagnetic Wave

A two-dimensional system with two nonequivalent valleys in the field of a strong circularly polarized electromagnetic wave is considered. It is assumed that the optical selection rules for a given polarization of light allow band-to-band transitions only in valleys of one, optically active, type (two-dimensional layer based on transition metal dichalcogenides, gapped graphene, etc.). This leads to the formation of photon-coupled electron–hole pairs, or an “optical insulator” state. It is assumed that the valleys of the second type (optically inactive) are populated with an equilibrium electron gas. The relaxation of elementary excitations in this hybrid system consisting of an electron gas and a gas of electron–hole pairs caused by the Coulomb interaction between the particles is investigated.     

2PI effective action and evolution equations of \mathcal{N} = 4 super Yang–Mills

We study the possibility of phase transitions between Lifshitz black holes and other configurations by using free energies explicitly. A phase transition between Lifshitz soliton and Lifshitz black hole might not occur in three dimensions. We find that a phase transition between Lifshitz and BTZ black holes is unlikely to occur because they have different asymptotes. Similarly, we point out that any phase transition between Lifshitz and black branes is unlikely to occur in four dimensions since they have different asymptotes. This is consistent with the necessary condition for taking a phase transition in a gravitational system, which requires the same asymptote.     

Auger electron spectroscopy - a local probe for solid surfaces

The Auger electron transition in solids is discussed under the aspect of a local excitation due to the strongly localized primary hole in an inner atomic core level. In first approximation the solid is represented by a cluster model, consisting of the excited atom and its neighbors. Using this simple model it is possible to describe the Auger electron energies, intensities and line shapes of transitions in solids in a satisfactory way. Only for the angular dependent Auger emission, characteristic long-range crystalline order has to be taken into account. It is the aim of this introductory review to point out that Auger spectra bear more information about the solid surface and particularly on its chemical bonds as has yet been exploited by surface spectroscopists.