Mixed state of a dirty two-band superconductor: application to MgB2

We investigate the vortex state in a two-band superconductor with strong intraband and weak interband electronic scattering rates. Coupled Usadel equations are solved numerically, and the distributions of the pair potentials and local densities of states are calculated for two bands at different values of magnetic fields. The existence of two distinct length scales corresponding to different bands is demonstrated. The results provide qualitative interpretation of recent scanning tunneling microscopy experiments on vortex structure imaging in MgB2.     

Der Einfluß von Spinfluktuationen auf die Sprungtemperatur eines Zweibandsupraleiters

The superconducting transition temperatureT _c of a two band superconductor in the presence of magnetic and nonmagnetic impurities as well as exchange fields is calculated using a new (8 × 8)-matrix formalism for the electron Green's function. In particular we investigate the influence of spin correlations onT _c near a magnetic phase transition. It is shown that in the strong interband phonon coupling limit the system behaves essentially as a one band superconductor. In the weak coupling limit we find typical deviations from one band theories.     

Local electronic structure of a single nonmagnetic impurity as a test of the pairing symmetry of electrons in (K,Tl)FexSe2 superconductors

We study the effect of a single nonmagnetic impurity on the recently discovered (K,Tl)Fe(x)Se(2) superconductors, within both a toy two-band model and a more realistic five-band model. We find that, out of five types of pairing symmetry under consideration, only the d(x(2)-y(2))-wave pairing gives rise to impurity resonance states. The intragap states have energies far away from the Fermi energy. The existence of these intragap states is robust against the presence or absence of interband scattering. However, the interband scattering does tune the relative distribution of local density of states at the resonance states. All these features can readily be accessed by STM experiments, and are proposed as a means to test the pairing symmetry of the new superconductors.     

Optical phonon assisted cyclotron harmonic transitions in p-InSb

The observation of optical-phonon induced cyclotron resonance harmonics in the valence band of InSb is reported. A photoconductivity technique was applied, using a CO₂ laser and magnetic fields up to 15 T. The observed resonances are well described by a corrected Pidgeon-Brown model calculation which is also consistent with experimentally observed magneto-optical intra-conduction and interband transitions.     

Semiconductor electrons in electric and magnetic fields

Optical properties of semiconductors in the simultaneous presence of electric and magnetic fields are reviewed, with particular emphasis on the possibilities of modulation techniques. First, the problem of an electron in crossed and parallel fields is solved in the one-level effective mass approximation (EMA), and the results are used to interpret the experimental interband transitions in Ge, with due account of the degenerate character of the valence band in this material. The limitations of the one-level EMA are discussed, and the two-level model is introduced, which correctly describes the experimentally observed transition from a magnetic type to an electric type of motion in increasing transverse electric field. Possibilities to observe electric field effects in cyclotron resonance transitions are discussed in this approximation. Finally, the three-level model is used to describe properly both orbital and spin properties of conduction electrons. It is demonstrated that in a small-gap semiconductor with large spin-orbit interaction a sufficiently strong transverse electric field destroys the Landau orbital quantization but not the Pauli spin quantization. Possible experimental consequences of this situation are discussed. Influence of finite dimensions of the sample on the character of the electron motion in crossed and parallel fields is examined. A possibility to achieve the semiconductor-semimetal transition in a symmetryinduced zero-gap semiconductor in crossed field configuration is predicted and described, taking into account the Luttinger effects in the magnetic level structure.     

Momentum matrix elements in III–V semiconductor alloys

The composition dependence of P², the square of the principal interband matrix element, is investigated. P² is calculated in a virtual crystal approximation within the empirical pseudopotential method. In all the alloys studied, the variation of P² with x is found to be nearly linear. The results are compared with experimental values, obtained from a five-band $\text{K}$, $\text{K}$ analysis of the conduction electron Landé factor and effective mass data. The agreement is good in Ga_1?xIn_xAs and Ga_1?xAl_xAs, but not in In_1?xGa_xSb, which shows a disorder induced deviation.     

Zeeman effect and magnetic anomalies in narrow-gap semiconductor quantum dots

We present a systematic theoretical study, based on the Kane–Weiler 8×8 k·p model, of the linear Zeeman splitting introduced by the interaction between the angular momentum and the magnetic field which can give a measure of the non-linear Zeeman effect associated with interband coupling and diamagnetic contributions. The conduction and valence bands g-factors are calculated for InSb spherical and semi-spherical quantum dots. The calculations of the g-factors showed an almost linear dependence, for the ground state, on the magnetic field. We have also found that the strong magnetic field dependence as well as the dependence on the dot size of the effective spin splitting can be unambiguously attributed to the strength of the inter-level mixing.     

Faraday rotation and the magnetocaloric effect in the Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> terbium gallium garnet at low temperatures in strong magnetic fields

The magnetocaloric effect and the Faraday rotation in a paramagnetic cubic crystal of terbium gallium garnet in strong magnetic fields oriented along different crystallographic directions are calculated theoretically. It is demonstrated that, in strong magnetic fields, the magnetocaloric effect and the Faraday effect are characterized by strong anisotropy, which disappears in weak magnetic fields.     

Quantum magneto-optics of the graphite family

The optical conductivity of graphene, bilayer graphene, and graphite in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall’s, are evaluated analytically. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. We show that trigonal warping can be considered within the perturbation theory for strong magnetic fields larger than 1 T. The semiclassical approach is applied for weak fields when the Fermi energy is much larger than the cyclotron frequency. The main optical transitions obey the selection rule with Δn = 1 for the Landau number n, but the Δn = 2 transitions due to the trigonal warping are also possible. The Faraday/Kerr rotation and light transmission/reflection in quantizing magnetic fields are calculated. Parameters of the Slonczewski-Weiss-McClure model are used in the fit taking the previous de Haas-van Alphen measurements into account and correcting some of them in the case of strong magnetic fields.     

Electron-ion collision integral in a strong magnetic field

Boltzmann’s collision integral is extended to the case of helical (Larmor) particle trajectories in a magnetic field of arbitrary strength. The main characteristics of collisions of electrons with positively charged ions in strong magnetic fields, where the Larmor radius of electrons becomes less than the characteristic impact parameter of close collisions in the absence of a magnetic field (Landau’s parameter), are investigated. The differential scattering cross section and the corresponding electron-ion collision integral in strong fields are found. The transport collision frequencies are calculated, and the results are compared with the similar quantities for weaker magnetic fields.     

State-filling and magneto-photoluminescence of excited states in InGaAs/GaAs self-assembled quantum dots

We present the first radiative lifetime measurements and magneto-photoluminescence results of excited states in InGaAs/GaAs semiconductor self-assembled quantum dots. By increasing the photo-excitation intensity, excited state interband transitions up ton= 5 can be observed in the emission spectrum. The dynamics of the interband transitions and the inter-sublevel relaxation in these zero-dimensional energy levels lead to state-filling of the lower-energy states, allowing the quasi-Fermi level to be raised by more than 200 meV due to the combined large inter-sublevel spacing and the low density of states. The decay time of each energy level obtained under various excitation conditions is used to evaluate the inter-sublevel thermalization time. Finally, the emission spectrum of the dots filled with an average of about eight excitons is measured in magnetic fields up to 13 Tesla. The dependences of the spectrum as a function of carrier density and magnetic field are compared to calculations and interpreted in terms of coherent many-exciton states and their destruction by the magnetic field.     

Parameter dependence of optical conductivity in antiferromagnetic phase of iron pnictides

We investigate the optical conductivity of iron pnictides in antiferromagnetic state by mean-field calculation in a five-band Hubbard model, focusing on its anisotropic behavior by examining several states calculated with different Hund coupling J, such as the states with a low or high magnetization and with or without a strong orbital ordering. In addition, we investigate the J dependence of the Dirac cone structure, which is crucial for the low energy excitation. In our calculations, a weakly ordered state with no orbital ordering shows the anisotropy of optical conductivity in accord with experiments. We conclude that the low energy part of the optical conductivity is relevant to the Dirac electron structure rather than the orbital ordering.     

Spectra of cylindrical quantum dots: The effect of electrical and magnetic fields together with AB flux field

We study the spectral properties of electron quantum dots (QDs) confined in 2D parabolic harmonic oscillator influenced by external uniform electrical and magnetic fields together with an Aharonov–Bohm (AB) flux field. We use the Nikiforov–Uvarov method in our calculations. Exact solutions for the energy levels and normalized wave functions are obtained for this exactly soluble quantum system. Based on the computed one-particle energetic spectrum and wave functions, the interband optical absorption GaAs spherical shape parabolic QDs is studied theoretically and the total optical absorption coefficient is calculated.     

Simulation of optically pumped intersubband laser in magnetic field

Simulations of an optically pumped intersubband laser in magnetic field up to 60 T are performed within the steady-state rate equations model. The electron-polar optical phonon scattering is calculated using the confined and interface phonon model. A strong oscillatory optical gain vs. magnetic field dependence is found, with two dominant gain peaks occurring at 20 and 40 T, the fields which bring appropriate states into resonance with optical phonons and thus open additional relaxation paths. The peak at 20 T exceeds the value of gain achieved at zero field.     

Electronic states and interband light absorption in semi-spherical quantum dot under the influence of strong magnetic field

In the framework of effective mass approximation the electronic states in semi-spherical quantum lens under the influence of strong magnetic field are investigated. We have used the adiabatic approximation for the case of strong magnetic field. The eigenfunctions and eigenvalues of this problem are determined. In strong confinement regime interband optical absorption of light is investigated in quantum lens from InAs. The threshold frequencies of absorption are determined. The comparison with the case of film under the influence of strong magnetic field with infinitely high confinement potential is performed.     

Magnetooptical investigation of PbTe/Pb1−xSnxTe superlattices

Intra- and interband magnetooptical experiments were carried out on PbTe/Pb_1?xSn_xTe superlattices (x=0.135) with layer thicknesses ranging from 13 – 225 nm. For the magnetic field parallel to the [111] growth direction, the Landau levels for the superlattice band structure are calculated within the framework of the envelope function approach for the [111] and the three obliquely oriented valleys. The experimental intra- and interband data agree qualitatively with the results of the model calculation and are consistent with the predictions of a LCAO calculation according to which the electrons or holes are confined in the Pb_1?xSn_xTe layers.     

Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field

The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.     

Magnetospectroscopy of double HgTe/CdHgTe QWs with inverted band structure in high magnetic fields up to 30 T

Magnetoabsorption in far and mid IR ranges in double HgTe/CdHgTe quantum wells with inverted band structure has been studied in high magnetic fields up to 30 T. Numerous intraband and interband transitions have been revealed in the spectra and interpreted within axial 8 × 8 k·p model. Splitting of dominant magnetoabsorption lines resulting from optical transitions from hole-like zero-mode Landau level has been discovered and discussed in terms of a built-in electric field and collective phenomena.     

Influence of an electric field on the magnetoabsorption in a field of resonant laser radiation

The frequency dependence of the coefficient of interband magnetoabsorption of a weak electromagnetic wave propagating in a constant electric field and in a field of resonant laser radiation at a frequency equal to the cyclotron frequency (infrared magnetic resonance) is calculated. The specific features observed in interband absorption of the electromagnetic wave in a uniform electric field are considered for the case in which the frequency of laser radiation is equal to the confinement frequency in a parabolic quantum well (infrared quantum-well resonance).