Narrow Results

We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.

Inserted narrow InAs quantum wells in InAs/InGaAs/InAlAs heterostructures have been used to achieve higher mobility for high-electron-mobility transistors (HEMTs) with ultra-low-power and low-noise amplification characteristics and for spin-based devices. Due to the large nonparabolicity of the conduction band of InAs and the penetration of the confined electronic envelope function into the adjacent layer(s), accurate calculations of effective mass and g-factor of charge carriers can be problematic. Methods of making precise determinations of the mass and other electronic parameters are thus of interest. We have applied magneto-photoresponse and -transmissions measurements at several THz laser frequencies in concert with dc magnetotransport measurements at low temperature (T = 1.6 K) to determine various electronic parameters (effective mass, carrier density, g-factor, mobility and the quantum scattering time) of the 2DEG in an InAs/In_0.75Ga_0.25As/In_0.75Al_0.25As inserted channel structure. This characterization method can also be used to probe the effect of strain, Rashba field, etc on the properties of charge carriers in such structures.

The effective gravitational mass as well as the energy and momentum distributions of a radiating charged particle in Einstein's universe are evaluated. The Møller's energy–momentum complex is employed for this computation. The spacetime under study is a generalization of Bonnor and Vaidya spacetime in the sense that the metric is described in the cosmological background of Einstein's universe in lieu of the flat background. Several spacetimes are limiting cases of the one considered here. In particular for the Reissner–Nordström black hole background, our results are exactly the same as those derived by Cohen and Gautreau using Whittaker's theorem and by Cohen and de Felice using Komar's mass. Furthermore, the power output for the spacetime under consideration is obtained.

The formalism of Darboux transformations is established for time-dependent Schrödinger equations with an effective (position-dependent) mass. Explicit formulas are obtained for the transformed wave function and the difference between the original and the transformed potential. It is shown that for a noneffective mass our Darboux transformation reduces correctly to the well-known Darboux transformation.

We set up a reality condition for Darboux transformations of time-dependent Schrödinger equations (TDSE) with position-dependent (effective) mass. The reality condition guarantees the potential in the transformed TDSE to be real-valued and hence physical. This paper is a sequel of our former one.³⁶

We define form-preserving transformations and Darboux transformations for time-dependent, effective mass Hamiltonians with additional linear terms. We give reality conditions for both transformations, guaranteeing the transformed potential to be real-valued. We further show that our form-preserving transformation preserves normalizability of the Schrödinger wave function. Our results generalize all former results on form-preserving transformations and Darboux transformations for the time-dependent Schrödinger equation. This paper is a sequel of Refs. 16–18.

We construct Darboux transformations of arbitrary order for stationary Schrödinger equations with effective mass that exhibit spherical symmetry in N dimensions (hyperspherical symmetry). The Darboux transformation and the associated transformed Schrödinger equation are obtained in closed form.

We construct first-order Darboux transformations for stationary Schrödinger equations with position-dependent (effective) mass and energy-dependent potential. We point out characteristic differences to the corresponding Darboux transformation for constant mass.¹⁴

We have analyzed what new fundamental information on the properties of superconductors can be obtained by systematic investigation of the Bernoulli effect. We show that the latter is a tool to determine the effective mass of Cooper pairs, the volume density of charge carriers, the temperature dependence of the penetration depth and the condensation energy. To this end, the theoretical results for disordered and anisotropic-gap superconductors are systematized. For clean anisotropic-gap superconductors we present a simple derivation of the temperature dependence of the penetration depth.

We use Feynman variational path integral method to study the effective mass of a charged particle in solids in which plasmons are an elementary excitation. This approach has an advantage as the ground state energy and the effective mass can be expressed analytically. We examine a particular case, i.e. the motion of a slow positron in metals. We find that the effective mass increases with r_s. The results are compared with those of a similar approach and of experiments. Nevertheless, the effect of the charge–plasmon interaction cannot fully account for the large positron effective mass in metals. The discrepancies are discussed.

Observation of band nonparabolicity is difficult because the electron energy in conduction band cannot be controlled widely. Using quantization energy in quantum well (QW) where the eigen energy is changed by QW thickness, nonparabolic effective mass inside a single QW of InGaAs was determined recently, up to 0.5 eV above bandedge. The dependence of effective mass on energy was analyzed and applied to calculate Landau level energy. Calculation fit well with cyclotron resonance experiments. Coupling between skew and normal cyclotron resonance was identified by this analysis.

By strictly adhering to the microscopic theory of composite fermions (CFs) for the Landau-level filling fractions ν_e=p/(2p+1), we reproduce, with remarkable accuracy, the surface-acoustic-wave (SAW)-based experimental results by Willett and co-workers concerning two-dimensional electron systems with ν_e close to ½. Our results imply that the electron band mass m_b, as distinct from the CF mass m_⋆, must undergo a substantial increase under the conditions corresponding to ν_e ≈ ½. In view of the relatively low aerial electronic densities n_e to which the underlying SAW experiments correspond, our finding conforms with the experimental results by Shashkin et al. [Phys. Rev. B 66, 073303 (2002)], concerning two-dimensional electrons in silicon, that signal sharp increase in m_b for n_e decreasing below approximately 2×10¹¹cm^-2. We further establish that a finite mean-free path ℓ₀ is essential for the observed linearity of the longitudinal conductivity σ_xx(q) as deduced from the SAW velocity shifts.

The ground state properties and the structural phase transformation of tin dioxide (SnO₂) have been investigated using first principle full potential-linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). We used local density approximation (LDA) and the generalized gradient approximation (GGA), which are based on exchange-correlation energy optimization, to optimize the internal parameters by relaxing the atomic positions in the force directions and to calculate the total energy. For band structure calculations, we utilized both the Engel-Vosko's generalized gradient approximation (EVGGA), which optimizes the exchange-correlation potential, and also GGA. From the obtained band structures, the electron (hole) valance and conduction effective masses are deduced. For compressed volumes SnO₂ is shown to undergo two structural phase transitions with increasing pressure from the rutile- to the CaCl₂-type phase at 12.4 GPa and to a cubic phase, space group at 22.1 GPa. The calculated total energy allowed us to investigate several structural properties, in particular, the equilibrium lattice constants, bulk modulus, cohesive energy, interatomic distances and the angles between different atomic bonds. In addition, we discuss the bonding parameter in term of charge density, which show the localization of charge around the anion side.

It is a fact that for ordinary metals, the electron–phonon interaction increases the quasi-particle mass, which is in contrast to the finding by Fulde et al. that, for some heavy Fermion (HF) systems, it decreases. Some experiments on HF systems suggest that there exists a strong coupling of the elastic degrees of freedom with these at the electronic and magnetic ones. To understand the effect of electron–phonon interaction on effective mass, the electron–phonon coupling mechanism in the framework of the periodic Anderson model is considered, and a simple expression is derived. This involves various model parameters namely, the position of the 4f level; the effective coupling strength, g, temperature, b; and the electron–phonon coupling strength, r. The influence of these parameters on the value of effective mass is studied, and interesting results were found. For simplicity, the numerical calculation is performed in the long wavelength limit.

In this paper some structural, magnetic and electronic properties of Zn_1-xV_xO for 0 ≤ x ≤ 0.5, such as optimized lattice constant, cohesive energy, formation enthalpy, density of states, band structure, effective mass and Fermi surface are being investigated. In calculating these properties first principle approach is being used. The calculations performed using DFT theory with full potential linear augmented plane wave (FP-LAPW) and GGA approximation. It is shown that by substituting V instead of Zn, Zn_1-xV_xO compound will gain magnetic properties. The band structure of Zn_1-xV_xO shows that metallic behavior increases with increasing substituted V. This substitution increases extremal area in Fermi surface around Γ point. The results obtained from calculated cohesive energy and formation enthalpy show that substituting V increases the stability of Zn_1-xV_xO. The calculated band gap is in a good agreement with other theoretical results.

By solving the Schrödinger equation and Poisson’s equation self-consistently, we have calculated the electronic structure for Si-doped GaAs/Al${}_x$Ga${}_{1-x}$As quantum well system at $T=100$ K in the effective mass approximation. We obtain the self-consistent potentials, eigen-envelope functions and the subband energies for different doping concentrations and for different thicknesses of the doping layer. The binding energies of exciton in GaAs/Al${}_x$Ga${}_{1-x}$As quantum wells under different doping conditions are calculated by using a variational method. And the variation of the binding energy with the thickness of the doped layer and the doping concentration is analyzed. It is found that at a given doping concentration, with the increase of thickness of the doping layer, the self-consistent potential becomes wider and more shallow, the binding energy of exciton decreases. At a given thickness of the doping layer, with the increase of the doping concentration, the self-consistent potential becomes narrower and deeper, the binding energy of exciton increases.

The carrier effective masses as well as thermoelectric and electronic properties of ternary chalcogenides compounds of the form Ag₃AuX₂(X = Se, Te) have been studied using first-principles method based on density functional theory. For the treatment of exchange-correlation energy, we have used the generalized gradient approximation (GGA) by Perdew, Burke and Ernzerhof (PBE-GGA) and Wu–Cohen (WU-GGA) schemes. Both the compounds (Ag₃AuSe₂ and Ag₃AuTe₂) are direct bandgap semiconductors. The p-type nature of these compounds is confirmed by the effective mass calculations. In thermoelectric measurements, different parameters (electrical conductivity, carrier concentration, Seebeck coefficient, thermal conductivity and thermoelectric power) are calculated. It is found that all these parameters increase with the increase in temperature for both the compounds. The obtained results for these compounds such as the direct bandgap nature and their high value of the thermoelectric power make them valuable candidates for different device applications.

We proposed the nonperturbative scheme for the calculation of the impurity spectrum in the Bose system at zero temperature. The method is based on the path-integral formulation and describes an impurity as a zero-density ideal Fermi gas interacting with Bose system for which the action is written in terms of density fluctuations. On the example of the ³He atom immersed in the liquid helium-4 a good consistency with experimental data and results of Monte Carlo simulations is shown.

We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron–electron interactions, where the wavefunction is expanded over a complete set of Luttinger–Kohn wavefunctions. We use the Luttinger–Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron–electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.

According to the first-principle method for the density functional theory (DFT), combined with the hybrid functional (HSE06), the electronic structure and effective mass of Mg-doped GaN and Mg–Fe co-doped GaN systems are calculated, and the stability of the co-doped structure is analyzed from the perspective of formation energy and phonon dispersion. The results showed that the introduction of Fe improved the characteristics of GaN:Mg system: the GaN material doped with Mg merely would cause the material’s valence band maximum to exceed the Fermi level, presenting a $p$-type conduction; the addition of Fe increased the energy band density of the system, and the insulation of the material was enhanced due to the higher energy level of the introduced impurity. Furthermore, the influence of Mg doping on the magnetic properties of GaN-based diluted magnetic semiconductor (DMS) was considered as well, with the magnetic moment obtained from co-doping Mg–Fe slightly reduced by a comparison of that of GaN:Fe measured by our research group. The results showed that the difference in the effective mass of GaN:Mg:Fe system in different directions was smaller than that of GaN:Mg system, indicating that the anisotropy of the system was reduced by doping Fe.