Improved Wigner-Brillouin Perturbation Theory Research Articles

The pinning effect in a polar semiconductor quantum dot with Gaussian confinement: A study using the improved Wigner–Brillouin perturbation theory

The effect of electron–phonon interaction on a few low-lying energy levels in a polar semiconductor quantum dot with Gaussian confinement is studied by using an improved Wigner–Brillouin perturbation theory (IWBPT). In the absence of the electron–phonon interaction, the electronic ground state plus one phonon state is degenerate with the first excited electronic state plus the zero-phonon state at some value of the confinement length. Similarly, the electronic ground state plus one phonon state is also degenerate with the second excited electronic state plus the zero-phonon state at a larger value of the confinement length. It is shown that the electron–phonon interaction lifts these degeneracies and as a result, the excited state energy levels bend downward and get pinned to the ground state plus one phonon state as the confinement frequency is increased. Our calculations are finally applied to GaAs and InSb quantum dots.

Plasmons and their interaction with electrons in trilayer graphene

The interaction between electrons and plasmons in trilayer graphene is investigated within the Overhauser approach resulting in the 'plasmaron' quasi-particle. This interaction is cast into a field theoretical problem, nd its effect on the energy spectrum is calculated using improved Wigner-Brillouin perturbation theory. The plasmaron spectrum is shifted with respect to the bare electron spectrum by $\Delta E(\mathbf{k})\sim 50\div200\,{\rm meV}$ for ABC stacked trilayer graphene and for ABA trilayer graphene by $\Delta E(\mathbf{k})\sim 30\div150\,{\rm meV}$ ($\Delta E(\mathbf{k})\sim 1\div5\,{\rm meV}$) for the hyperbolic linear) part of the spectrum. The shift in general increases with the electron concentration $n_{e}$ and electron momentum. The dispersion of plasmarons is more pronounced in \textit{ABC} stacked than in ABA tacked trilayer graphene, because of the different energy band structure and their different plasmon dispersion.

Polaronic effects on the intra-donor 1s→2p± transition energies in GaN structures

We report a calculation of the electron–phonon interaction effects on the 1s→2p± transition energies of a donor impurity present in a GaN-bulk in the presence of an external magnetic field. The energy levels are calculated through a variational method by choosing a two parameters gaussian trial wave function. The electron–LO phonon interaction is included by the Improved Wigner–Brillouin Perturbation Theory (IWBPT) as modified by Cohn, Larsen and Lax. Effects of non-parabolicity of the conduction band are also considered. In order to correctly describe the experimental data obtained by Moore et al. for GaN structures, the electron effective mass was used as a fitting parameter, and good agreement between the results was found for electron effective mass mb=0.23me. A resonant split of the 1s→2p+ transition energy is predicted to occur for magnetic field around 140T.

Cyclotron resonance of polarons in ternary mixed crystals

Rayleigh-Schrodinger perturbation theory and an improved Wigner-Brillouin perturbation theory has been used to study the cyclotron resonance of the polarons in ternary mixed crystals in the zero-temperature limit. The interaction between an electron and two branches of longitudinal optical phonon modes is taken into account in the framework of the random-element-isodisplacement model. The numerical results for several ternary mixed crystals show that the polaronic cyclotron energy and mass split successively twice related to the higher and lower branches of longitudinal optical phonon modes of ternary mixed crystals. A non-linear dependence of the polaronic cyclotron energy and mass on the composition x is found.

The pinning effect in a parabolic quantum dot

Using improved Wigner–Brillouin perturbation theory we study resonantelectron–phonon interaction in a semiconductor quantum dot. We predict pinningof the excited energy levels to the ground state level plus one opticalphonon as a function of the strength of the confinement potential. Thiseffect should be observable through optical spectroscopic measurements.

Interface Magnetopolaron in III-V Nitride Single Heterostructures

Polaronic corrections due to the electron-interface-phonon interaction in AIN/GaN single heterostructures are calculated within the improved Wigner-Brillouin perturbation theory using a dielectric continuum approach for the optical phonons, and a simplified triangular quantum well potential model for the conduction band electrons. The renormalization of the GaN electron effective mass is particularly investigated in order to be compared with cyclotron resonance measurements.

Cyclotron mass of electrons in GaN-Al xGa1-xN heterostructures

The quasi-two-dimensional electron cyclotron mass in GaN-Al xGa1<FONT FACE=Symbol>-</FONT> xN heterostructures is theoretically calculated. The shifting in Landau Levels due to the electron Longitudinal Optical phonon interaction is calculated through the Second Order Improved Wigner Brillouin Perturbation Theory (IWBPT). Experimental results recently obtained for GaN heterojunction are well described by the theory. We have also investigated the e ects of the electronic density on the Cyclotron Resonance frequency.

Magnetopolarons in quasi-one-dimensional quantum-well wires

The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons in the presense of a quantizing magnetic field is calculated. Results are detailed presented for the polaron correction to the subband energies, the polaron cyclotron mass and the polaron effective mass. The calculations are done by using different approaches, Rayleigh–Schrödinger perturbation theory, Wigner–Brillouin perturbation theory, improved Wigner–Brillouin perturbation theory and Green's function technique. In the framework of a diagrammatic approach a modified Hartree–Fock approximation is developed, which allows the calculation of the quasi-particle properties of lower-dimensional semiconductor nanostructures in the subband space. It is shown that the Rayleigh–Schrödinger perturbation theory, improved Wigner–Brillouin perturbation theory and the modified Hartree–Fock approximation well describe the ground-state renormalization, but only the improved Wigner–Brillouin perturbation theory and the modified Hartree–Fock approximation well describe the bend-over and pinning behaviour of the subbands at the boundary of the phonon continuum. Rayleigh–Schrödinger and Wigner–Brillouin perturbation theories fail for the calculation of the renormalization of the excited subband energies in quantum-well wires with strong confining potential even for vanishing magnetic field and polaron momentum. In addition to the symmetric scattering processes, which are the only processes involved in the self-energy of the old-fashioned perturbation theories, Green's function technique allows also to calculate the contribution of all asymmetric scattering processes of two electrons by exchanging an optical phonon.

An exactly solvable model for the large polaron

We present an exactly diagonalizable model Hamiltonian for the large polaron derived by analyzing the variational ansatz by Haga-Larsen (HL) for the Frohlich Hamiltonian. The lowest energy eigenvalue of the model Hamiltonian for fixed wave numbers reproduces the energy of the variational ansatz by Haga-Larsen and is, therefore, an upper bound with respect to the corresponding energy eigenvalue of the Frohlich Hamiltonian. This is valid for any momentum which is proven by extending the Haga-Larsen approach. Furthermore, since all integrations can be performed analytically, the model Hamiltonian is easily tractable. The energy eigenvalue spectrum of the model Hamiltonian is studied below and above the phonon-emission threshold. The quality of the model Hamiltonian is determined by the variational ansatz of Haga and Larsen. Incorporating an improved energy-momentum relation, a generalized model Hamiltonian is derived possessing a larger validity range with respect to the coupling strength. Furthermore, a second exactly diagonalizable model Hamiltonian based on improved Wigner-Brillouin perturbation theory due to Warmenbol, Peeters, and Devreese (WPD) is presented. It is briefly demonstrated that one is able to construct all mentioned model Hamiltonians also in the 2D polaron problem. In contrast to the 3D case, where the HL-type model Hamiltonian possesses the higher quality for any momentum, in the 2D case, it works well only for small momenta. For large momenta, only the WPD-type model Hamiltonian describes the energy-momentum relation correctly. We demonstrate the usefulness of the model Hamiltonian concept by exactly calculating the one-electron Green’s function for all mentioned model Hamiltonians and comment why significant advantages of the model Hamilton concept for the treating of low-dimensional systems (planar semiconducting quantum-well structures) can be expected.

Influence of the electron-electron and electron-phonon interaction on the cyclotron resonance of 2DEG in GaAs

The resonant polaron effect was investigated for cyclotron transitions N → N + 1 in magnetic field regimes where the Landau levels N = 2 and 3 cross with the level N = 0 plus one bulk longitudinal optical phonon. The experiment is analyzed in the framework of the improved Wigner-Brillouin perturbation theory taking into account band-coupling phenomena, a finite thickness of the inversion layer in the growth direction, and coupling of the cyclotron transitions due to electron-electron interactions. From the cyclotron mass enhancements, a Fröhlich coupling constant α = 0.06 to 0.07 was obtained.

Energy-momentum relation for polarons in quantum-well wires

The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons is calculated. Results are presented for the polaron correction to the electric subbands and the polaron effective mass. Using improved Wigner-Brillouin perturbation theory, we have investigated in detail the energy-momentum relation for quasi-one-dimensional polarons. It is shown that the dispersion curves of all subbands bend over and are pinned at the phonon continuum above the renormalized ground state. This should result in a spatial oscillation of the electron group velocity in real quantum-well wires.

Energy-momentum relation for polarons in quantum-well wires

The static and dynamical properties of electrons confined in quantum-well-wire structures are modified because of the interaction with unconfined phonon modes. The interaction with virtual phonons leads to a mass renormalization, a binding energy, and a nonparabolic energy-momentum relation. Using the improved Wigner-Brillouin perturbation theory, we have investigated the energy-momentum relation for electrons confined in rectangular quantum-well wires of GaAs surrounded by ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As, as a function of the transverse sizes of the wire. There is observed a significant energy lowering when the electron momentum k approaches ${k}_{\mathrm{LO}}$, and this bending over of the dispersion curve increases when the electron confinement is enhanced.