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No description available.

Th.--Sci. phys.--Grenoble 1, 1984. N°: 127.

A detailed experimental study has been made of the spin-splitting factors ℊc for magnetic Landau levels associated with conduction electrons in extremal orbits on the Fermi surface of lead. This information has been derived from the waveform of the de Haas-van Alphen (dHvA) quantum oscillations in the magnetization of single-crystal lead spheres at temperatures of about 1.2 K and with applied magnetic fields in the range 50-75 kG. A commercial spectrum analyzer has been used to provide on-line values of the harmonic amplitudes in the dHvA waveform, and the values of ℊc have been extracted from the relative strengths of the harmonics. Serious systematic errors in ℊc can arise on account of waveform distortions caused by the small and subtle difference between the externally applied field H and the magnetizing field B acting on the conduction electrons. In 1981 Gold and Van Schyndel demonstrated that these 'magnetic-interaction' distortions could be suppressed to a large extent by using negative magnetic feedback to make the induction B within the sample be the same as H (or very nearly so). This thesis describes the first in-depth application of the magnetic-feedback technique to the systematic study of any metal. Particular attention has been paid to the effect of sample inhomogeneity, and Shoenberg's treatment of the magnetic interaction in a non-uniform sample has been generalized to include magnetic feedback. This theory accounts well for many features in the experimental data, especially those which remained a puzzle in the earlier work of Gold and Van Schyndel. Experimental ℊc values are given for the first time for most of the extremal orbits on the lead Fermi surface and for high-symmetry directions of the magnetic field. Indeed these are the most detailed data reported for any polyvalent metal. The ℊc factors for the different orbits and field directions are found to span the range from 0.56 to 1.147. These large net deviations from the free-electron value ℊ₀ = 2.0023 are consequences of the strong spin-orbit and electron-phonon interactions, and an attempt has been made to separate these two contributions to the ℊ-shifts. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Electron-phonon interactions (EPIs) are ubiquitous in condensed matter physics and materials science. They are crucial for understanding numerous phenomena, including conventional superconductivity, charge-transport and, most pertinent for this thesis, polaron formation. A polaron is a charge carrier (electron or hole) dressed with a “cloud” of phonons. The polaronic quasiparticle may have vastly different ground- and excited-state properties from that of the bare, constituent charge carrier. While polarons are well-studied and largely understood in canonical model Hamiltonians, recent advances have made it possible to study more complex, fully ab initio systems. Here, the numerically exact methods which are available for some model systems become much more challenging to apply, so accurate approximate methods are a necessity. In this dissertation, we present several advancements in approximate but accurate methods for different polaronic problems and polaron observables. With respect to polaron dynamics, we focus on low-scaling methods to produce wave vector-dependent single-particle spectral function. We present a thorough study of the accuracy of the second- and fourth-order cumulant expansions (CE) of the electronic Green’s function by comparing them against numerically-exact reference data for the one-dimensional Holstein model. We find that the second-order CE is accurate at zero electronic-momentum across a wide range of temperatures, while for non-zero electronic momenta, the CE is only accurate at high-temperatures. The fourth-order cumulant expansion improves on the dynamics at short times and can improve the spectra; however, it can also introduce non-physical divergences and negative spectral weight. The second-order cumulant expansion is thus a useful tool for determining spectral functions in some instances. However, increasing the order of the CE introduces pathologies that may persist at arbitrarily high-order. As an alternate approach to improving the CE, we introduce a new self-consistent cumulant expansion (SC-CE) which remedies many of the deficits of the CE. We compare the results for this new approximation against those from the second-order cumulant expansion as well as reference data for the one-dimensional Holstein model. Unlike the CE, the SC-CE can produce accurate spectra across the entire Brillouin-zone, and captures non-perturbative features excellently. The trade-off for this increased accuracy is the introduction of some degree of negative spectral-weight and the potential for rapid divergences in time in some instances. We find that these problems can be minimized, but not completely eliminated in the thermodynamic limit and in more realistic cases where phonon dispersion exists. We also demonstrate how the SC-CE fits into the greater scheme of Green’s function methods which approximate the self-energy non-diagrammatically as has recently been proposed by Pandey and Littlewood, and we note the potential applications of the SC-CE both in ab initio polaron problems and in general many-body problems. We finally consider a new method to determine the ground-state structure of the polaron in ab initio materials, a topic which has only recently appeared in the literature. We present a new all-coupling variational method based on the Nagy-Markoš variational ansatz for the Fröhlich model. The ansatz is a projected unitary transform which naturally interpolates between the weak-coupling (Lee-Low-Pines) ansatz and the strong-coupling adiabatic ansatz by modulating the momentum conservation of the electron-phonon scattering processes. We demonstrate our ab initio Nagy-Markoš ansatz on the Holstein model and the Fröhlich model, and show that it always improves upon the better of the weak or strong coupling result. We consider the ab initio case of lithium fluoride (LiF), and find that the ansatz provides accurate polaron binding energies for both the hole-polaron and the electron-polaron which are classical cases of small and large polarons, respectively. We note how our flexible variational ansatz is an ideal starting point for perturbative energy corrections and cumulant Green’s function methods. Future developments and applications of the efficient methodologies presented in this dissertation may enable quantitative calculations of polarons in large-intermediately coupled ab initio systems, such as the lead-halide perovskites and other systems where it has hitherto been difficult to fully understand the effects of the electron-phonon interactions.

Investigamos os efeitos de tamanho e do potencial de confinamento finito V0 nas taxas de espalhamento de absorção e de emissão de elétrons interagindo com os fônons longitudinais ópticos (fônons LO) de um fio quântico cilíndrico de GaAs à temperatura ambiente. Calculamos as taxas de espalhamento inter e intra-sub-banda e a taxa de espalhamento total para uma temperatura de 300 K, pois nesta temperatura o mecanismo de espalhamento dominante em semicondutores do tipo III-V é aquele devido aos fônons LO. Qualitativamente a taxa de emissão intra-sub-banda neste sistema tem o mesmo comportamento da sua correspondente em estruturas 2D. Para a absorção encontramos uma mudança suave de comportamento da taxa de absorção intra-sub-banda quando o raio do fio é da ordem do diâmetro do polaron (ou seja, da ordem de 80 ANGSTROM). Para raios pequenos ela tem um comportamento similar ao do bulk, mas para raios maiores ela cresce até atingir um máximo e depois cai monotonicamente à medida que aumentamos a energia do portador. Vimos que, o tamanho do fio e o potencial de confinamento têm grande influência na taxa de espalhamento total. / We investigated the size effects and the effects of the finite confining potential V0 on the absorption and emission scattering rates of electron interacting with longitudinal optical (LO) phonons for a cylindrical GaAs quantum wire. We calculated the inter and intrasubband total scattering rate for a temperature of 300K, because in this temperature the dominant mechanism of scattering in semiconductors III-V is that due LO phonons. Qualitatively the intrasubband emission scattering rate in this system has the same behavior of the correspondent in 2D structures. For absorption we found a smooth change in the intrasubband absorption scattering rate behavior when the radius the wire is near the polaron diameter (ie, about 80 ANGSTROM). For small radius the scattering rate has a similar behavior as that of the bulk, but for large radius it increases until reach a maximum and after ir drops monotonicaly with increase of carrier energy. We found that the size effect and the confining potential have a large influence in the total scattering rate

In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Padé–resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin–boson model, and non-crossing approximations (NCA) for the Anderson–Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin–boson model. I propose well–defined criteria for assessing the accuracy of Padé-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Padé approximation is reliable. I continue the investigation of spin–boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin–boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system–bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. Finally, I investigate the dynamical interplay between the electron–electron interaction and the electron–phonon coupling within the Anderson–Holstein model via two complementary NCAs: the first is constructed around the weak-coupling limit and the second around the polaron limit. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. I find the two NCAs disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The complementary frameworks used here pave the way for numerically exact methods based on inchworm dQMC algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.