京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20551号 / 理博第4309号 / 新制||理||1619(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 北川 宏, 教授 竹腰 清乃理, 教授 吉村 一良 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

No description available.

Density Functional Theory (DFT) was used to study fundamental characteristics of electrides. Electronic structure calculations were performed with the generalized gradient approximation (GGA) and GGA+U (U- “on-site" electron-electron repulsion). Fundamental properties of Y2C were investigated in the first project. The nature of strongly localized anionic electrons in Y2C was demonstrated using the distribution of charge density. Magnetic properties were analyzed with magnetization density and magnetic anisotropy energies. The magnetic anisotropy of Y2C originates from anionic electrons at interlayer spaces. The predicted work functions are in good agreement with reported experimental data. We also investigated the enhancement of magnetic properties by varying the degree of localization of anionic electrons. The exchange splitting of interstitial electrons is more prominent than that of d-orbitals of Y and exchange splitting increases with decreasing c-axis parameter. In the second study, fundamental properties of Gd2C are discussed. The GGA+U method was applied for 4f states of Gd and predicted the best U value. Our model predicted Gd2C has a layered-hexagonal structure. Local density of states (LDOS) and projected density of states (PDOS) were analyzed for understanding of anionic electrons and atoms on magnetic and electronic properties. The Curie temperatures of Gd and Gd2C were calculated and noticed that interactions in Gd2C are influential to increase the Curie temperature. The chemical formula can be written as [Gd2C]1.9.1.9e- from charge analysis. Additionally, fundamental properties of two ionized states, Q=+1 and Q=+2 were studied. Results indicate anionic electrons at interlayer spaces will initiate the ejecting of electrons. Density functional perturbation theory (DFPT) with DFT under the harmonic approximations was applied to study the structural stabilities, phase transitions and variation of thermodynamic quantities at finite temperature of two phases of Hf2S. Phonon dispersion curves without any imaginary frequencies are evidence for stability of two phases. The resulting quadratic flexural phonon branch indicates Hf2S has 2D characteristics. At T= 0 K the Helmholtz free energy of anti- NbS2 structure of Hf2S lies ≈23 kJ/f.u. below that of the higher energy phase. The critical temperature for the phase transition was estimated, and the effect of finite temperature on thermodynamics quantities were studied.

Phase transitions are critical in understanding the properties of different phases of matter, and their identification is an essential research focus in condensed matter physics. However, defining phase transitions for topological systems is more complex than for common mesoscale materials. This complexity is further compounded when disorders are present in the system. In this thesis work, we provide a comprehensive review of machine learning, topological insulators, and the conventional approach to classifying different topological phases. We focus on the Benalcazar, Bernevig, and Hughes (BBH) model, a higher-order topological insulator model, and investigate the challenges of identifying phase transitions in topological systems, particularly in the presence of disorders. To overcome these challenges, we implement the diffusion maps method, which accurately predicts the same transition points as traditional numerical calculations for both clean and disordered systems. Moreover, we demonstrate the efficacy of the diffusion maps method in predicting the transition point for the topological Anderson insulator. Our findings suggest that this approach has the potential to be generalized and applied to a broader range of disordered systems. Overall, this thesis work provides a novel method for identifying phase transition points in topological systems, which could have significant implications for the design and development of future topological materials.

In this thesis we study the scaling properties of unconventional metals that arise at quantum critical points using low-energy effective field theories. Due to high rate of scatterings between electrons and critical fluctuations of the order parameter associated with spontaneous symmetry breaking, Landau’s Fermi liquid theory breaks down at the critical points. The theories that describe these critical points generally flow into strong coupling regimes at low energy in two space dimensions. Here we develop and utilize renormalization group methods that are suitable for the interacting non-Fermi liquids. We focus on the critical points arising at excitonic, and commensurate spin and charge density wave transitions. By controlled analyses we find stable non-Fermi liquid and marginal Fermi liquid states, and extract the scaling behaviour. The field theories for the non-Fermi liquids are characterized by symmetry groups, local curvature of the Fermi surface, the dispersion of the order parameter fluctuations, and dimensions of space and Fermi surface. / Thesis / Doctor of Philosophy (PhD)

No description available.

No description available.

No description available.

This thesis explores the effects singularities have on stationary and dynamical properties of many-body quantum systems. In papers I and II we find that the ground state suffers a Z2 symmetry breaking phase transition (PT) when a single impurity is added to a Bose-Einstein condensate (BEC) in a double well (bosonic Josephson junction). The PT occurs for a certain value of the BEC-impurity interaction energy, Λc . A result of the PT is the mean-field dynamics undergo chaotic motion in phase space once the symmetry is broken. We determine the critical scaling exponents that characterize the divergence of the correlation length and fidelity susceptibility at the PT, finding that the BEC-impurity system belongs to the same universality class as the Dicke and Lipkin-Meshkov-Glick models (which also describe symmetry breaking PTs in systems of bosons). In paper III we study the dynamics of a generic two-mode quantum field following a quench where one of the terms in the Hamiltonian is flashed on and off. This model is relevant to BECs in double wells as well as other simple many-particle systems found in quantum optics and optomechanics. We find that when plotted in Fock-space plus time, the semiclassical wave function develops prominent cusp-shaped structures after the quench. These structures are singular in the classical limit and we identify them as catastrophes (as described by the Thom-Arnold catastrophe theory) and show that they arise from the coalescence of classical (mean-field) trajectories in a path integral description. Furthermore, close to the cusp the wave function obeys a remarkable set of scaling relations signifying these structures as examples of universality in quantum dynamics. Within the cusp we find a network of vortex-antivortex pairs which are phase singularities caused by interference. When the mean-field Hamiltonian displays a Z2 symmetry breaking PT modelled by the Landau theory of PTs we calculate scaling exponents describing how the separation distance between the members of each pair diverges as the PT is approached. We also find that the cusp becomes infinitely stretched out at the PT due to critical slowing down. In paper IV we investigate in greater detail the morphology of the vortex network found within cusp catastrophes in many-body wave functions following a quench. In contrast to the cusp catastrophes studied so far in the literature, these structures live in Fock space which is fundamentally granular. As such, these cusps represent a new iii type of catastrophe, which we term a ‘quantum catastrophe’. The granularity of Fock space introduces a new length scale, the quantum length lq = N −1 which effectively removes the vortex cores. Nevertheless, a subset of the vortices persist as phase singularities as can be shown by integrating the phase of the wave function around circuits in Fock-space plus time. Whether or not the vortices survive in a quantum catastrophe is governed by the separation of the vortex-antivortex pairs lv ∝ N −3/4 in comparison to lq , i.e. they survive if lv lq . When particle numbers are reached such that lq ≈ lv the vortices annihilate in pairs. / Thesis / Doctor of Philosophy (PhD)

We study the phase diagram of an interacting lattice gas of two species of particles and holes, driven out of equilibrium by a local hopping bias (denoted by `E'). Particles interact by excluded volume and nearest-neighbor attractions. We present a detailed Monte Carlo investigation of the phase diagram. Three phases are found, with a homogenous phase at high temperatures and two distinct ordered phases at lower temperatures. Which ordered phase is observed depends on the parameter f, which controls the ratio of the two types of particles. At small f, there is nearly a single species, and a transition is observed into a KLS-type ordered phase. At larger f, the minority species are sufficiently dense to form a transverse blockage, and a sequence of two transitions are observed as the temperature is lowered. First, a continuous boundary is crossed into an SHZ-type ordered phase, then at a lower temperature a first-order boundary is crossed into the KLS-type ordered phase. At some critical value of f is a bicritical point, where the first-order line branches from the two continuous boundaries. We also consider correlations in the homogenous phase, by constructing a continuum description and comparing to the results of simulations. Long range correlations are present in both the theoretical results and the simulations, though certain details of the theory do not fit the observations very well. Finally, we examine the beahvior of three-point correlations in the single-species (KLS) limit. Nontrivial three-point correlations are directly related to the nonzero bias E. We therefore consider the behavior of the three-point correlations as a function of E. We find that the three-point signal saturates very rapidly with E. There are some difficulties interpreting the data at small E. / Ph. D.