Band structures of ultrathin films of heavy elements, £\-Sn and Sb, were investigated using first-principle calculations with the inclusion of spin-orbit coupling. The band structures were gradually varied as the physical parameters were adjusted. The band inversion was obtained at the high symmetry point in Brillouin zone, making a topological phase transition. In this study, the band inversion at £F point of the Brillouin zone was predicted in single bi-layer of Sb(111) and single bi-layer and two bi-layers of £\-Sn(111). The topological phase transition is from trivial insulator to topological insulator for single bi-layer of Sb(111). Finally, the topological phase transition is from trivial semi-metal to topological semi-metal for single bi-layer of £\-Sn(111), whereas as it is from topological semi-metal to trivial metal for two bi-layers of £\-Sn(111).

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22824号 / 理博第4634号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 高橋 義朗, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20889号 / 理博第4341号 / 新制||理||1623(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 佐藤 昌利 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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.

From its beginning in the early 20th century, quantum theory has become progressively more important especially due to its contributions to the development of technologies. Quantum mechanics is crucial for current technology such as semiconductors, and also holds promise for future technologies such as superconductors and quantum computing. Despite of the success of quantum theory, its applications have been mostly limited to equilibrium or static systems due to 1. lack of experimental controllability of non-equilibrium quantum systems 2. lack of theoretical frameworks to understand non-equilibrium dynamics. Consequently, physicists have not yet discovered too many interesting phenomena in non-equilibrium quantum systems from both theoretical and experimental point of view and thus, non-equilibrium quantum physics did not attract too much attentions. / Physics

Motivated by the recent experimental progress in the search for Majorana fermions, we identify signatures of topological superconductivity and propose realistic experiments to observe these signatures. In the first part of this thesis, we study charge transport through a topological superconductor with a pair of Majorana end states, coupled to leads via quantum dots with resonant levels. The nonlocality of the Majorana bound states opens the possibility of Cooper pair splitting with nonlocal shot noise. In the space of quantum dot energy levels, we find a characteristic four-peaked cloverlike pattern for the strength of noise due to Cooper pair splitting, distinct from the single ellipsoidal peak found in the absence of Majorana end states. Semiconductor-superconductor hybrid systems are promising candidates for the realiza- tion Majorana fermions and topological order in solid state devices. In the second part, we show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the ex- citation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic h/e magnetic flux periodicity in the nontrivial phase. The transition between the trivial and nontrivial phase is reflected in the closing and reopening of an excitation gap. In the third part, we investigate characteristic features in the spin response of doped three-dimensional topological insulators with odd-parity unequal-spin superconducting pairing, which are predicted to have gapless Majorana surface modes. These Majorana modes contribute to the spin response, giving rise to a characteristic temperature behavior of the Knight shift and the spin-lattice relaxation time in magnetic resonance experiments.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18779号 / 理博第4037号 / 新制||理||1581(附属図書館) / 31730 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 佐々 真一, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20163号 / 理博第4248号 / 新制||理||1611(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 高橋 義朗, 准教授 柳瀬 陽一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The quantum Spin Hall Insulator (QSHI) is a two-dimensional variant of a novel class of materials characterized by topological order, whose unique properties have recently triggered much interest and excitement in the condensed matter community. Most notably, the topological properties of these systems hold great promise in mitigating the difficult problem of decoherence in implementations of quantum computers. Although QSHI has been theoretically predicted in a few different materials, prior to the work presented in this thesis, only the HgTe/CdTe semiconductor system has shown direct evidence for the existence of this phase. Ideally insulating in the bulk, QSHI is characterized by one-dimensional channels at the sample perimeter, which have a helical property, with carrier spin tied to the carrier direction of motion, and protected from elastic back-scattering by time-reversal symmetry. In this thesis we present low temperature transport measurements, showing strong evidence for the existence of proposed helical edge channels in InAs/CaSb quantum wells, which thus emerge as an important alternate to HgTe/CdTe quantum wells in studies of two-dimensional topological insulators and superconductors. Surprisingly, edge modes persist in spite of comparable bulk conduction of non-trivial origin and show only weak dependence on magnetic field in mesoscopic devices. We elucidate that the seeming independence of edge on bulk transport comes due to the disparity in Fermi wave-vectors between the bulk and the edge, leading to a total internal reflection of the edge modes. Furthermore, low Schottky barrier of this material system and good interface to superconductors allows us to probe topological properties of helical channels in Andreev reflection measurements, opening a promising route towards the realization of topologically superconducting phases hosting exotic Majorana modes.

We study the possibility of constructing quantum gates using topological phases, which originate from local SU(2) evolution of entangled multiqubit systems. For this purpose, logical codewords using two-, three- and nine-qubit entangled states are defined and possible implementations of topological gates on these codes, are examined. For two-qubit systems, it is shown that for only two of the Pauli gates, a topological implementation is possible, the third must be non-topological. Furthermore, it is shown that a topological implementation of Hadamard gate is also possible on the two-qubit code. For the three-qubit code, the logical Pauli gates are found to be topologically implementable and a topological implementation of the logical S gate seems to be possible as well. Lastly, for the nine-qubit code, the logical Pauli gates, the logical S gate and the logical T gate are shown to be implementable topologically on the code. It remains an open question whether topological implementation of logical Hadamard gate by invertible local operators is possible on the nine-qubit code.