archives@tulane.edu / The discovery of topological semimetals has attracted enormous interest since they not only possess many unusual exotic properties, but also offer a fertile ground for searching for new fermions in the low energy spectrum. The first established example of a topological state of matter is the quantum Hall effect, which supports a gapless edge state protected by topological invariance. Later the concept of topology has been extended to describe electronic band structure of solid state materials and this effort leads to discoveries of many new topological quantum states, such as Dirac cone state in graphene, quantum spin Hall insulator states in semiconductor quantum wells, 3D topological insulators, etc. The recently discovered Dirac/Weyl semimetals can be viewed as a 3D analog of graphene. This thesis work aims to discover new Dirac/Weyl semimetals through single crystal synthesis and characterization. This thesis is organized as follows: In chapter 1, I will first briefly review several basic concepts of topological properties and introduce a few prototype topological semimetals related to my thesis work. Since one important part of my thesis work involves single crystal growth of topological semimetals, I will introduce the crystal growth methods used in my research in chapter 2. In chapters 3, 4 and 5, I will present my experimental discoveries of new topological semimetals, including YSn2, CaSn3 and TbPtBi. I will not only show property characterization of these material, but also discuss their underlying physics. For YSn2, my work reveals that its slightly distorted square lattice of Sn generates multiple topologically non-trivial bands, one of which likely hosts nodal line and tunable Weyl semimetal state induced by the Rashba spin-orbit coupling (SOC) and proper external magnetic field. The quasiparticles described as relativistic fermions from these bands are manifested by nearly zero mass, and non-trivial Berry phases probed in de Haas–van Alphen (dHvA) oscillations. The dHvA study also reveals YSn2 has a complex Fermi surface (FS), consisting of several 3D and one 2D pocket. Our first principle calculations show the point-like 3D pocket at Y point on the Brillouin zone boundary hosts the possible Weyl state. Our findings establish YSn2 as a new interesting platform for observing novel topological phases and studying their underlying physics. In the study of CaSn3, we not only found it possesses non-trivial band topology, but also discovered its intrinsic superconductivity at 1.178 K. Its topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the dHvA quantum oscillation studies of this material. Our findings make CaSn3 a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g., topological superconductivity. For the Half-Heusler compound TbPtBi, we have studied its field-induced Weyl semimetal state. We have observed remarkable transport signatures of its Weyl state, including the chiral anomaly, intrinsic anomalous Hall effect (AHE), and in-plane Hall effect. Moreover, we found TbPtBi exhibits a much larger AHE than the previously reported field-induced Weyl semimetal state in GdPtBi. The distinct aspect of TbPtBi is that Tb ions carry greater magnetic moments than Gd ions in GdPtBi (9.0B/Tb vs.7.0B/Gd). We find that such a moment increase in TbPtBi drastically enhances its AHE, with its anomalous Hall angle reaching as large as 0.50-0.76 in its antiferromagnetic (AFM) state. This finding not only strongly supports that the Zeeman effect due to the large exchange field from 4f electrons plays a critical role in creating the field-included Weyl state, but also provides clear evidence for the theoretical prediction that the intrinsic anomalous Hall conductivity is proportional to the separation of the Weyl points with opposite chirality. / 1 / Yanglin Zhu

<p>Scientific progress often relies on unexpected discoveries and unique observations. In</p> <p>fact, many of the most groundbreaking scientific advances throughout history have been the</p> <p>result of serendipitous events. For instance, the discovery of penicillin by Alexander Fleming</p> <p>was a result of him noticing a mold growing on a petri dish that was contaminating his</p> <p>bacterial culture. Similarly, the discovery of the cosmic microwave background radiation,</p> <p>which is considered one of the strongest pieces of evidence for the Big Bang theory, was</p> <p>the result of two scientists accidentally stumbling upon it while conducting a completely</p> <p>different experiment. These types of unexpected discoveries can lead to new avenues of</p> <p>research and open up entirely new fields of study. During my PhD, I experienced a similar</p> <p>phenomenon when I stumbled upon an anomaly in my experimental data that led me down a</p> <p>completely new path of investigation. This unexpected discovery not only provided me with</p> <p>new insights into the underlying mechanisms of my research, but also opened new avenues for</p> <p>future research directions. It was a reminder that sometimes the greatest scientific progress</p> <p>can come from the most unexpected places.</p> <p>My primary focus was initially directed towards topological superconductivity. However,</p> <p>this research direction was modified by unexpected findings while characterizing a SQUID.</p> <p>Specifically, a unique response by a Josephson junction was observed when exposed to an inplane</p> <p>magnetic field. Chapter 1 details our experimental results on the SQUID. We observed</p> <p>intriguing effects resulting from the in-plane magnetic field in the asymmetric evolution of</p> <p>the Fraunhofer pattern suggesting the existence of additional underlying physics in the heterostructure,</p> <p>which may have been previously overlooked. This serendipitous finding served</p> <p>as the impetus to explore simpler superconducting devices such as nanowires and rings.</p> <p>Remarkably, subsequent investigations into the critical current of a superconducting ring revealed</p> <p>a bi-modal histogram arising from the application of an in-plane magnetic field, which</p> <p>was an unforeseen outcome. This adds to our observations made in chapter 1. Chapter 2 details</p> <p>the unique properties of Al-InAs superconducting rings. Further experiments involving</p> <p>a superconducting nanowire resulted in the observation of non-reciprocal critical current under</p> <p>an in-plane magnetic field perpendicular to the current direction, subsequently referred to as the superconducting diode effect. Chapter 3 delves into the non-reciprocal properties</p> <p>of an Al-InAs superconducting nanowire. Our findings revealed the diamagnetic source of</p> <p>non-reciprocity generic to multi-layer superconductors. Finally, chapter 4 provides a detailed</p> <p>account of the fabrication processes for the superconducting devices, along with a discussion</p> <p>of the measurement techniques employed to unveil the underlying physics.</p>

We perform microscopic mean-field studies of topological order in a two-dimensional topological superconductor in the Bogoliubov-de Gennes (BdG) formalism. By adopting a two-dimensional s-wave topological superconductivity (TSC) model on a minimal tight-binding system, we solve the BdG equations self-consistently to obtain not only the superconducting order parameter, but also the Hartree potential. By computing the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) number and investigating the bulk-boundary correspondence, we study the nature of Abelian and non-Abelian TSC in terms of self-consistent solutions to the BdG equations. In particular, we examine the effects of temperature and a single non-magnetic impurity deposited in the centre of the system and how they vary depending on topology. We find that the non-Abelian phase exhibits signs of unconventional superconductivity, and by examining the behaviour of this phase under both low and high Zeeman field conditions, we show that the magnitude of the Zeeman field largely dictates the susceptibility of the system to temperature. Furthermore, we investigate the possible interplay of charge density waves (CDW) and TSC. By self-consistently solving for the mean fields, we show that TSC and topological CDW are degenerate ground states---with the same excitation spectrum in the presence of surfaces---and thus can coexist in the Abelian phase. The effects of a non-magnetic impurity, which tends to pin the phase of charge density modulations, are examined in the context of topological CDW.

Neste trabalho investigamos a fusão entre estados ligados de Majorana em nanoestruturas compostas por um ponto quântico conectado a contatos metálicos e acoplado lateralmente a dois fios quânticos supercondutores que sustentam modos de Majorana em suas pontas. Modelando cada fio quântico por uma cadeia de Kitaev, nós adotamos duas abordagens: inicialmente usando as funções de Green do ponto obtidas através do método recursivo calculamos a condutância e a densidade local de estados (LDOS), posteriormente diagonalizamos o sistema no formalismo de Bogoliubov-de Gennes (BdG) e obtemos o espectro completo dos autoestados. Como descrito em (1), o LDOS do ponto quântico acoplado a uma única cadeia de Kitaev mostra claramente o vazamento do modo de Majorana inicialmente presente na ponta da cadeia para o ponto quântico, onde este modo surge fixo na energia de Fermi dos contatos metálicos (&epsilon;&fnof;). A condutância de dois terminais medida através do ponto mostra uma assinatura dos estados de Majorana neste sistema, uma ressonância fixa mesmo quando o nível do ponto está vazio ou não. Interessante ressaltar que mesmo na presença de interações no ponto essa assinatura de Majorana é válida como mostrado em (2). Motivados por estes resultados anteriores estamos particularmente interessados em investigar a hibridização (aqui denominada de fusão) entre dois modos de Majorana resultando em um modo fermiônicos ordinário dentro do ponto quântico. Nossos resultados demonstram que controlando a diferença de fase supercondutora entre os fios e a voltagem de gate do ponto quântico somos capazes de controlar a emergência e fusão dos modos de Majorana. Além disso nós reforçamos a proposta de se utilizar o efeito Josephson a.c. de período 4&pi; para identificar os modos de Majorana pela reprodução dos resultados obtidos por (3). / In this work we investigate the fusion between Majorana bound states in nanostructures composed of a quantum dot connected to source and drain leads and side coupled to two topological superconducting nanowires sustaining Majorana end modes. Modeling the nanowire via a Kitaev chain, we have used two approaches: first using a recursive Greensfunction approach we calculate the conductance and local density of states (LDOS) and then by the diagonalization using the Bogoliubov-de Gennes (BdG) formalism we obtain the full spectrum of eigenstates. As described in (1) the LDOS of quantum dot coupled to a single wire clearly shows a leakage of the Majorana end mode from the wire into the dot, where it emerges as a unique dot level pinned to the Fermi energy of the leads (&epsilon;&fnof;). The calculated two-terminal conductance through the dot displays an unambiguous signature of the Majorana bound states, i. e., a pinned resonance occurring even when the dot level is far above &epsilon;&fnof; . Interestingly this Majorana signature remains even in the presence of interactions within the dot as showed in (2). Motivated by these earlier results we are particularly interested to investigate the fusion of Majonana end modes into ordinary fermionic modes within the dot. Our results demonstrate that by tuning the superconducting phase difference between the wires and the quantum-dot gate voltage we are able to control the emergence and splitting of Majorana modes. Furthermore we reinforce the proposal of using the 4&pi; periodic a.c Josephson effect to identify Majorana modes by reproducing the results obtained by (3).

<div>The quantum phase transitions and exotic excitations are exciting and important topics of nowadays condensed matter theory. Topologically protected excitations are of great interest for potential applications in quantum computing. This Thesis explores two examples of exotic topologically protected excitations, Majorana fermions and parafermions in hybrid superconductor/semiconductor systems.</div><div><br></div><div>In the first part of the thesis, after a brief review of ideas on Majorana zero modes in solid state systems obtained by researchers over the past decade, I present our study of the emergence of Majorana fermions in charge carrier holes doped quantum wires. Study of Majorana modes in this system requires understanding Luttinger holes in low dimensions, which is also crucial for numerous spin-dependent phenomena, emerging field of spintronics and nanotechnology. We find that hole-doped quantum wires that are proximity coupled to a conventional s-wave superconductor is a promising system for the observation of Majorana fermions. We advanced understanding of Luttinger holes in quantum wells and quantum wires. We have shown that the vast majority of earlier treatments of Luttinger holes ignored an important effect, a mutual transformation of heavy and light holes at the heteroboundaries. We have derived the effective hole Hamiltonians in the ground size-quantized sub-bands of quantum wells and quantum wires. The effect of mutual transformation of holes is crucial for understanding Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole-doped quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems and show that GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, providing additional opportunities for its control compared to intensively studies InSb and InAs electron systems.</div><div><br></div><div>In the second part of the thesis, I first introduce the basic facts of the current theoretical understanding of the fractional quantum Hall effect and a theoretical model of parafermion excitations. Parafermion zero modes are promising for universal quantum computing. However, physical systems that are predicted to host these exotic excitations are rare and difficult to realize in experiments. I present our work on modeling domain walls on the boundary between gate-induced polarized and unpolarized domains of the fractional quantum Hall effect system near the spin transitions, and the emergence of the parafermion zero modes when such domain wall is proximity coupled to an s-wave superconductor. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves formation of the counter-propagating edge states with different spin polarizations at the boundaries between areas of the electron liquid in polarized and unpolarized filling factor $\nu=2/3$ phases. By analytical and numerical methods we find the conditions for emergence of parafermion zero modes in hybrid fractional quantum Hall/s-wave superconductor system. The phase diagram indicates that the parafermionic phase, which is represented by the six-fold ground state degeneracy, is separated from other phases by a topological phase transition. Such parafermion modes are experimentally feasible. They present a vital step toward the realization of Fibonacci anyons that allow a full universal set of quantum operations with topologically protected quasiparticles.</div><div><br></div>

Neste trabalho investigamos a fusão entre estados ligados de Majorana em nanoestruturas compostas por um ponto quântico conectado a contatos metálicos e acoplado lateralmente a dois fios quânticos supercondutores que sustentam modos de Majorana em suas pontas. Modelando cada fio quântico por uma cadeia de Kitaev, nós adotamos duas abordagens: inicialmente usando as funções de Green do ponto obtidas através do método recursivo calculamos a condutância e a densidade local de estados (LDOS), posteriormente diagonalizamos o sistema no formalismo de Bogoliubov-de Gennes (BdG) e obtemos o espectro completo dos autoestados. Como descrito em (1), o LDOS do ponto quântico acoplado a uma única cadeia de Kitaev mostra claramente o vazamento do modo de Majorana inicialmente presente na ponta da cadeia para o ponto quântico, onde este modo surge fixo na energia de Fermi dos contatos metálicos (&epsilon;&fnof;). A condutância de dois terminais medida através do ponto mostra uma assinatura dos estados de Majorana neste sistema, uma ressonância fixa mesmo quando o nível do ponto está vazio ou não. Interessante ressaltar que mesmo na presença de interações no ponto essa assinatura de Majorana é válida como mostrado em (2). Motivados por estes resultados anteriores estamos particularmente interessados em investigar a hibridização (aqui denominada de fusão) entre dois modos de Majorana resultando em um modo fermiônicos ordinário dentro do ponto quântico. Nossos resultados demonstram que controlando a diferença de fase supercondutora entre os fios e a voltagem de gate do ponto quântico somos capazes de controlar a emergência e fusão dos modos de Majorana. Além disso nós reforçamos a proposta de se utilizar o efeito Josephson a.c. de período 4&pi; para identificar os modos de Majorana pela reprodução dos resultados obtidos por (3). / In this work we investigate the fusion between Majorana bound states in nanostructures composed of a quantum dot connected to source and drain leads and side coupled to two topological superconducting nanowires sustaining Majorana end modes. Modeling the nanowire via a Kitaev chain, we have used two approaches: first using a recursive Greensfunction approach we calculate the conductance and local density of states (LDOS) and then by the diagonalization using the Bogoliubov-de Gennes (BdG) formalism we obtain the full spectrum of eigenstates. As described in (1) the LDOS of quantum dot coupled to a single wire clearly shows a leakage of the Majorana end mode from the wire into the dot, where it emerges as a unique dot level pinned to the Fermi energy of the leads (&epsilon;&fnof;). The calculated two-terminal conductance through the dot displays an unambiguous signature of the Majorana bound states, i. e., a pinned resonance occurring even when the dot level is far above &epsilon;&fnof; . Interestingly this Majorana signature remains even in the presence of interactions within the dot as showed in (2). Motivated by these earlier results we are particularly interested to investigate the fusion of Majonana end modes into ordinary fermionic modes within the dot. Our results demonstrate that by tuning the superconducting phase difference between the wires and the quantum-dot gate voltage we are able to control the emergence and splitting of Majorana modes. Furthermore we reinforce the proposal of using the 4&pi; periodic a.c Josephson effect to identify Majorana modes by reproducing the results obtained by (3).

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22237号 / 理博第4551号 / 新制||理||1654(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 柳瀬 陽一, 教授 川上 則雄, 教授 松田 祐司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22988号 / 理博第4665号 / 新制||理||1669(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 柳瀬 陽一, 教授 田中 耕一郎, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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Nanowires with Rashba spin-orbit coupling represent a promising platform for the realization of one-dimensional topological superconductivity and Majorana bound states. In this work we investigate Majorana bound states in hybrid normal-superconductor and short superconductor-normal-superconductor junctions based on nanowires with Rashba spin-orbit coupling. In particular, we explore consequences of the topological phase transition as well as the non-locality and self conjugation properties of the Majorana states on the low-energy spectrum and the Josephson effect in the case of superconductor-normal-superconductor junctions. Our work shows the great potential of hybrid junctions as a platform for the study of topological superconductivity and Majorana bound states.