The study of topological magnetic excitations has attracted widespread attention in the past few years. In this thesis, I have studied some examples of novel topological magnonic phases/phenomena in low-dimensional quantum magnets. The first chapter motivates the research based on the research gap in this field of study. The second chapter is written to make the thesis self-sufficient and the concepts are explained through examples. In the second chapter, the following formalisms and physical observables are described: Holstein-Primakoff, bond operator, Schwinger boson, Bogoliubov-Valatin, Group theory, Berry-phase, Berry-curvature, Chern number, thermal Hall conductance, Nernst conductivity, dynamical spin structure factor, edge-current. The main results of the thesis are shown in the third, fourth, and fifth chapters. In the third chapter, I have shown that anti-chiral edge states (co-propagating edge states) arise in the ferromagnetic Heisenberg model on the honeycomb lattice with Dzyaloshinskii-Moriya (DM) interactions. My results suggest that such anti-chiral edge states may be induced in certain realistic models of quantum magnets. In the fourth chapter, I have found the emergence of many magnon band-topological phases in the flux state of the Shastry-Sutherland model. I have derived a simple analytical form of the temperature dependence of derivative of thermal Hall conductivity near the band topological transition point which I propose to be experimentally useful. In the fifth chapter, I have investigated the emergence of Weyl triplons due to inter-layer DM-interaction in a microscopic model of SrCu2(BO3)2, a widely studied frustrated quantum magnet. I have shown that the thermal magnon Hall conductivity has a quasi-linear dependence as a function of the magnetic field in a Weyl-triplon region.
Intervalley Tunneling and Crossover from the Positive to Negative Interlayer Magnetoresistance in Quasi-Two-Dimensional Dirac Fermion System with or without Mass Gap
Magnetic phase diagram slightly below the saturation field in the stacked $J_1$-$J_2$ model in the square lattice with the $J_{\text{C}}$ interlayer coupling
Coherent vs incoherent interlayer transport in layered metals
报道了两种准二维有机超导体的层间磁电阻随磁场、温度和角度的变化关系。对于$κ$ -（BEDT-TTF）$_2$ I $_3$，我们发现在$Θ= 90^\circ$（平行于层的场）处的角度依赖性磁阻中的良好分辨的峰。对于$β$“-（BEDT-TTF）$_2$ SF $_5$ CH $_2$ CF $_2$ SO $_3$，不存在层间输运的相干性质的这种明确证明。这和非金属行为的磁阻建议非相干准粒子运动后2D金属。
本文从理论上研究了在无磁场的情况下，电子和空穴双电层系统中的层内和层间交换效应。我们使用变分Hartree-Fock近似分析层分离，层密度，隧穿，和施加的栅极电压上的层密度和层间相位相干性的影响。在协议与早期的工作，我们发现，非常小的层间距和低层密度，层间相关的基态具有自发层间相干性（SILC），即使在没有层间隧穿。在早期的工作相比，我们发现，作为总密度的函数，存在四个，而不是三个，不同的非晶相平衡的双层系统没有层间隧穿。新发现的相位存在于一个狭窄的密度范围内，有三个组成部分和稍微不等的层密度，一层是自旋极化的，另一层是非极化的。在存在足够强的偏压或隧穿的情况下，额外的双组分相也是可能的。最低密度SILC相是Zheng { \it et al.}讨论的完全自旋和赝自旋极化的"单组分“相。[Phys. Rev. B { \bf 55}，4506（1997）]。我们认为，这一阶段将产生一个有限的层间库仑阻力在零温度下，由于SILC。我们计算了每层中的粒子密度作为栅极电压和总粒子密度的函数，并发现层间交换可以减少或防止两层之间的电荷突然转移。计算了层间交换对层间电容的影响。
Dynamical decoherence of the light induced interlayer coupling in YBa$_{2}$Cu$_{3}$O$_{6+δ}$
YBa $_{2}$ Cu $_{3}$ O $_{6+δ}$中顶端氧振动的光激发已被证明可以增强其c轴超导相的刚性，正如平衡双层间约瑟夫森等离子体共振的瞬态蓝移所证明的那样。令人惊讶的是，瞬态c轴等离子体模式也可以诱导以上T $_{c}$由相同的顶端氧激发，这表明光激活的超流体隧道在整个赝隙相的YBa $_{2}$铜$_{3}$ O $_{6+δ}$。然而，尽管上述T $_{c}$瞬态等离子体模式和平衡约瑟夫森等离子体激元之间的相似性，涉及高迁移率准粒子输运的替代解释应被考虑。在这里，我们报告了一个广泛的研究的光诱导等离子体激元的松弛到平衡非相干相。这些新的实验允许对这种模式的性质进行批判性评估。我们确定，瞬态等离子体松弛通过其相干长度的崩溃，而不是其载体（或超流体）密度。这些意见是不容易调和与准粒子层间输运，而是支持瞬态超流隧穿的光致层间耦合的YBa $_{2}$铜$_{3}$ O $_{6+δ}$的起源。
