Title Page
Abstract
Contents
Chapter 1. Introduction 14
Chapter 2. Chiral topological phase 18
2.1. Haldane model of QAH 19
2.2. Kitaev Quantum Spin Liquid 24
Chapter 3. Numerical Computation of Thermal Current 30
3.1. Method 31
3.1.1. Set up & Diagonalization 31
3.1.2. The thermal current distribution 36
3.2. Result 43
Chapter 4. Conclusion 47
References 50
국문초록 54
Table 3.1. Matlab code. The momentum k from −π to π is divided by 60. The matrix has 20 × 20 since the number of unit cells along the transverse... 35
Table 3.2. Matlab code. The thermal expectation value of the energy current operator is summed over all momentum and energy eigenstates. The code... 42
Table 3.3. Matlab code. After computing the expectation value, we calculate the vector components of the energy current according to the equation(3.14). 46
Figure 1.1. Consider a triangular lattice and a spin on each of its vertices. If two spins are aligned anti-aligned with each other and interact mutually, one... 15
Figure 2.1. (a) Graphene honeycomb lattice. Sublattice A(black circle) and B(white circle) form a unit cell. Three vectors a₁, a₂ and a₃ directing from... 20
Figure 2.2. Energy spectrum of Graphene. At six corners two bands touch and the gap is closed. 21
Figure 2.3. (a) Graphene energy dispersion with a zigzag ribbon (b) When only the mass term M is included to equation (2.9) with M=0.2t₁, just... 23
Figure 2.4. A honeycomb lattice. In a dashed line, unit cell is formed with two sublattices A(black) and B(white). A nearest neighbor pair of one A site... 25
Figure 2.5. Majorana representation. A spin consists of four Majorana fermions bx, by, bz and c.[이미지참조] 26
Figure 3.1. Zigzag ribbon of a honeycomb lattice. We set two directions, the 'n-direction' and the 'm-direction' as shown in the figure. The periodic... 31
Figure 3.2. (a) The electrical quantum Hall effect. When an external magnetic field(grey arrows) is applied, the Hall conductivity occurs and elec-... 38
Figure 3.3. A phase diagram of α-RuCl₃. The half-integer quantized plateau of the conductance is observed at the bottom(red region). The figure is... 39
Figure 3.4. The probability distribution of the eigenstates. Red one is the probability of site A and blue one for site B. One can see that the the edge... 44
Figure 3.5. The expectation value of the current vector along the n-direction is presented. (a) The current of the top edge of the ribbon, Figure 3.1. Ac-...[이미지참조] 45