电路中的拓扑态

图 3  三维LC电路示意图. 　(a) 单层LC蜂窝电路沿c方向上无连接的堆叠起来, 每个原胞内的两个不等价节点A和B在层内由$C_{1, 2, 3}$连接. 每个节点$A(B)$都通过并联的$L_{A}(L_{B})$和$C_{GA}(C_{GB})$回路接地. a, b和c表示格矢. 小图: 单层LC电路频谱中包含两个简并点, 沿着${k}_{c}$方向扩展将在布里渊区中形成两条直线状的结线(红线). (b) 电容$C_{4}$连接最近邻层间的节点A和B, 结线在给定合适的$C_{4}$时将弯曲成闭合环形. (c) 电容$C_{A}(C_{B})$连接最近邻层间的A-A(B-B)节点对, $C_{A}\neq C_{B}$且$C_{GA}\neq C_{GB}$时空间反演对称破缺, 环状结线可能退化成离散的外尔点. 此外, LC网络可以变形成(d), 简化实验装置的同时保证频谱不变

Fig. 3.  Schematic setup of the 3 D LC circuit lattice. (a) LC honeycomb layers stacked along c-direction without any interlayer connection. Two inequivalent nodes A and B within a unit cell, linked by capacitors $C_{1, 2, 3}$. Each node A(B) is grounded through the parallel connected inductor $L_{A}$($L_{B}$) and capacitor $C_{GA}$($C_{GB}$). a, b, and c denote lattice vectors. Inset: spectra of a single layer LC lattice includes two band-crossing points, extended uniformly along ${k}_{c}$-direction and form two straight nodal lines (red) in the BZ. (b) Connecting nodes A and B between the nearest neighbor-layers with $C_{4}$. The straight lines could be curved to a closed ring given appropriate $C_{4}$. (c) Connect node-pairs A-A(B-B) between the nearest neighbor-layers with $C_{A}$($C_{B}$), to break space inversion symmetry by setting $C_{A}\neq C_{B}$ and $C_{GA}\neq C_{GB}$, and the nodal ring may be degenerated to discrete Weyl points. The LC network can be deformed into (d), which is convenient to construct circuit elements in experiments while spectrum invariant.