First-principles calculations have been used to investigate the electronic and topological properties of the two-dimensional C6-2x(BN)x biphenylene network, a graphene-like structure composed of not only hexagonal ring but also octagonal and square rings. Nontrivial topological properties have been found in two of them, with a stoichiometry of C4BN and C2(BN)2. The former C4BN is predicted to be a type-II Dirac semimetal with a superconducting critical temperature Tc=0.38K, which is similar to the pure carbon biphenylene network (C-BPN). The latter shows a novel isolated edge state exists between the conduction and valence bands. By regulation of strains and virtual-crystal approximation calculations, we found the annihilation of two pairs of Dirac points (DPs) in the non-high symmetric region (non-HSR) causes the two corresponding edge states stick together to generate this isolated edge state. In addition, we found that one pair of DPs arises from the shift of DPs in the C-BPN, while another new pair of DPs emerges around the Time Reversal Invariant Momenta (TRIM) point X due to the doping of boron and nitrogen. We constructed a tight-binding (TB) model to reveal the mechanism of forming the isolated edge state from the C-BPN to C2(BN)2. This study not only demonstrates the existence and mechanism of forming the isolated edge state in semimetals, but also provides an example in which the DPs can move away from the high-symmetry region.
Magnetic, superconducting, and topological surface states on Fe$_{1+y}$Te$_{1-x}$Se$_{x}$
利用非阿贝尔统计进行无误差量子计算的想法引发了最近关于FeTe $_{0.55}$ Se $_{0.45}$中拓扑表面超导性和马约拉纳零模（MZM）的报道的兴趣。一个相关的难题是，在整个样品表面上观察到的拓扑特征和超导性质并不均匀。这些电子不均匀性的理解和实际控制提出了一个突出的挑战，潜在的应用。在这里，我们结合中子散射，扫描角分辨光电子能谱（ARPES），和微探针组成和电阻率测量，以表征电子状态的Fe $_{1+y}$ Te $_{1-x}$ Se $_{x}$。我们建立了一个相图，其中观察到的超导电性只有在足够低的Fe浓度，与不同的反铁磁相关，而共存的拓扑表面状态只发生在足够高的Te浓度。我们发现FeTe $_{0.55}$ Se $_{0.45}$位于两个相界附近，这解释了超导态和拓扑态的不均匀性。我们的研究结果表明，在实际应用中使用拓扑MZM所需的成分控制。
