Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekulé Bond Ordering

键无序石墨烯中的带中心金属-绝缘体转变

Band-center metal-insulator transition in bond-disordered graphene

本文研究键无序蜂窝晶格费米子输运，发现交错二聚化下金属-绝缘体转变的标度指数约为1.05，而plaquette二聚化下约为1.55，揭示BDI对称类转变的非普适性。

Various facets of magnetic charge correlation: Micromagnetic and distorted waveBorn approximation simulations study

The emergent concept of magnetic charge quasi-particle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. We report on the exploration of magnetic phases due to various magnetic charge correlation using the complementary numerical techniques of micromagnetic and distorted wave Born approximation simulations in artificial permalloy honeycomb lattice. The honeycomb element length varies between 10 nm and 100 nm, while the width and thickness are kept within the single domain limit. In addition to the charge ordered loop state, w…

无序石墨烯的多重分形零模

Multifractal zero mode for disordered graphene

非对角无序与随机跳跃之间的二分晶格的子晶格描述的哈密顿具有手征（子晶格）对称性。的能谱是对称的E=0和奇数总数的晶格站点的孤立的零模式总是存在的，这符合在二维（2D）的安德森过渡的迁移率边缘。在手性正交对称类BDI中，我们计算了具有边缘的石墨烯样品的零模的分形维数$D_{2}$。在没有无序$D_{2}=1$，这对应于一个一维的边缘状态，而对于强无序$D_{2}$衰减到0和零模式变得本地化。指出了蜂窝晶格和正方形二分晶格中零模的异同。

Topological transitions and Anderson localization of light in disordered atomic arrays

We explore the interplay of disorder and topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. On the one hand, disorder can trigger transitions between distinct topological phases and drive the lattice into the topological Anderson insulator state. On the other hand, the nontrivial topology of the photonic band structure suppresses Anderson localization of modes that disorder introduces inside the band gap of the ideal lattice. Furthermore, we discover that disorder can both open a topological pseudogap in the spectrum of an otherwise topologically trivial…

无序石墨烯的局域态密度

Local density of states in disordered graphene

我们研究了两种晶格模型，蜂窝晶格（HCL）和一种特殊的正方形晶格（SQL），这两种晶格模型都在连续极限下简化为Dirac方程。在存在无序（高斯势无序和随机矢量势）的情况下，我们研究了态密度（DOS）的数值和解析行为。虽然可以推导出一个上限的SQL上的DOS在狄拉克点，这也证实了数值计算，没有这样的上限存在的随机矢量势的存在下的HCL。对最低本征值的仔细研究确实表明，在HCL上的狄拉克点处，DOS可能是发散的。尽管有一个共同的连续极限，这些晶格模型表现出不同的行为。

无序石墨烯中的Anderson相变

Anderson Transition in Disordered Graphene

我们使用正则化核多项式方法（RKPM）数值研究单层石墨烯上的无序效应。这种精确的数值方法使我们能够研究具有数百万个位点的非常大的晶格，因此几乎没有有限尺寸误差。在这种方法中，弱无序和强无序状态都是在相同的基础上处理的。研究了蜂窝晶格上在位无序的紧束缚模型。我们发现，在弱无序区，狄拉克费米子保持扩展和他们的速度降低无序强度的增加。然而，如果无序足够强，则将存在{ \em迁移率边缘}，其将{围绕费米点的\em局域态}与剩余的扩展态分离。这与局域化的标度理论相反，标度理论预测所有的状态都是二维的。

Anderson transitions in disordered two-dimensional lattices

We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagomé, the square, and the triangular lattice. By calculating the well-known statistical measures viz., nearest neighbor spacing distribution, number variance, the partition number and the dc electrical conductivity from Kubo-Greenwood formula, we show that there is clearly a delocalization to localization transition with increasing disorder. Though the statistics in different lattice …

Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional…

石墨烯中无序狄拉克费米子的超导电性

Superconductivity of disordered Dirac fermions in graphene

采用空间非均匀自洽Bogoliubov-de Gennes（BdG）方法，数值研究了具有现场Hubbard吸引相互作用U的石墨烯蜂窝晶格的超导性和无序性之间的相互作用.在没有无序的情况下，在电荷中性处有两个相。低于临界值Uc的吸引力相互作用有狄拉克半金属相，并在它上面有超导相。我们在系统中加入标量势无序，同时平均保持电荷中性。BdG方程的数值解表明，在强吸引区（U > Uc），无序通常具有抑制超导电性的作用，而在弱吸引区（U < Uc），弱无序增强超导电性。在弱吸引机制中，太强的无序最终会抑制超导性，即，存在使临界温度Tc最大化的最佳无序强度。我们的数值结果还表明，在弱无序制度，介观不均匀性增强超导性显着超过空间均匀的平均场论a` la Abrikosov-Gorkov的预测。在这种情况下，超导性由罕见的相位相干超导岛组成。我们还研究了无序和介观不均匀性对超导邻近效应的增强，并获得了典型的隧穿态密度和超流磁化率的空间图，这些图可以直接与石墨烯中邻近诱导超导的扫描隧道显微镜（STM）实验进行比较。

High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity

Disorder is a key factor influencing the behavior of condensed states of matter, however the true extent of its impact is generally difficult to determine due to the prominent roles played by quantum interference, entanglement between spin and orbital degrees of freedom and proximity to quantum critical points. Here we show that the one-particle disorder self-energy -- a direct probe of the renormalization of low-energy excitations due to defects and impurities distributed randomly in a crystal -- can be obtained by means of unbiased spectral expansions of lattice Green's functions in a comput…