Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two-or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes with large angles as higher-order topological insulators, hosting topological corner charges. At large commensurate angles, the intervalley scattering opens up the bulk gap and the corner states occur at half filling. Based on both first-principles calculations and analytic analysis, we show the striking results that the emergence of the corner states do not depend on the choice of the specific angles as long as the underlying symmetries are intact. Our results show that the twisted bilayer graphene can serve as a robust candidate material of twodimensional higher-order topological insulator.

We present a detailed analysis of the stability of synchronized solutions to the Kuramoto system of oscillators. We derive an analytical expression counting the dimension of the unstable manifold associated to a given stationary solution. From this we are able to derive a number of consequences, including: analytic expressions for the first and last frequency vectors to synchronize, upper and lower bounds on the probability that a randomly chosen frequency vector will synchronize, and very sharp results on the large N limit of this model. One of the surprises in this calculation is that for frequencies that are Gaussian distributed the correct scaling for full synchrony is not the one commonly studied in the literature-rather, there is a logarithmic correction to the scaling which is related to the extremal value statistics of the random frequency vector.

Unconventional superconductivity arising from the interplay between strong spin–orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the three-dimensional topological insulator Bi2Se3. We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi2Se3 and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the emergence of an anomalous Fraunhofer pattern. We describe how the anomalous Fraunhofer patterns evolve for different device parameters, and we use this to understand the microscopic origin of the oscillating order parameter. The agreement between the experimental data and simulations shows that the finite momentum pairing originates from the coexistence of the Zeeman effect and Aharonov–Bohm flux.

Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.Introduction-Weyl semimetals (WSM), which are characterized by the gapless bulk states whose Fermi surfaces are either nodal points or lines, have been an intense area of research 1-9 . The bulk nodal points of a WSM possess non-degenerate band crossings that are robust under a small perturbations to the Hamiltonian. The low energy excitations of these materials are Weyl fermions that are described by two component spinors. The topological nature of the WSM are revealed through examination of the monopoles of Berry curvature present in the Brillouin zone(BZ) referred to as Weyl nodes. In the WSM, the net monopole charge integrated over the entire BZ is zero as the WSM possesses an equal number of the nodes with the positive and the negative charges 10;11 . In the noninteracting theory, these nodal points can only be eliminated by coming into contact with an oppositely charged Weyl node in momentum space, thereby annihilating one another. WSM have been predicted in a number of different materials and structures each of which is characterized by the symmetries broken. The most studied WSM are type-I WSM (WSM1), characterized by the presence of broken inversion or time-reversal symmetry, and type-II WSM (WSM2) 5;6 , which possess broken Lorentz invariance. Inversion broken WSM1, such as T aAs 4;12 , are characterized by the presence of disconnected Fermi arcs at the surface 1 that give rise to unconventional transport signatures such as quantum anomalous Hall (QAH) effect 13 and the chiral anomaly 14 . More recently, promising materials that may harbor experimental signatures of WSM2, such as M oT e 2 and W T e 2 , have been proposed thereby bringing WSM2 closer to realization 15-18 . WSM2 are characterized by an exotic hyperboloid Fermi surface, where the nodes are tilted in the BZ. Due to the tilted nodes, WSM2 exhibit transport properties that are distinct from the WSM1 including the absence of the chiral anomaly at certain magnetic field angles 19 , magnetic break down re...

Unconventional superconductivity has been predicted to arise in the topologically non-trivial Fermi surface of doped inversion symmetric Weyl semimetals (WSM). In particular, Fulde-FerrellLarkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion symmetric doped WSM. In an effort to resolve preferred pairing state, we theoretically study two separate four terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Josephson junction that consists of a doped WSM and an s-wave superconductor in which we show that the application of a transverse uniform current in s-wave superconductor effectively cancels the momentum carried by FFLO states in doped WSM. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in s-wave superconductor that serves as an indicator of FFLO states in doped WSMs. Furthermore, we show using a four terminal measurement configuration that the nodal points may be shifted by an application of transverse uniform current in doped WSM. We analyze the topological phase transitions induced by nodal pair annihilation in non-equilibrium by constructing the phase diagram and we find a characteristic decrease in the density of states that serves as a signature of the quantum critical point in the topological phase transition, thereby identifying nodal BCS states in doped WSM.