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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 Letter, 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

Long range order in the absence of translational symmetry gives rise to drastic revolution of our common knowledge in condensed-matter physics. Quasicrystals, as such an unconventional system, became a plethora to test our insights and to find exotic states of matter. In particular, electronic properties in quasicrystals have gotten lots of attention along with their experimental realization and controllability in twisted bilayer systems. In this work, we study how quasicrystalline order in bila

Weyl semimetals (WSM) have quickly gained popularity since their discovery and they are now the subject of intense theoretical and experimental research. In general, the WSM is categorized as being either type I or type II. The type-I WSM is characterized by broken inversion symmetry, while the type II by broken Lorentz symmetry. Due to this characteristic difference in the Fermi surfaces of the two types, it is necessary to extend our understanding of WSMs to include the different physical prop

Abstract Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads to a nontrivial Berry phase in addition to an exchange of eigenstates. Based on these phenomena, we propose in this work an exhaustive classification framework for EPs in non-Hermitian physical systems. In contrast to previous classifications that only

Abstract It has been known that the bulk-boundary correspondence (BBC) of the non-Hermitian skin effect is characterized by the topology of the complex eigenvalue spectra, while the topology of the wave function gives rise to Hermitian BBC with conventional boundary modes. In this work, we go beyond the known description of the non-Hermitian topological phase and find a different type of BBC that appears in generalized boundary conditions. The generalized Brillouin zone (GBZ) possesses non-trivi

Twist engineering of van der Waals magnets has emerged as an outstanding platform for manipulating exotic magnetic states. However, the complicated form of spin interactions in the large moiré superlattice obstructs a concrete understanding of such spin systems. To tackle this problem, for the first time, we developed a generic ab initio spin Hamiltonian for twisted bilayer magnets. Our atomistic model reveals that strong AB sublattice symmetry breaking due to the twist introduces a promising ro

Abstract Open quantum systems provide a plethora of exotic topological phases of matter that have no Hermitian counterpart. Non-Hermitian skin effect, macroscopic collapse of bulk states to the boundary, has been extensively studied in various experimental platforms. However, it remains an open question whether such topological phases persist in the presence of many-body interactions. Previous studies have shown that the Pauli exclusion principle suppresses the skin effect. In this study, we pre

We propose that noncollinear magnetic order in magnetic systems can harbor a higher-order topological magnon phase with non-Hermitian topology and hinge magnon modes. We consider a three-dimensional system of interacting local moments on stacked layers of honeycomb lattice. It initially favors a collinear magnetic order along an in-plane direction, which turns into a noncollinear order upon applying an external magnetic field perpendicular to the easy axis. We exploit the non-Hermitian nature of

Abstract The Hofstadter energy spectrum of twisted bilayer graphene (TBG) is found to have recursive higher-order topological properties. We demonstrate that higher-order topological insulator (HOTI) phases, characterized by localized corner states, occur as replicas of the original HOTIs to fulfill the self-similarity of the Hofstadter spectrum. We show the existence of exact flux translational symmetry in TBG at all commensurate angles. Based on this result, we identify that the original HOTI

We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped time-reversal invariant topological insulator (TI). Using mean-field theory, we show that Fulde-Ferrell (FF) pairing can be induced in the conventional superconductor through the inverse proximity effect (IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal bands of the superconductor possess a proximity induced spin-orbit coupling and ma

Topological nodal superconductors possess gapless low energy excitations that are characterized by point or line nodal Fermi surfaces. In this work, using a coupled wire construction, we study topological nodal superconductors that have protected Dirac nodal points. In this construction, the low-energy electronic degrees of freedom are confined in a three-dimensional array of wires, which emerge as pairing vortices of a microscopic superconducting system. The vortex array harbors an antiferromag

Abstract Non-trivial linking invariant encodes robust information of topological matter. It has been recently shown that the linking and winding of complex eigenenergy strings can classify one-dimensional non-Hermitian topological matter. However, in higher dimensions, bundles of linked strings can emerge such that every string is mutually linked with all the other strings. To the best of our knowledge, a non-Hermitian Hopf bundle has not been experimentally clarified. Here, we attempt to explor

Electrons on the lattice subject to a strong magnetic field exhibit the fractal spectrum of electrons, which is known as the Hofstadter butterfly. In this work, we investigate unconventional superconductivity in a three-dimensional Hofstadter butterfly system. While it is generally difficult to achieve the Hofstadter regime, we show that the quasi-two-dimensional materials with a tilted magnetic field produce the large-scale superlattices, which generate the Hofstadter butterfly even at the mode

Universality class of wave chaos emerges in many areas of science, such as molecular dynamics, optics, and network theory. In this work, we generalize the wave chaos theory to cavity lattice systems by discovering the intrinsic coupling of the crystal momentum to the internal cavity dynamics. The cavity-momentum locking substitutes the role of the deformed boundary shape in the ordinary single microcavity problem, providing a new platform for the in situ study of microcavity light dynamics. The