We study an exotic state which is localized only at intersection of edges a topological material. This "edge-of-edge" shown to exist generically. construct explicitly generic edge-of-edge states in 5-dimensional Weyl semimetals and their dimensional reductions, such as 4-dimensional insulators class A 3-dimensional chiral AIII. The existence the due charge edge states. notion Berry connection generalized include space all possible boundary conditions, where Chern-Simons forms are be nontrivial.

We find that generic boundary conditions of the Weyl semimetal are dictated by only a single real parameter in continuum limit. determine how energy dispersions (the Fermi arcs) and wave functions edge states depend on this parameter. Lattice models found to be consistent with our observation. Furthermore, enhanced space condition is shown support novel topological number.

Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have focused on systems which the Hamiltonian consists matrices that commute with each other satisfy Clifford algebra. In this work we consider Hamiltonians are beyond minimal model. Specifically, two types layered is studied, consist do not all We find terms anticommute others can hold common band-inversion surfaces, controls topology bands,...

A scheme is proposed for generating a multiparticle three-dimensional entangled state by appropriately adiabatic evolutions, where atoms are respectively trapped in separated cavities so that individual addressing needless. In the ideal case, losses due to spontaneous transition of an atom and excitation photons efficiently suppressed since all ground states fields remain vacuum state. Compared with previous proposals, present reduces its required operation time via simultaneously...

Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between number given Chern character of Berry curvature and Chern-Simons level low energy effective action for a general class Hamiltonians bilinear fermion with U(1) gauge interactions including nonminimal couplings an explicit calculation. A series Ward-Takahashi identities crucial to relate winding number, which could then be directly reduced carrying out integral over...

We discuss anomalous fractional quantum Hall effect that exists without external magnetic field.We propose excitations in such systems may be described effectively by non-interacting particles with the Hamiltonians defined on Brillouin zone a branch cut.Hall conductivity of system is expressed through one-particle Green function.We demonstrate for proposed type this expression takes values times Klitzing constant.Possible relation construction degeneracy ground state discussed as well.

It is well known that the quantum Hall conductivity in presence of constant magnetic field expressed through topological TKNN invariant. The same invariant responsible for intrinsic anomalous effect (AQHE), which, addition, may be represented as one momentum space composed two point Green's functions. We propose generalization this expression to QHE non-uniform field. proposed phase Weyl symbols two-point function. applicable a wide range tight-binding models, including interacting ones.

Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have focused on systems which the Hamiltonian consists matrices that commute with each other satisfy Clifford algebra. In this work, we consider Hamiltonians are beyond minimal model. Specifically, two types layered is studied, consisting do not all We find terms anti-commute others can hold common band-inversion surfaces, controls topology...

We study multilayer Haldane models with irregular type of stacking, considering the nearest interlayer hopping. prove that value topological invariant is equal to number layers times monolayer model, regardless stacking type, and hoppings do not induce gap closing phase transitions.

We study multilayer Haldane models with irregular type of stacking. Considering the nearest interlayer hopping, we prove that value topological invariant is equal to number layers times monolayer model for stacking(except AA), and hoppings do not induce direct gap closing or phase transitions. However, if next-to-nearest hopping taken into account, transitions can occur.

As growing usage of social media websites in the recent decades, amount news articles spreading online rapidly, resulting an unprecedented scale potentially fraudulent information. Although a plenty studies have applied supervised machine learning approaches to detect such content, lack gold standard training data has hindered development. Analysing single format, either fake text description or image, is mainstream direction for current research. However, misinformation real-world scenario...

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective interaction strength conductivity given by filling fraction Landau levels averaged over ground state system. This conclusion remains valid for both integer and fractional effect.

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that, irrespective interaction strength, conductivity given by filling fraction Landau levels averaged over ground state system. This conclusion remains valid for both integer and fractional effect.

Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between number given Chern character of Berry curvature and Chern-Simons level low energy effective action for a general class Hamiltonians bilinear fermion with U(1) gauge interactions including non-minimal couplings an explicit calculation. A series Ward-Takahashi identities crucial to relate winding number, which could then be directly reduced carrying out integral over...

We analytically study boundary conditions of the Dirac fermion models on a lattice, which describe first and second order topological insulators. obtain dispersion relations edge hinge states by solving these conditions, clarify that Hamiltonian symmetry may provide constraint condition. also demonstrate edge-hinge analog bulk-edge correspondence, in nontrivial topology gapped state ensures gaplessness state.

We analytically study boundary conditions of the Dirac fermion models on a lattice, which describe first and second order topological insulators. obtain dispersion relations edge hinge states by solving these conditions, clarify that Hamiltonian symmetry may provide constraint condition. also demonstrate edgehinge analog bulk-edge correspondence, in nontrivial topology gapped state ensures gaplessness state.