相关论文: Zak phase and band inversion in dimerized one-dime…

Zak phase, i.e. the Berry phase acquired during an adiabatic motion of a Bloch particle across the Brillouin zone, provides a measure of the topological invariant of Bloch bands in one-dimensional crystalline potentials. Here a photonic…

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the modern band theory of solids. Here we report on the direct measurement of the geometric phase acquired by cold atoms moving in…

Bloch waves in 1D periodic systems carry Zak phase, which plays a key role in determining the band topology. In general, for systems that possess inversion symmetry, the Zak phase of an isolated band is quantized as 0 or Pi and is…

The theoretical identification of crystalline topological materials has enjoyed sustained success in simplified materials models, often by singling out discrete symmetry operations protecting the topological phase. When band structure…

This work presents a rigorous theory for topological photonic materials in one dimension. The main focus is on the existence and stability of interface modes that are induced by topological properties of the bulk structure. For a general 1D…

In this work, we derive some analytical properties of Berry's phase in one-dimensional quantum and classical crystals, also named Zak's phase, when computed with a Fourier basis. We show that Zak's phase can be divided in two terms: a…

Zak phase labels the topological property of one-dimensional Bloch Bands. Here we propose a scheme and experimentally measure the Zak phase in a photonic system. The Zak phase of a bulk band of is related to the topological properties of…

The Zak phase $\gamma$, the generalization of the Berry phase to Bloch wave functions in solids, is often used to characterize inversion-symmetric 1D topological insulators; however, since its value can depend on the choice of real-space…

A new method is proposed to predict the topological properties of one-dimensional periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and…

Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ.…

The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…

Wave propagation in periodic media is governed by energy-momentum relation and geometric phases characterizing band topology, such as Zak phase in one-dimensional lattices. We demonstrate that in the off-diagonal trimer lattices Zak phase…

Recently, optical lattices with non-zero Berry's phases of Bloch bands have been realized. New approaches for measuring Berry's phases and topological properties of bands with experimental tools appropriate for ultracold atoms need to be…

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological…

We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry…

The concept of the Zak phase lies at the core of the modern theory of electric polarization. It is defined using the components of the Bloch wave functions in a certain basis, which is not captured by the standard expression for Berry…

Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…

Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials. Through the bulk-boundary correspondence, these topological phases have a one-to-one…

Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wavepacket takes to traverse a Brillouin-zone loop. We introduce a new type of Bloch…

In various topological phases, nontrivial states appear at the boundaries of the system. In this paper, we investigate anomalous dielectric response caused by such states caused by the pi Zak phase. First, by using the one-dimensional…