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Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization…

The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…

The geometric phase and topological property for one-dimensional hybrid plasmonic-photonic crystals consisting of a simple lattice of graphene sheets are investigated systematically. For transverse magnetic waves, both plasmonic and…

Berry phase physics is closely related to a number of topological states of matter. Recently discovered topological semimetals are believed to host a nontrivial $\pi$ Berry phase to induce a phase shift of $\pm 1/8$ in the quantum…

Topological edge states arise in parity-time ($\mathcal{PT}$)-symmetric non-unitary quantum dynamics but have so far only been discussed in the $\mathcal{PT}$-symmetry-unbroken regime. Here we report the experimental detection of robust…

Non-Hermiticity can vary the topology of system, induce topological phase transition, and even invalidate the conventional bulk-boundary correspondence. Here, we show the introducing of non-Hermiticity without affecting the topological…

I investigate the two-dimensional Dirac fermion analogue of artificial atoms (Fock-Darwin states, FD) in a circular n-p junction on a topological insulator surface. The FD states in this non-parabolic potential exhibit a unique…

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…

Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge connections behave as non-Abelian antisymmetric tensor gauge fields in momentum space and naturally generalize…

Recent realizations of exotic topological states in condensed matter and cold atoms have advanced the exploration for topological characteristics, such as invariant topological orders and band inversion. Here we construct a 1D optical…

(BEDT-TFF)$_2$I$_3$ charge transfer salts are reported to show superconductivity and pressure induced quasi two-dimensional Dirac cones at the Fermi level. By performing state of the art ab initio calculations in the framework of density…

We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely…

Mathematically, topological invariants arise from the parallel transport of eigenstates on the energy bands, which, in physics, correspond to the adiabatic dynamical evolution of transient states. It determines the presence of boundary…

Transport due to spin-helical massless Dirac fermion surface state is of paramount importance to realize various new physical phenomena in topological insulators, ranging from quantum anomalous Hall effect to Majorana fermions. However, one…

The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant…

The $\alpha$-$T_3$ lattice, an interpolation model between the honeycomb lattice of graphene($\alpha=0$) and the dice lattice($\alpha=1$), undergoes a topological phase transition across $\alpha=1/\sqrt{2}$ when exposed to a circularly…

Transfer of information between topological edge states is a robust way of spatially manipulating quantum states while preserving their coherence in lattice environments. This method is particularly efficient when the edge modes are kept…

The discovery of novel topological phase advances our knowledge of nature and stimulates the development of applications. In non-Hermitian topological systems, the topology of band touching exceptional points is very important. Here we…

Here we study the systematic evolution of the topological properties of a Chern insulator in presence of an electronic dispersion that can be tuned smoothly from being Dirac-like till a semi-Dirac one and beyond. The band structure under…

We have studied the excited states of a one-dimensional donor dimer array by using time-dependent Hartree-Fock and density-functional theories. We find that tuning the inter-donor distances can induce a topological phase transition from a…