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We investigate topological phase transitions for the Haldane and Kane-Mele model in a lattice with $p6$ symmetry, which consists of triangles and hexagons arranged in a two-dimensional geometry. For the Haldane model, which breaks…
We investigate the fractional energy spectrum and quantum Hall response of a two-dimensional 1/5-depleted square lattice subjected to a perpendicular magnetic field. Using a tight-binding model that includes both nearest-neighbor (t_1) and…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
Photonic Chern insulators can be implemented in gyromagnetic photonic crystals with broken time-reversal (TR) symmetry. They exhibit gapless chiral edge states (CESs), enabling unidirectional propagation and demonstrating exceptional…
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves…
The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields…
Recent technological advances in integrated photonics have spurred on the study of topological phenomena in engineered bosonic systems. Indeed, the controllability of silicon ring-resonator arrays has opened up new perspectives for building…
We consider a time reversal symmetry (TRS) broken Kane-Mele model superimposed with Haldane model and chart out the phase diagram using spin Chern number to investigate the fate of quantum anomalous Hall insulator (QAHI) and quantum spin…
Topological insulating states in two-dimensional (2D) materials are ideal systems to study different types of quantized response signals due to their in gap metallic states. Very recently, the quantum spin Hall (QSH) effect was discovered…
Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is…
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
Symmetry-protected photonic topological insulator exhibiting robust pseudo-spin-dependent transportation, analogous to quantum spin Hall (QSH) phases and topological insulators, are of great importance in fundamental physics. Such…
Chern insulator is a building block of many topological quantum matters, ranging from quantum spin Hall insulators to fractional Chern insulators. Here, we discuss a new type of insulator, which consists of two half filled ordinary Chern…
This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum…
The Chern insulator displays a quantized Hall effect without Landau levels. In a landmark paper in 1988, Haldane showed that a Chern insulator could be realized through complex next-nearest-neighbor hopping in a honeycomb lattice. Despite…
We present a model for a topological quasicrystalline system which is suitable for realisation in cold-atom experiments. We define the model in terms of complex momentum-space couplings which break time-reversal symmetry (TRS), and detail…
Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most topological photonic structures can be understood by solving the eigenvalue problem of Maxwell's equations for a static linear…
We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and…