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Photonic topological insulators (PTIs) have been proposed as an analogy to topological insulators in electronic systems. In particular, two-dimensional PTIs have gained attention for the integrated circuit applications. However, controlling…
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological…
Topological insulators (TIs) are an important family of quantum materials that exhibit a Dirac point (DP) in the surface band structure but have a finite band gap in bulk. A large degree of spin-orbit interaction and low bandgap is a…
Amorphous topological states, which are independent of the specific spatial distribution of microscopic constructions, have gained much attention. Recently, higher-order topological insulators, which are a new class of topological phases of…
In the past two decades, various classes of topological materials have been discovered, spanning topological insulators, semimetals, and metals. While the observation and understanding of the topology of a material has been a primary focus…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…
A 3D fermionic topological insulator has a gapless Dirac surface state protected by time-reversal symmetry and charge conservation symmetry. The surface state can be gapped by introducing ferromagnetism to break time-reversal symmetry,…
Topological phases of matter are known to be unstable against strong onsite disorder in one dimension. In this work, however, we propose that in the case of a topological ladder, an onsite quasiperiodic disorder under proper conditions,…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A…
Tuning band gaps in two-dimensional (2D) materials is of great interest in the fundamental and practical aspects of contemporary material sciences. Recently, black phosphorus (BP) consisting of stacked layers of phosphorene was…
Topological quantum phase transitions (TQPTs) in a material induced by external perturbations are often characterized by band touching points in the Brillouin zone. The low-energy excitations near the degenerate band touching points host…
We have experimentally realized novel space-time inversion (P-T) invariant Z2-type topological semimetal-bands, via an analogy between the momentum space and a controllable parameter space in superconducting quantum circuits. By measuring…
We study symmetry-protected topological (SPT) phase transitions induced by stacking two gapped one-dimensional subsystems in BDI symmetry class. The topological invariant of the entire system is a sum of three topological invariants: two…
We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy…
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…
A wide class of materials that were discovered to carry a topologically protected phase order has led to a highly active area of research called topological insulators. This phenomenon has radically changed our thinking because of their…