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Disorder in atomic positions can induce a topologically nontrivial phase - topological Anderson insulator (TAI) - for transverse electric optical quasimodes of a two-dimensional honeycomb lattice of immobile atoms. TAI requires both…
There have been considerable efforts devoted to the study of topological phases in certain non-Hermitian systems that possess real eigenfrequencies in the presence of gain and loss. However, it is challenging to experimentally realize such…
Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two period-two and four period-eight cycles,…
We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multi-valley Dirac fermion surface states. We find that…
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…
The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based…
We show that topological characterization and classification in $D$-dimensional systems, which are thermodynamically large in only $D-\delta$ dimensions and finite in size in $\delta$ dimensions, is fundamentally different from that of…
Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological…
The surface states of the three dimensional (3D) Topological Insulators are described by two-dimensional (2D) massless dirac equation. A gate voltage induced one dimensional potential barrier on such surface creates a discrete bound state…
We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only…
Recently extended from the modern theory of electric polarization, quantized multipole topological insulators (QMTIs) describe higher-order multipole moments, lying in nested Wilson loops, which are inherently quantized by lattice…
Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological…
Topological insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In…
One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character…
Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett. 61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be engineered…
Fractal lattices, featuring the self-similarity symmetry, are often geometric descents of parent crystals, possessing all their discrete symmetries (such as rotations and reflections) except the translational ones. Here, we formulate three…
We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological…