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The ability in experiments to control the relative twist angle between successive layers in two-dimensional (2D) materials offers a new approach to manipulating their electronic properties; we refer to this approach as "twistronics". A…
Topologically protected surface states of three-dimensional topological insulators provide a model framework for studying massless Dirac electrons in two dimensions. Usually a step on the surface of a topological insulator is treated as a…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
Higher-order topological insulators have been introduced in the precursory Benalcazar-Bernevig-Hughes quadrupole model, but no electronic compound has been proposed to be a quadrupole topological insulator (QTI) yet. In this work, we…
Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating,…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing Kagome and pyrochlore lattices. They are known to possess three phases (trivial…
Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
Topological magnetism has sparked an unprecedented age in quantum technologies. Marked by twisted spin structures with exotic dynamical modes, topological magnets have motivated a new generation of spintronic devices which transcend the…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy…
A $d$-dimensional, $n$th-order topological insulator or superconductor has localized eigenmodes at its $(d-n)$-dimensional boundaries ($n\leq d$). In this work, we apply periodic driving fields to two-dimensional superconductors, and obtain…
Surface states refer to electronic states emerging as a solid material terminates at a surface, and can be present in many systems. Despite their spatial proximity to material surfaces, surface states have been largely overlooked in…
Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk…
We propose ferroelectric layer sliding as a new approach to realize and manipulate topological quantum states in two-dimensional (2D) bilayer magnetic van der Waals materials. We show that stacking monolayer ferromagnetic topological states…
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…
We report the discovery of several classes of novel topological insulators (TIs) with hybrid-order boundary states generated from the first-order TIs with additional crystalline symmetries. Unlike the current studies on hybrid-order TIs…