519,064 articles
Topological defect states in mechanical metamaterials
Topological defect states in mechanical metamaterials are protected modes bound to engineered defects such as dislocations, positioned inside the bulk rather than at edges, first shown in 2015.
Topological defect-driven ORR in carbon
Topological defect-driven ORR in carbon is the catalysis of the oxygen reduction reaction by non-hexagonal ring defects like pentagons and Stone–Wales defects in metal-free sp² carbon.
Topological defects in liquid crystals
Topological defects in liquid crystals are singular points, lines, or structures in the orientational order where the director cannot be continuously unwound to a uniform state.
Topological dislocations
A topological dislocation is a line defect in a periodic lattice that binds protected modes of electrons, light, or sound, fixed by the defect's topology rather than its geometry.
Topological edge modes in active matter
Topological edge modes in active matter are edge-confined wave states in nonequilibrium materials whose activity itself breaks time-reversal symmetry, giving unidirectional transport observed in metamaterials and chiral active fluids.
Topological edge state
A topological edge state is an electronic, photonic, or mechanical mode confined to a material's boundary by its nontrivial band topology, surviving disorder that destroys ordinary boundary modes.
Topological edge states in acoustic metamaterials
Topological edge states in acoustic metamaterials are sound-wave modes confined to the boundaries of engineered structures, robust against defects, bends, and disorder that stop ordinary sound.
Topological edge states in cold atoms
Topological edge states in cold atoms are boundary-localized quantum states appearing when ultracold gases are engineered into topological phases, mostly in optical lattices, allowing direct imaging.
Topological edge states in continuous acoustic and elastic media
Topological edge states in continuous acoustic and elastic media are boundary-confined wave modes whose existence is fixed by bulk band topology, first proposed for fluids in 2015.
Topological edge-state lasers
Topological edge-state lasers are laser devices whose lasing mode is a topological edge state at an interface, offering robust single-mode operation; first demonstrated in 2017.
Topological electrical circuits
Topological electrical circuits, also called topolectrical circuits (TECs), are electrical networks whose wiring graph encodes topological band theory, formalized in 2018 and used to study topological phases robustly.
Topological entropy
Topological entropy is a nonnegative number attached to a topological dynamical system that measures the exponential growth rate of distinguishable orbits, introduced by Adler, Konheim, and McAndrew in the mid-1960s.
Topological flat bands in twisted bilayer transition-metal dichalcogenides
Topological flat bands in twisted bilayer transition-metal dichalcogenides are nearly dispersionless moiré minibands with nonzero Chern number, predicted over a range of twist angles and supporting fractional Chern insulators at zero magnetic field.
Topological flocking
Topological flocking is a class of collective-motion models in which each agent aligns with a fixed number of nearest neighbors regardless of distance, unlike metric flocking.
Topological fluid dynamics
Topological fluid dynamics is the branch of fluid mechanics studying flow properties invariant under continuous deformation, such as the knottedness of vortex lines, with helicity as its central invariant.
Topological fractal metamaterials
Topological fractal metamaterials are artificial structures combining fractal geometry, such as the Sierpiński carpet, with topological insulator phases, demonstrated in acoustic, photonic, elastic, and nonlinear optical platforms.
Topological graph theory
Topological graph theory is the branch of graph theory that studies how graphs can be embedded, or drawn without edge crossings, on surfaces such as the sphere and torus.
Topological Hall effect
The topological Hall effect is an extra Hall voltage in magnetic materials with noncollinear spin textures like skyrmions, caused by an emergent magnetic field acting on conduction electrons.
Topological Hochschild homology
Topological Hochschild homology (THH) is a homology theory for ring spectra introduced by Marcel Bökstedt in 1985 as a spectrum-level analog of Hochschild homology, and is the target of trace maps from algebraic K-theory.
Topological insulator
A topological insulator is a material that insulates in its bulk but conducts on its surface or edges, protected by time-reversal symmetry and strong spin-orbit coupling.
Topological insulator laser
A topological insulator laser is a laser whose lasing mode is a topological edge state circulating unidirectionally around the cavity, robust against defects, introduced in 2018.
Topological insulator surface states
Topological insulator surface states are gapless, spin-momentum-locked electronic states forming a single Dirac cone protected by time-reversal symmetry, experimentally demonstrated by ARPES on Bi2Se3-family materials from 2008 onward.
Topological K-theory
Topological K-theory is a generalized cohomology theory assigning to a space the Grothendieck group of its vector bundles, introduced by Atiyah and Hirzebruch in 1961.
Topological Kondo insulator
A topological Kondo insulator is an insulating state whose gap comes from Kondo exchange between itinerant electrons and local magnetic moments, proposed in 2010 for SmB6.
Topological Kondo insulator candidate YbB12
YbB12, or ytterbium dodecaboride, is the only ytterbium-based Kondo insulator and a leading topological Kondo insulator candidate, showing metallic surface states and charge-neutral heat-carrying excitations.
Topological laser
A topological laser is a laser that emits from a topologically protected boundary state of a photonic lattice, first demonstrated in 2017 and resistant to structural defects and disorder.
Topological lasing
Topological lasing is laser operation in a topologically protected mode of a photonic lattice, combining coherence with robustness against disorder; the first 2D demonstrations appeared in 2018.
Topological magnon insulator
A topological magnon insulator is a magnetic insulator whose magnons, quantized spin waves, form bands with nonzero Chern numbers, giving protected chiral edge states that conduct spin waves.
Topological magnon insulators
Topological magnon insulators are magnetic insulators whose magnon bands carry nonzero Chern numbers, producing disorder-protected chiral edge modes, first realized experimentally in 2015 in a kagome-lattice ferromagnet.
Topological magnon insulators in kagome ferromagnets
A topological magnon insulator in a kagome ferromagnet is a ferromagnet whose magnon excitations acquire topological character, predicted in 2013 and first observed by neutron scattering in 2015.