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Topological Superconductor
In condensed matter physics and materials chemistry, a topological superconductor is a material that conducts electricity with zero electrical resistivity, and has non-trivial topology which gives it certain unique properties. These materials behave as superconductors that feature exotic edge states, known as Majorana zero modes. Classification and examples Topological superconductors are characterized by the topological order related to their electronic band structure. These materials can be classified using the periodic table of topological superconductors, which categorizes topological phases based on time-reversal symmetry, particle-hole symmetry, and chiral symmetry. An example of a simple topological superconductor in one-dimension is the Kitaev chain. Experimental evidence In 2015, uranium ditelluride (UTe2) was found to behave as a topological superconductor. Applications A notable application of topological superconductors is in the realm of topological qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-symmetry
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, : T: t \mapsto -t. Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium, contrary to their classical counterparts, although this has not yet been experimentally confirmed. Time ''asymmetries'' (see Arrow of time) generally are caused by one of three categories: # intrinsic to the dynamic physical law (e.g., for the weak force) # due to the initial conditions of the universe (e.g., for the second law of thermodynamics) # due to measurements (e.g., for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Insulator
A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an insulator for the same reason a " trivial" (ordinary) insulator is: there exists an energy gap between the valence and conduction bands of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot be continuously transformed into a trivial one without untwisting the bands, which closes the band gap and creates a conducting state. Thus, due to the continuity of the underlying field, the border of a topological insulator with a trivial insulator (including vacuum, which is topologically trivial) is forced to support conducting edge states. Since this results from a global property of the topological insulator's band structure, local (s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Quantum Computer
A topological quantum computer is a type of quantum computer. It utilizes anyons, a type of quasiparticle that occurs in two-dimensional systems. The anyons' world lines intertwine to form braids in a three-dimensional spacetime (one temporal and two spatial dimensions). The braids act as the logic gates of the computer. The primary advantage of using quantum braids over trapped quantum particles is in their stability. While small but cumulative perturbations can cause quantum states to decohere and introduce errors in traditional quantum computations, such perturbations do not alter the topological properties of the braids. This stability is akin to the difference between cutting and reattaching a string to form a different braid versus a ball (representing an ordinary quantum particle in four-dimensional spacetime) colliding with a wall. It was proposed by Russian-American physicist Alexei Kitaev in 1997. While the elements of a topological quantum computer originate in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uranium Ditelluride
Uranium ditelluride is an inorganic compound with the formula UTe2. It was discovered to be an unconventional superconductor in 2018. * Superconductivity Superconductivity in UTe2 appears to be a consequence of triplet electrons spin-pairing. The material acts as a topological superconductor, stably conducting electricity without resistance even in high magnetic fields. With recent crystal growth techniques a superconducting transition temperature of 2.10 K has been reached as of 2025. Charge density waves (CDW) and pair density waves (PDW) have been described in UTe2, with the latest case being the first time it has been described in a p-wave superconductor. See also * Distrontium ruthenate a ''p''-wave triplet state superconductor candidate. * Helium-3 a spin-triplet superfluid * Ferromagnetic superconductor Ferromagnetic superconductors are materials that display intrinsic coexistence of ferromagnetism and superconductivity. They include UGe2, URhGe, and UCoGe. Evi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kitaev Chain
In condensed matter physics, the Kitaev chain or Kitaev–Majorana chain is a simplified model for a topological superconductor. It models a one dimensional lattice featuring Majorana bound states. The Kitaev chain has been used as a toy model of semiconductor nanowires for the development of topological quantum computers. The model was first proposed by Alexei Kitaev in 2000. Description Hamiltonian The tight binding Hamiltonian of a Kitaev chain considers a one dimensional lattice with ''N'' site and spinless particles at zero temperature, subjected to nearest neighbour hopping interactions, given in second quantization formalism as :H=-\mu\sum_^N \left(c_j^\dagger c_j-\frac12\right)+\sum_^\left \Delta, \left(c_^\dagger c_j^\dagger+c_j c_\right)\right/math> where \mu is the chemical potential, c_j^\dagger,c_j are creation and annihilation operators, t\geq 0 the energy needed for a particle to hop from one location of the lattice to another, \Delta=, \Delta, e^ is the induced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive ("right-handed") if the direction of its spin is the same as the direction of its motion. It is negative ("left-handed") if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. The chirality of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C-symmetry
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal). These discrete symmetries, C, P and T, are symmetries of the equations that describe the known fundamental forces of nature: electromagnetism, gravity, the strong and the weak interactions. Verifying whether some given mathematical equation correctly models nature requires giving physical interpretation not only to continuous symmetries, such as motion in time, but also to its discrete symmetries, and then determining whether nature adheres to these symmetries. Unlike the continuous symmetri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Table Of Topological Insulators And Topological Superconductors
The periodic table of topological insulators and topological superconductors, also called tenfold classification of topological insulators and superconductors, is an application of topology to condensed matter physics. It indicates the mathematical group for the topological invariant of the topological insulators and topological superconductors, given a dimension and discrete symmetry class. The ten possible discrete symmetry families are classified according to three main symmetries: particle-hole symmetry, time-reversal symmetry and chiral symmetry. The table was developed between 2008–2010 by the collaboration of Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig; and independently by Alexei Kitaev. Overview These table applies to topological insulators and topological superconductors with an energy gap, when particle-particle interactions are excluded. The table is no longer valid when interactions are included. The topological insulators and superc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Materials Chemistry
Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering. As such, the field was long considered by academic institutions as a sub-field of these related fields. Beginning in the 1940s, materials science began to be more widely recognized as a specific and distinct field of science and engineering, and major technical universities around the world created dedicated schools for its study. Materials scientists emphasize understanding how the history of a material (''processing'') influences its structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Band Structure
In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ''forbidden bands''). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). Why bands and band gaps occur The formation of electronic bands and band gaps can be illustrated with two complementary models for electrons in solids. The first one is the nearly free electron model, in which the electrons are assumed to move almost freely within the material. In this model, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Order
In physics, topological order describes a state or phase of matter that arises system with non-local interactions, such as entanglement in quantum mechanics, and floppy modes in elastic systems. Whereas classical phases of matter such as gases and solids correspond to microscopic patterns in the spatial arrangement of particles arising from short range interactions, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition. Technically, topological order occurs at zero temperature. Various topologically ordered states have interesting properties, such as (1) ground state degeneracy and fractional statistics or non-abelian group statistics that can be used to realize a topological quantum computer; (2) perfect conducting edge states that may have important device applications; (3) emergent gauge field and Fermi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
