Weyl fermions are massless
chiral
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from i ...
fermions
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
embodying the mathematical concept of a
Weyl spinor
In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three p ...
. Weyl spinors in turn play an important role in
quantum field theory and the
Standard Model, where they are a building block for fermions in quantum field theory. Weyl spinors are a solution to the
Dirac equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...
derived by
Hermann Weyl, called the
Weyl equation
In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three ...
.
For example, one-half of a charged
Dirac fermion of a definite
chirality is a Weyl fermion.
Weyl fermions may be realized as emergent
quasiparticle
In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
For exa ...
s in a low-energy condensed matter system. This prediction was first proposed by
Conyers Herring
William Conyers Herring (November 15, 1914 – July 23, 2009) was an American physicist. He was a Professor of Applied Physics at Stanford University and the Wolf Prize in Physics recipient in 1984/5.
Academic career
Conyers Herring completed ...
in 1937, in the context of
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 ' ...
s of solid state systems such as electronic crystals.
Topological materials in the vicinity of band inversion transition became a primary target in search of topologically protected bulk electronic band crossings.
The first (non-electronic) liquid state which is suggested, has similarly emergent but neutral excitation and theoretically interpreted
superfluid
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
's
chiral anomaly
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have mor ...
as observation of
Fermi points is in
Helium-3 A superfluid phase. Crystalline tantalum arsenide (TaAs) is the first discovered topological Weyl fermion semimetal which exhibits topological surface
Fermi arc
In the field of unconventional superconductivity, a Fermi arc is a phenomenon visible in the pseudogap state of a superconductor. Seen in momentum space, part of the space exhibits a gap in the density of states, like in a superconductor. This ...
s where Weyl fermion is electrically charged along the line of original suggestion by Herring.
An electronic Weyl fermion is not only charged but stable at room temperature where there is no such superfluid or liquid state known.
Experimental observation
A Weyl semimetal is a solid state
crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
whose low energy excitations are Weyl fermions that carry electrical charge even at room temperatures.
A Weyl semimetal enables realization of Weyl fermions in electronic systems.
It is a topologically nontrivial phase of matter, together with Helium-3 A superfluid phase, that broadens the topological classification beyond topological insulators.
The Weyl fermions at zero energy correspond to points of bulk band degeneracy, the Weyl nodes (or Fermi points) that are separated in
momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension.
Position space (also real space or coordinate space) is the set of all ''position vectors'' r in space, and h ...
. Weyl fermions have distinct chiralities, either left handed or right handed.
In a Weyl semimetal crystal, the chiralities associated with the Weyl nodes (Fermi points) can be understood as topological charges, leading to
monopoles and anti-monopoles of
Berry curvature in
momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension.
Position space (also real space or coordinate space) is the set of all ''position vectors'' r in space, and h ...
, which (the splitting) serve as the topological invariant of this phase.
Comparable to the Dirac fermions in
graphene
Graphene () is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. or on the surface of
topological insulators
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 ...
, Weyl fermions in a Weyl semimetal are the most robust electrons and do not depend on
symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
except the
translation symmetry
Translation is the communication of the Meaning (linguistic), meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The ...
of the crystal lattice. Hence the Weyl fermion
quasiparticles
In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
For exa ...
in a Weyl semimetal possess a high degree of mobility. Due to the nontrivial topology, a Weyl semimetal is expected to demonstrate
Fermi arc
In the field of unconventional superconductivity, a Fermi arc is a phenomenon visible in the pseudogap state of a superconductor. Seen in momentum space, part of the space exhibits a gap in the density of states, like in a superconductor. This ...
electron states on its surface.
These arcs are discontinuous or disjoint segments of a two dimensional Fermi contour, which are terminated onto the projections of the Weyl fermion nodes on the surface. A 2012 theoretical investigation of superfluid Helium-3 suggested Fermi arcs in neutral superfluids.
On 16 July 2015 the first experimental observations of Weyl fermion semimetal and topological Fermi arcs in an inversion symmetry-breaking single crystal material
tantalum arsenide
Tantalum arsenide is a compound of tantalum and arsenic with the formula TaAs. It is notable as being the first topological Weyl semimetal that was identified and characterized by ARPES.
Structure
Tantalum arsenide crystallizes in a body-centere ...
(TaAs) were made.
Both Weyl fermions and Fermi arc surface states were observed using direct electronic imaging using
ARPES
Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelec ...
, which established its topological character for the first time.
This discovery was built upon previous theoretical predictions proposed in November 2014 by a team led by Bangladeshi scientist
M Zahid Hasan.
Weyl points (Fermi points) were also observed in non-electronic systems such as photonic crystals, in fact even before their experimental observation in electronic systems
and Helium-3 superfluid quasiparticle spectrum (neutral fermions).
Note that while these systems are different from electronic condensed matter systems, the basic physics is very similar.
Crystal growth, structure and morphology
TaAs is the first discovered Weyl semimetal (conductor). Large-size (~1 cm), high-quality TaAs single crystals can be obtained by
chemical vapor transport method using iodine as the transport agent.
TaAs crystallizes in a
body-centered tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a squa ...
unit cell with
lattice constant
A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal. A simple cubic crystal has o ...
s a = 3.44 Å and c = 11.64 Å and
space group
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it uncha ...
I41md (No. 109). Ta and As atoms are six coordinated to each other. This structure lacks a horizontal mirror plane and thus inversion symmetry, which is essential to realize Weyl semimetal.
TaAs single crystals have shiny facets, which can be divided into three groups: the two truncated surfaces are , the trapezoid or isosceles triangular surfaces are , and the rectangular ones . TaAs belongs to
point group 4mm, the equivalent and planes should form a ditetragonal appearance. The observed morphology can be vary of degenerated cases of the ideal form.
Beside the initial discovery of TaAs as Weyl semimetal, many other materials such as Co2TiGe, MoTe2, WTe2, LaAlGe, PrAlGe have been identified to exhibit Weyl semimetallic behavior
Applications
The Weyl fermions in the bulk and the Fermi arcs on the surfaces of Weyl semimetals are of interest in physics and materials technology.
The high mobility of charged Weyl fermions may find use in electronics and computing.
In 2017, a research team from Vienna University of Technology carrying out experimental work to develop new materials, and a team at Rice University carrying out theoretical work, have produced material which they term Weyl–Kondo semimetals.
A group of international researchers led by a team from Boston College discovered in 2019 that the Weyl semimetal Tantalum Arsenide delivers the largest intrinsic conversion of light to electricity of any material, more than ten times larger than previously achieved.
Further reading
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See also
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Dirac cone
Dirac cones, named after Paul Dirac, are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators.
In these materials, at energies near ...
*
Dirac matter
The term Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation itself was formulated for fermions, the quasi-particles present within Dirac matter can be ...
*
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 ...
References
{{reflist
Condensed matter physics
Superfluidity