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Dirac cones, named after
Dirac cones, named after Paul Dirac
Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...
, are features that occur in some 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 that describe unusual electron transport properties of materials like graphene
Graphene () is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure.
and 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 ...
.
In these materials, at energies near the Fermi level
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by ''µ'' or ''E''F
for brevity. The Fermi level does not include the work required to remove ...
, the valence band and conduction band take the shape of the upper and lower halves of a conical surface
In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point — the ''apex'' or ''vertex'' — and any point of some fixed space curve — the ''dire ...
, meeting at what are called Dirac points.
Description
Inquantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, Dirac cones are a kind of crossing-point which electrons avoid,
where the energy of the valence and conduction bands are not equal anywhere in two dimensional lattice -space, except at the zero dimensional Dirac points. As a result of the cones, electrical conduction can be described by the movement of charge carriers
In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is ...
which are massless fermion
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 an ...
s, a situation which is handled theoretically by the relativistic 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 ...
.
The massless fermions lead to various quantum Hall effect
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
s, magnetoelectric effects in topological materials, and ultra high carrier mobility
In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobi ...
.
Dirac cones were observed in 2008-2009, using angle-resolved photoemission spectroscopy
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 ...
(ARPES) on the potassium-graphite intercalation compound
Graphite intercalation compounds are complex materials having a formula where the ion or is inserted ( intercalated) between the oppositely charged carbon layers. Typically ''m'' is much less than 1. These materials are deeply colored solids t ...
KC8.
and on several bismuth-based alloys.
As an object with three dimensions, Dirac cones are a feature of two-dimensional materials
In materials science, the term single-layer materials or 2D materials refers to crystalline solids consisting of a single layer of atoms. These materials are promising for some applications but remain the focus of research. Single-layer materials ...
or surface states, based on a linear dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
between energy and the two components of the crystal momentum x and y. However, this concept can be extended to three dimensions, where Dirac semimetals are defined by a linear dispersion relation between energy and x, y, and z. In -space, this shows up as a hypercone, which have doubly degenerate bands which also meet at Dirac points. Dirac semimetals contain both time reversal and spatial inversion symmetry; when one of these is broken, the Dirac points are split into two constituent Weyl points, and the material becomes a Weyl semimetal.
In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal cadmium arsenide
Cadmium arsenide (cadmium, Cd3arsenic, As2) is an inorganic semimetal in the List of semiconductor materials#Types of semiconductor materials, II-V family. It exhibits the Nernst effect.
Properties
Thermal
Cd3As2 dissociates between 220 and ...
.
Analog systems
Dirac points have been realized in many physical areas such asplasmonics
Plasmonics or nanoplasmonics refers to the generation, detection, and manipulation of signals at optical frequencies along metal-dielectric interfaces in the nanometer scale. Inspired by photonics, plasmonics follows the trend of miniaturizing opt ...
, phononics, or nanophotonics
Nanophotonics or nano-optics is the study of the behavior of light on the nanometer scale, and of the interaction of nanometer-scale objects with light. It is a branch of optics, optical engineering, electrical engineering, and nanotechnology. It ...
(microcavities, photonic crystals).
See also
*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 ...
References
Further reading
* * * * * * Electronic band structures {{quantum-stub