| Condensed matter physics |
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Condensed matter physics is the field ofphysics that deals with the macroscopic and microscopic physical properties ofmatter, especially thesolid andliquidphases, that arise fromelectromagnetic forces betweenatoms andelectrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include thesuperconducting phase exhibited by certain materials at extremely lowcryogenictemperatures, theferromagnetic andantiferromagnetic phases ofspins oncrystal lattices of atoms, theBose–Einstein condensates found inultracold atomic systems, andliquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying thephysical laws ofquantum mechanics,electromagnetism,statistical mechanics, and otherphysics theories to develop mathematical models and predict the properties of extremely large groups of atoms.[1]
The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists,[2] and the Division of Condensed Matter Physics is the largest division of theAmerican Physical Society.[3] These include solid state andsoft matter physicists, who studyquantum and non-quantum physical properties of matter respectively.[4] Both types study a great range of materials, providing many research, funding and employment opportunities.[5] The field overlaps withchemistry,materials science,engineering andnanotechnology, and relates closely toatomic physics andbiophysics. Thetheoretical physics of condensed matter shares important concepts and methods with that ofparticle physics andnuclear physics.[6]
A variety of topics in physics such ascrystallography,metallurgy,elasticity,magnetism, etc., were treated as distinct areas until the 1940s, when they were grouped together assolid-state physics. Around the 1960s, the study of physical properties ofliquids was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics.[7] TheBell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics.[7] According to the founding director of theMax Planck Institute for Solid State Research, physics professor Manuel Cardona, it wasAlbert Einstein who created the modern field of condensed matter physics starting with his seminal 1905 article on thephotoelectric effect andphotoluminescence which opened the fields ofphotoelectron spectroscopy andphotoluminescence spectroscopy, and later his 1907 article on thespecific heat of solids which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular thespecific heat.[8] Deputy Director of the Yale Quantum InstituteA. Douglas Stone makes a similar priority case for Einstein in his work on the synthetic history ofquantum mechanics.[9]
According to physicistPhilip Warren Anderson, the use of the term "condensed matter" to designate a field of study was coined by him andVolker Heine, when they changed the name of their group at theCavendish Laboratories,Cambridge, fromSolid state theory toTheory of Condensed Matter in 1967,[10] as they felt it better included their interest in liquids,nuclear matter, and so on.[11][12] Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in theSpringer-Verlag journalPhysics of Condensed Matter, launched in 1963.[13] The name "condensed matter physics" emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, whereas "solid state physics" was often associated with restricted industrial applications of metals and semiconductors. In the 1960s and 70s, some physicists felt the more comprehensive name better fit the funding environment andCold War politics of the time.[14]
References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 bookKinetic Theory of Liquids,[15]Yakov Frenkel proposed that "The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies. As a matter of fact, it would be more correct to unify them under the title of 'condensed bodies'".
One of the first studies of condensed states of matter was byEnglishchemistHumphry Davy, in the first decades of the nineteenth century. Davy observed that of the fortychemical elements known at the time, twenty-six hadmetallic properties such aslustre,ductility and high electrical and thermal conductivity.[16] This indicated that the atoms inJohn Dalton'satomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such asnitrogen andhydrogen could be liquefied under the right conditions and would then behave as metals.[17][note 1]
In 1823,Michael Faraday, then an assistant in Davy's lab, successfully liquefiedchlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, andoxygen.[16] Shortly after, in 1869,Irish chemistThomas Andrews studied thephase transition from a liquid to a gas and coined the termcritical point to describe the condition where a gas and a liquid were indistinguishable as phases,[19] andDutch physicistJohannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.[20]: 35–38 By 1908,James Dewar andHeike Kamerlingh Onnes were successfully able to liquefy hydrogen and the then newly discoveredhelium respectively.[16]
Paul Drude in 1900 proposed the first theoretical model for a classicalelectron moving through a metallic solid.[6] Drude's model described properties of metals in terms of a gas of free electrons, and was the first microscopic model to explain empirical observations such as theWiedemann–Franz law.[21][22]: 27–29 However, despite the success ofDrude's model, it had one notable problem: it was unable to correctly explain the electronic contribution to thespecific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.[23]: 366–368
In 1911, three years after helium was first liquefied, Onnes working atUniversity of Leiden discoveredsuperconductivity inmercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.[24] The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.[25]Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."[26]
Drude's classical model was augmented byWolfgang Pauli,Arnold Sommerfeld,Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey theFermi–Dirac statistics. Using this idea, he developed the theory ofparamagnetism in 1926. Shortly after, Sommerfeld incorporated theFermi–Dirac statistics into thefree electron model and made it better to explain the heat capacity. Two years later, Bloch usedquantum mechanics to describe the motion of an electron in a periodic lattice.[23]: 366–368
The mathematics of crystal structures developed byAuguste Bravais,Yevgraf Fyodorov and others was used to classify crystals by theirsymmetry group, and tables of crystal structures were the basis for the seriesInternational Tables of Crystallography, first published in 1935.[27]Band structure calculations were first used in 1930 to predict the properties of new materials, and in 1947John Bardeen,Walter Brattain andWilliam Shockley developed the firstsemiconductor-basedtransistor, heralding a revolution in electronics.[6]
In 1879,Edwin Herbert Hall working at theJohns Hopkins University discovered that a voltage developed across conductors which was transverse to both an electric current in the conductor and a magnetic field applied perpendicular to the current.[28] This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed theHall effect, but it was not properly explained at the time because the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics,Lev Landau in 1930 developed the theory ofLandau quantization and laid the foundation for a theoretical explanation of thequantum Hall effect which was discovered half a century later.[29]: 458–460 [30]
Magnetism as a property of matter has been known in China since 4000 BC.[31]: 1–2 However, the first modern studies of magnetism only started with the development ofelectrodynamics by Faraday,Maxwell and others in the nineteenth century, which included classifying materials asferromagnetic,paramagnetic anddiamagnetic based on their response to magnetization.[32]Pierre Curie studied the dependence of magnetization on temperature and discovered theCurie point phase transition in ferromagnetic materials.[31] In 1906,Pierre Weiss introduced the concept ofmagnetic domains to explain the main properties of ferromagnets.[33]: 9 The first attempt at a microscopic description of magnetism was byWilhelm Lenz andErnst Ising through theIsing model that described magnetic materials as consisting of a periodic lattice ofspins that collectively acquired magnetization.[31] The Ising model was solved exactly to show thatspontaneous magnetization can occur in one dimension and it is possible in higher-dimensional lattices. Further research such as by Bloch onspin waves andNéel onantiferromagnetism led to developing new magnetic materials with applications tomagnetic storage devices.[31]: 36–38, g48
The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description ofsuperconductivity and theKondo effect.[35] AfterWorld War II, several ideas from quantum field theory were applied to condensed matter problems. These included recognition ofcollective excitation modes of solids and the important notion of a quasiparticle. Soviet physicistLev Landau used the idea for theFermi liquid theory wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles.[35] Landau also developed amean-field theory for continuous phase transitions, which described ordered phases asspontaneous breakdown of symmetry. The theory also introduced the notion of anorder parameter to distinguish between ordered phases.[36] Eventually in 1956,John Bardeen,Leon Cooper andRobert Schrieffer developed the so-calledBCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated byphonons in the lattice can give rise to a bound state called aCooper pair.[37]
The study of phase transitions and the critical behavior of observables, termedcritical phenomena, was a major field of interest in the 1960s.[39]Leo Kadanoff,Benjamin Widom andMichael Fisher developed the ideas ofcritical exponents andwidom scaling. These ideas were unified byKenneth G. Wilson in 1972, under the formalism of therenormalization group in the context of quantum field theory.[39]
Thequantum Hall effect was discovered byKlaus von Klitzing, Dorda and Pepper in 1980 when they observed the Hall conductance to be integer multiples of a fundamental constant.(see figure) The effect was observed to be independent of parameters such as system size and impurities.[38] In 1981, theoristRobert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance is proportional to a topological invariant, calledChern number, whose relevance for the band structure of solids was formulated byDavid J. Thouless and collaborators.[40][41]: 69, 74 Shortly after, in 1982,Horst Störmer andDaniel Tsui observed thefractional quantum Hall effect where the conductance was now a rational multiple of the constant. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated avariational method solution, named theLaughlin wavefunction.[42] The study of topological properties of the fractional Hall effect remains an active field of research.[43] Decades later, the aforementioned topological band theory advanced byDavid J. Thouless and collaborators[44] was further expanded leading to the discovery oftopological insulators.[45][46]
In 1986,Karl Müller andJohannes Bednorz discovered the firsthigh temperature superconductor, La2-xBaxCuO4, which is superconducting at temperatures as high as 39kelvin.[47] It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role.[48] A satisfactory theoretical description of high-temperature superconductors is still not known and the field ofstrongly correlated materials continues to be an active research topic.
In 2012, several groups released preprints which suggest thatsamarium hexaboride has the properties of atopological insulator[49] in accord with the earlier theoretical predictions.[50] Since samarium hexaboride is an establishedKondo insulator, i.e. a strongly correlated electron material, it is expected that the existence of a topological Dirac surface state in this material would lead to a topological insulator with strong electronic correlations.
Theoretical condensed matter physics involves the use of theoretical models to understand properties of states of matter. These include models to study the electronic properties of solids, such as theDrude model, theband structure and thedensity functional theory. Theoretical models have also been developed to study the physics ofphase transitions, such as theGinzburg–Landau theory,critical exponents and the use of mathematical methods ofquantum field theory and therenormalization group. Modern theoretical studies involve the use ofnumerical computation of electronic structure and mathematical tools to understand phenomena such ashigh-temperature superconductivity,topological phases, andgauge symmetries.
Theoretical understanding of condensed matter physics is closely related to the notion ofemergence, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents.[37][43] For example, a range of phenomena related to high temperature superconductivity are understood poorly, although the microscopic physics of individual electrons and lattices is well known.[51] Similarly, models of condensed matter systems have been studied wherecollective excitations behave likephotons andelectrons, thereby describingelectromagnetism as an emergent phenomenon.[52] Emergent properties can also occur at the interface between materials: one example is thelanthanum aluminate-strontium titanate interface, where two band-insulators are joined to create conductivity andsuperconductivity.
The metallic state has historically been an important building block for studying properties of solids.[53] The first theoretical description of metals was given byPaul Drude in 1900 with theDrude model, which explained electrical and thermal properties by describing a metal as anideal gas of then-newly discoveredelectrons. He was able to derive the empiricalWiedemann-Franz law and get results in close agreement with the experiments.[22]: 90–91 This classical model was then improved byArnold Sommerfeld who incorporated theFermi–Dirac statistics of electrons and was able to explain the anomalous behavior of thespecific heat of metals in theWiedemann–Franz law.[22]: 101–103 In 1912, The structure of crystalline solids was studied byMax von Laue and Paul Knipping, when they observed theX-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodiclattices of atoms.[22]: 48 [54] In 1928, Swiss physicistFelix Bloch provided a wave function solution to theSchrödinger equation with aperiodic potential, known asBloch's theorem.[55]
Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions.[56] TheThomas–Fermi theory, developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as avariational parameter. Later in the 1930s,Douglas Hartree,Vladimir Fock andJohn Slater developed the so-calledHartree–Fock wavefunction as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted forexchange statistics of single particle electron wavefunctions. In general, it is very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly.[53]: 330–337 Finally in 1964–65,Walter Kohn,Pierre Hohenberg andLu Jeu Sham proposed thedensity functional theory (DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.[56]
Some states of matter exhibitsymmetry breaking, where the relevant laws of physics possess some form ofsymmetry that is broken. A common example iscrystalline solids, which break continuoustranslational symmetry. Other examples include magnetizedferromagnets, which breakrotational symmetry, and more exotic states such as the ground state of aBCSsuperconductor, that breaksU(1) phase rotational symmetry.[57][58]
Goldstone's theorem inquantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstonebosons. For example, in crystalline solids, these correspond tophonons, which are quantized versions of lattice vibrations.[59]
Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such astemperature,pressure, ormolar composition. In a single-component system, a classical phase transition occurs at a temperature (at a specific pressure) where there is an abrupt change in the order of the system. For example, when ice melts and becomes water, the ordered hexagonal crystal structure of ice is modified to a hydrogen bonded, mobile arrangement of water molecules.
Inquantum phase transitions, the temperature is set toabsolute zero, and the non-thermal control parameter, such as pressure or magnetic field, causes the phase transitions when order is destroyed byquantum fluctuations originating from theHeisenberg uncertainty principle. Here, the different quantum phases of the system refer to distinctground states of theHamiltonian matrix. Understanding the behavior of quantum phase transition is important in the difficult tasks of explaining the properties of rare-earth magnetic insulators, high-temperature superconductors, and other substances.[60]
Two classes of phase transitions occur:first-order transitions andsecond-order orcontinuous transitions. For the latter, the two phases involved do not co-exist at the transition temperature, also called thecritical point. Near the critical point, systems undergo critical behavior, wherein several of their properties such ascorrelation length,specific heat, andmagnetic susceptibility diverge exponentially.[60] These critical phenomena present serious challenges to physicists because normalmacroscopic laws are no longer valid in the region, and novel ideas and methods must be invented to find the new laws that can describe the system.[61]: 75ff
The simplest theory that can describe continuous phase transitions is theGinzburg–Landau theory, which works in the so-calledmean-field approximation. However, it can only roughly explain continuous phase transition for ferroelectrics and type I superconductors which involves long range microscopic interactions. For other types of systems that involves short range interactions near the critical point, a better theory is needed.[62]: 8–11
Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant.Renormalization group methods successively average out the shortest wavelength fluctuations in stages while retaining their effects into the next stage. Thus, the changes of a physical system as viewed at different size scales can be investigated systematically. The methods, together with powerful computer simulation, contribute greatly to the explanation of the critical phenomena associated with continuous phase transition.[61]: 11
Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects ofelectric andmagnetic fields, measuringresponse functions,transport properties andthermometry.[63] Commonly used experimental methods includespectroscopy, with probes such asX-rays,infrared light andinelastic neutron scattering; study of thermal response, such asspecific heat and measuring transport via thermal and heatconduction.
Several condensed matter experiments involve scattering of an experimental probe, such asX-ray, opticalphotons,neutrons, etc., on constituents of a material. The choice of scattering probe depends on the observation energy scale of interest.Visible light has energy on the scale of 1electron volt (eV) and is used as a scattering probe to measure variations in material properties such as thedielectric constant andrefractive index. X-rays have energies of the order of 10keV and hence are able to probe atomic length scales, and are used to measure variations in electron charge density and crystal structure.[64]: 33–34
Neutrons can also probe atomic length scales and are used to study the scattering off nuclei and electronspins and magnetization (as neutrons have spin but no charge). Coulomb andMott scattering measurements can be made by usingelectron beams as scattering probes.[64]: 33–34 [65]: 39–43 Similarly,positron annihilation can be used as an indirect measurement of local electron density.[66]Laser spectroscopy is an excellent tool for studying the microscopic properties of a medium, for example, to studyforbidden transitions in media withnonlinear optical spectroscopy.[61]: 258–259
In experimental condensed matter physics, externalmagnetic fields act asthermodynamic variables that control the state, phase transitions and properties of material systems.[67]Nuclear magnetic resonance (NMR) is a method by which externalmagnetic fields are used to find resonance modes of individual nuclei, thus giving information about the atomic, molecular, and bond structure of their environment. NMR experiments can be made in magnetic fields with strengths up to 60tesla. Higher magnetic fields can improve the quality of NMR measurement data.[68]: 69 [69]: 185 Quantum oscillations is another experimental method where high magnetic fields are used to study material properties such as the geometry of theFermi surface.[70] High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantizedmagnetoelectric effect, imagemagnetic monopole, and the half-integerquantum Hall effect.[68]: 57
Thelocal structure, as well as the structure of the nearest neighbour atoms, can be investigated in condensed matter with magnetic resonance methods, such aselectron paramagnetic resonance (EPR) andnuclear magnetic resonance (NMR), which are very sensitive to the details of the surrounding of nuclei and electrons by means of the hyperfine coupling. Both localized electrons and specific stable or unstable isotopes of thenuclei become the probe of thesehyperfine interactions), which couple the electron or nuclear spin to the local electric and magnetic fields. These methods are suitable to study defects, diffusion, phase transitions and magnetic order. Common experimental methods includeNMR,nuclear quadrupole resonance (NQR), implanted radioactive probes as in the case ofmuon spin spectroscopy (SR),Mössbauer spectroscopy,NMR andperturbed angular correlation (PAC). PAC is especially ideal for the study of phase changes at extreme temperatures above 2000 °C due to the temperature independence of the method.
Ultracold atom trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and inatomic, molecular, and optical physics. The method involves using optical lasers to form aninterference pattern, which acts as alattice, in which ions or atoms can be placed at very low temperatures. Cold atoms in optical lattices are used asquantum simulators, that is, they act as controllable systems that can model behavior of more complicated systems, such asfrustrated magnets.[71] In particular, they are used to engineer one-, two- and three-dimensional lattices for aHubbard model with pre-specified parameters, and to study phase transitions forantiferromagnetic andspin liquid ordering.[72][73][43]
In 1995, a gas ofrubidium atoms cooled down to a temperature of 170nK was used to experimentally realize theBose–Einstein condensate, a novel state of matter originally predicted byS. N. Bose andAlbert Einstein, wherein a large number of atoms occupy onequantum state.[74]
Research in condensed matter physics[43][75] has given rise to several device applications, such as the development of thesemiconductortransistor,[6]laser technology,[61]magnetic storage,liquid crystals,optical fibres[76] and several phenomena studied in the context ofnanotechnology.[77]: 111ff Methods such asscanning-tunneling microscopy can be used to control processes at thenanometer scale, and have given rise to the study of nanofabrication.[78] Such molecular machines were developed for example by Nobel laureates in chemistryBen Feringa,Jean-Pierre Sauvage andFraser Stoddart. Feringa and his team developed multiple molecular machines such as themolecular car, molecular windmill and many more.[79]
Inquantum computation, information is represented by quantum bits, orqubits. The qubits maydecohere quickly before useful computation is completed. This serious problem must be solved before quantum computing may be realized. To solve this problem, several promising approaches are proposed in condensed matter physics, includingJosephson junction qubits,spintronic qubits using thespin orientation of magnetic materials, and the topological non-Abeliananyons fromfractional quantum Hall effect states.[78]
Condensed matter physics also has important uses forbiomedicine. For example,magnetic resonance imaging is widely used in medical imaging of soft tissue and other physiological features which cannot be viewed with traditional x-ray imaging.[78]
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