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condensed matter physics

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**Condensed matter physics**is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the constituents are strong. The most familiar examples of condensed phases are solids and liquids, which arise from the electromagnetic forces between atoms. Condensed matter physicists seek to understand the behavior of these phases by using physical laws. In particular, they include the laws of quantum mechanics, electromagnetism and statistical mechanics.The most familiar condensed phases are solids and liquids while more exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Boseâ€“Einstein condensate found in ultracold atomic systems. The study of condensed matter physics involves measuring various material properties via experimental probes along with using methods of theoretical physics to develop mathematical models that help in understanding physical behavior.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,WEB,weblinkweblink" title="web.archive.org/web/20090327141400weblink">weblink 2009-03-27, Physics Today Jobs, Condensed Matter Physics Jobs: Careers in Condensed Matter Physics, 2010-11-01, and the Division of Condensed Matter Physics is the largest division at the American Physical Society.WEB, History of Condensed Matter Physics,weblink American Physical Society, 27 March 2012, The field overlaps with chemistry, materials science, and nanotechnology, and relates closely to atomic physics and biophysics. The theoretical physics of condensed matter shares important concepts and methods with that of particle physics and nuclear physics.JOURNAL, Cohen, Marvin L., Essay: Fifty Years of Condensed Matter Physics, Physical Review Letters, 2008, 101, 25, 10.1103/PhysRevLett.101.250001,weblink 31 March 2012, 2008PhRvL.101y0001C, 19113681, 250001, A variety of topics in physics such as crystallography, metallurgy, elasticity, magnetism, etc., were treated as distinct areas until the 1940s, when they were grouped together as

*solid state physics*. Around the 1960s, the study of physical properties of liquids was added to this list, forming the basis for the new, related specialty of condensed matter physics. According to physicist Philip Warren Anderson, the term was coined by him and Volker Heine, when they changed the name of their group at the Cavendish Laboratories, Cambridge from

*Solid state theory*to

*Theory of Condensed Matter*in 1967,WEB, Philip Anderson,weblink Department of Physics, Princeton University, 27 March 2012, as they felt it did not exclude their interests in the study of liquids, nuclear matter, and so on.JOURNAL, In Focus: More and Different,weblink World Scientific Newsletter, November 2011, 33, 2, Anderson, Philip W., Although Anderson and Heine helped popularize the name "condensed matter", it had been present in Europe for some years, most prominently in the form of a journal published in English, French, and German by Springer-Verlag titled

*Physics of Condensed Matter*, which was launched in 1963.WEB,weblink

*Physics of Condensed Matter*, 1, 20 April 2015, 1963, The funding environment and Cold War politics of the 1960s and 1970s were also factors that lead some physicists to prefer the name "condensed matter physics", which emphasized the commonality of scientific problems encountered by physicists working on solids, liquids, plasmas, and other complex matter, over "solid state physics", which was often associated with the industrial applications of metals and semiconductors.JOURNAL, Martin, Joseph D., What's in a Name Change? Solid State Physics, Condensed Matter Physics, and Materials Science, Physics in Perspective, 2015, 17, 1, 10.1007/s00016-014-0151-7, 3â€“32, 2015PhP....17....3M, The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics.JOURNAL, Kohn, W., An essay on condensed matter physics in the twentieth century, Reviews of Modern Physics, 1999, 71, 2,weblink 27 March 2012, 10.1103/RevModPhys.71.S59, S59â€“S77, 1999RvMPS..71...59K, dead,weblink" title="web.archive.org/web/20130825164926weblink">weblink 25 August 2013, References to "condensed" state can be traced to earlier sources. For example, in the introduction to his 1947 book

*Kinetic Theory of Liquids*,BOOK, Frenkel, J., Kinetic Theory of Liquids, 1947, Oxford University Press, 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'".

## History of classical physics

### Classical physics

File:Heike Kamerlingh Onnes and Johannes Diderik van der Waals.jpg|thumb|right|Heike Kamerlingh Onnes and Johannes van der Waals with the heliumheliumOne of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity.JOURNAL, Goodstein, David, David Goodstein, Goodstein, Judith, Judith R. Goodstein, Richard Feynman and the History of Superconductivity, Physics in Perspective, 2000, 2, 1,weblink 7 April 2012, 10.1007/s000160050035, 30, 2000PhP.....2...30G, This indicated that the atoms in John Dalton's atomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as nitrogen and hydrogen could be liquefied under the right conditions and would then behave as metals.BOOK, Davy, John, The collected works of Sir Humphry Davy: Vol. II, 1839, Smith Elder & Co., Cornhill,weblink {{NoteTag|Both hydrogen and nitrogen have since been liquified; however, ordinary liquid nitrogen and hydrogen do not possess metallic properties. Physicists Eugene Wigner and Hillard Bell Huntington predicted in 1935JOURNAL, Silvera, Isaac F., Cole, John W., Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist, Journal of Physics, 2010, 215, 1, 10.1088/1742-6596/215/1/012194, 2010JPhCS.215a2194S, 012194,weblink that a state metallic hydrogen exists at sufficiently high pressures (over 25 GPa), but this has not yet been observed.}}In 1823, Michael Faraday, then an assistant in Davy's lab, successfully liquefied chlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and oxygen. Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase transition from a liquid to a gas and coined the term critical point to describe the condition where a gas and a liquid were indistinguishable as phases,JOURNAL, Rowlinson, J. S., Thomas Andrews and the Critical Point, Nature, 1969, 224, 8, 10.1038/224541a0, 541â€“543, 1969Natur.224..541R, and Dutch physicist Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.BOOK, Atkins, Peter, de Paula, Julio, Elements of Physical Chemistry, 2009, Oxford University Press, 978-1-4292-1813-9, {{rp|35â€“38}} By 1908, James Dewar and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively.Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. 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 the Wiedemannâ€“Franz law.BOOK, Kittel, Charles, Introduction to Solid State Physics, 1996, John Wiley & Sons, 978-0-471-11181-8, BOOK, Hoddeson, Lillian, Out of the Crystal Maze: Chapters from The History of Solid State Physics, 1992, Oxford University Press, 978-0-19-505329-6,weblink {{rp|27â€“29}} However, despite the success of Drude's free electron model, it had one notable problem: it was unable to correctly explain the electronic contribution to the specific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures.BOOK, Kragh, Helge, Quantum Generations: A History of Physics in the Twentieth Century, Princeton University Press, Reprint, 2002, 978-0-691-09552-3, {{rp|366â€“368}}In 1911, three years after helium was first liquefied, Onnes working at University of Leiden discovered superconductivity in mercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.JOURNAL, van Delft, Dirk, Kes, Peter, The discovery of superconductivity, Physics Today, September 2010, 63, 9, 10.1063/1.3490499,weblink 7 April 2012, 2010PhT....63i..38V, 38â€“43, The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.WEB, Slichter, Charles, Introduction to the History of Superconductivity,weblink Moments of Discovery, American Institute of Physics, 13 June 2012, 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."JOURNAL, Schmalian, Joerg, Failed theories of superconductivity, 2010, 1008.0447, 2010MPLB...24.2679S, 10.1142/S0217984910025280, Modern Physics Letters B, 24, 27, 2679â€“2691,### Advent of quantum mechanics

Drude's classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey the Fermiâ€“Dirac statistics. Using this idea, he developed the theory of paramagnetism in 1926. Shortly after, Sommerfeld incorporated the Fermiâ€“Dirac statistics into the free electron model and made it better to explain the heat capacity. Two years later, Bloch used quantum mechanics to describe the motion of an electron in a periodic lattice.{{rp|366â€“368}} The mathematics of crystal structures developed by Auguste Bravais, Yevgraf Fyodorov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series*International Tables of Crystallography*, first published in 1935.BOOK, Aroyo, Mois, I., MÃ¼ller, Ulrich, Wondratschek, Hans, Historical introduction, 2006, A, 2â€“5, 10.1107/97809553602060000537, International Tables for Crystallography, 978-1-4020-2355-2,weblink 10.1.1.471.4170, Band structure calculations was first used in 1930 to predict the properties of new materials, and in 1947 John Bardeen, Walter Brattain and William Shockley developed the first semiconductor-based transistor, heralding a revolution in electronics.File:Replica-of-first-transistor.jpg|thumb|left|A replica of the first point-contact transistor in Bell labsBell labsIn 1879, Edwin Herbert Hall working at the Johns Hopkins University discovered a voltage developed across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current.JOURNAL, On a New Action of the Magnet on Electric Currents, Hall, Edwin, American Journal of Mathematics, 2, 1879, 287â€“92,weblink 2008-02-28, 10.2307/2369245, 3, 2369245, dead,weblink" title="web.archive.org/web/20070208040346weblink">weblink 2007-02-08, This phenomenon arising due to the nature of charge carriers in the conductor came to be termed the Hall effect, but it was not properly explained at the time, since the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics, Lev Landau in 1930 developed the theory of Landau quantization and laid the foundation for the theoretical explanation for the quantum Hall effect discovered half a century later.BOOK, L. D., Landau, E. M., Lifshitz, Quantum Mechanics: Nonrelativistic Theory, 1977, Pergamon Press, 978-0-7506-3539-4, {{rp|458â€“460}}WEB,weblink Focus: Landmarksâ€”Accidental Discovery Leads to Calibration Standard, 2015-05-15, David, Lindley, APS Physics, 2016-01-09,weblink" title="web.archive.org/web/20150907134436weblink">weblink 2015-09-07, Magnetism as a property of matter has been known in China since 4000 BC.BOOK, Mattis, Daniel, The Theory of Magnetism Made Simple, 2006, World Scientific, 978-981-238-671-7, {{rp|1â€“2}} However, the first modern studies of magnetism only started with the development of electrodynamics by Faraday, Maxwell and others in the nineteenth century, which included classifying materials as ferromagnetic, paramagnetic and diamagnetic based on their response to magnetization.JOURNAL, Chatterjee, Sabyasachi, Heisenberg and Ferromagnetism, Resonance, August 2004, 9, 8, 10.1007/BF02837578,weblink 13 June 2012, 57â€“66, Pierre Curie studied the dependence of magnetization on temperature and discovered the Curie point phase transition in ferromagnetic materials. In 1906, Pierre Weiss introduced the concept of magnetic domains to explain the main properties of ferromagnets.BOOK, Visintin, Augusto, Differential Models of Hysteresis, 1994, Springer, 978-3-540-54793-8,weblink {{rp|9}} The first attempt at a microscopic description of magnetism was by Wilhelm Lenz and Ernst Ising through the Ising model that described magnetic materials as consisting of a periodic lattice of spins that collectively acquired magnetization. The Ising model was solved exactly to show that spontaneous magnetization cannot occur in one dimension but is possible in higher-dimensional lattices. Further research such as by Bloch on spin waves and NÃ©el on antiferromagnetism led to developing new magnetic materials with applications to magnetic storage devices.{{rp|36â€“38,g48}}

### Modern many-body physics

File:Meissner effect p1390048.jpg|thumb|left|200px|alt=A magnet levitating over a superconducting material.|A magnet levitating above a (high-temperature superconductor]]. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.JOURNAL, Merali, Zeeya, Collaborative physics: string theory finds a bench mate, Nature, 478, 302â€“304, 2011, 10.1038/478302a, 22012369, 7369, 2011Natur.478..302M, )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 of superconductivity and the Kondo effect.JOURNAL, Coleman, Piers, Many-Body Physics: Unfinished Revolution, Annales Henri PoincarÃ©, 2003, 4, 2, 10.1007/s00023-003-0943-9, cond-mat/0307004, 2003AnHP....4..559C, 559â€“580, 10.1.1.242.6214, After World War II, several ideas from quantum field theory were applied to condensed matter problems. These included recognition of collective excitation modes of solids and the important notion of a quasiparticle. Russian physicist Lev Landau used the idea for the Fermi liquid theory wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles. Landau also developed a mean field theory for continuous phase transitions, which described ordered phases as spontaneous breakdown of symmetry. The theory also introduced the notion of an order parameter to distinguish between ordered phases.BOOK, Kadanoff, Leo, P., Phases of Matter and Phase Transitions; From Mean Field Theory to Critical Phenomena, 2009, The University of Chicago,weblink Eventually in 1965, John Bardeen, Leon Cooper and John Schrieffer developed the so-called BCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by phonons in the lattice can give rise to a bound state called a Cooper pair.File:Quantum Hall effect - Russian.png|thumb|right|The (quantum Hall effect]]: Components of the Hall resistivity as a function of the external magnetic field{{rp|fig. 14}})The study of phase transition and the critical behavior of observables, termed critical phenomena, was a major field of interest in the 1960s.JOURNAL, Fisher, Michael E., Renormalization group theory: Its basis and formulation in statistical physics, Reviews of Modern Physics, 1998, 70, 2, 10.1103/RevModPhys.70.653, 1998RvMP...70..653F, 653â€“681, 10.1.1.129.3194, Leo Kadanoff, Benjamin Widom and Michael Fisher developed the ideas of critical exponents and widom scaling. These ideas were unified by Kenneth G. Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory.The quantum Hall effect was discovered by Klaus von Klitzing in 1980 when he observed the Hall conductance to be integer multiples of a fundamental constant e^2/h.(see figure) The effect was observed to be independent of parameters such as system size and impurities.WEB,weblink The Quantized Hall Effect, von Klitzing, Klaus, 9 Dec 1985, Nobelprize.org, In 1981, theorist Robert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance can be characterized in terms of a topological invariable called Chern number.JOURNAL, Avron, Joseph E., Osadchy, Daniel, Seiler, Ruedi, A Topological Look at the Quantum Hall Effect, Physics Today, 2003, 56, 8, 10.1063/1.1611351, 2003PhT....56h..38A, 38â€“42, BOOK, David J Thouless, Topological Quantum Numbers in Nonrelativistic Physics, 12 March 1998, World Scientific, 978-981-4498-03-6, {{rp|69, 74}} Shortly after, in 1982, Horst StÃ¶rmer and Daniel Tsui observed the fractional quantum Hall effect where the conductance was now a rational multiple of a constant. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a variational method solution, named the Laughlin wavefunction.JOURNAL, Wen, Xiao-Gang, Theory of the edge states in fractional quantum Hall effects, International Journal of Modern Physics C, 1992, 6, 10, 1711â€“1762,weblink 14 June 2012, 10.1142/S0217979292000840, 1992IJMPB...6.1711W, 10.1.1.455.2763,weblink" title="web.archive.org/web/20050522083243weblink">weblink 22 May 2005, dead, The study of topological properties of the fractional Hall effect remains an active field of research.In 1986, Karl MÃ¼ller and Johannes Bednorz discovered the first high temperature superconductor, a material which was superconducting at temperatures as high as 50 kelvins. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electronâ€“electron interactions play an important role.JOURNAL, Quintanilla, Jorge, Hooley, Chris, The strong-correlations puzzle, Physics World, June 2009,weblink 14 June 2012, dead,weblink" title="web.archive.org/web/20120906002714weblink">weblink 6 September 2012, A satisfactory theoretical description of high-temperature superconductors is still not known and the field of strongly correlated materials continues to be an active research topic.In 2009, David Field and researchers at Aarhus University discovered spontaneous electric fields when creating prosaic films{{clarify|date=April 2016}} of various gases. This has more recently expanded to form the research area of spontelectrics.JOURNAL, Field, David, Plekan, O., Cassidy, A., Balog, R., Jones, N.C. and Dunger, J., Spontaneous electric fields in solid films: spontelectrics, Int.Rev.Phys.Chem., 12 Mar 2013, 10.1080/0144235X.2013.767109, 32, 3, 345â€“392, In 2012 several groups released preprints which suggest that samarium hexaboride has the properties of a topological insulator JOURNAL,weblink Nature (journal), Nature, Hopes surface for exotic insulator, Eugenie Samuel Reich, in accord with the earlier theoretical predictions.JOURNAL, 10.1103/PhysRevLett.104.106408, 20366446, 104, 10, 106408, Dzero, V., K. Sun, V. Galitski, P. Coleman, Topological Kondo Insulators, Physical Review Letters, 2010, 0912.3750, 2010PhRvL.104j6408D, Since samarium hexaboride is an established Kondo insulator, i.e. a strongly correlated electron material, the existence of a topological surface state in this material would lead to a topological insulator with strong electronic correlations.## Theoretical

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 the Drude model, the Band structure and the density functional theory. Theoretical models have also been developed to study the physics of phase transitions, such as the Ginzburgâ€“Landau theory, critical exponents and the use of mathematical methods of quantum field theory and the renormalization group. Modern theoretical studies involve the use of numerical computation of electronic structure and mathematical tools to understand phenomena such as high-temperature superconductivity, topological phases, and gauge symmetries.### Emergence

Theoretical understanding of condensed matter physics is closely related to the notion of emergence, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents.BOOK, Coleman, Piers, Introduction to Many Body Physics, 2016, Cambridge University Press, 978-0-521-86488-6,weblink 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.WEB, Understanding Emergence,weblink National Science Foundation, 30 March 2012, Similarly, models of condensed matter systems have been studied where collective excitations behave like photons and electrons, thereby describing electromagnetism as an emergent phenomenon.JOURNAL, Levin, Michael, Wen, Xiao-Gang, Colloquium: Photons and electrons as emergent phenomena, Reviews of Modern Physics, 2005, 77, 3, 10.1103/RevModPhys.77.871, cond-mat/0407140, 2005RvMP...77..871L, 871â€“879, Emergent properties can also occur at the interface between materials: one example is the lanthanum aluminate-strontium titanate interface, where two non-magnetic insulators are joined to create conductivity, superconductivity, and ferromagnetism.### Electronic theory of solids

The metallic state has historically been an important building block for studying properties of solids. The first theoretical description of metals was given by Paul Drude in 1900 with the Drude model, which explained electrical and thermal properties by describing a metal as an ideal gas of then-newly discovered electrons. He was able to derive the empirical Wiedemann-Franz law and get results in close agreement with the experiments.{{rp|90â€“91}} This classical model was then improved by Arnold Sommerfeld who incorporated the Fermiâ€“Dirac statistics of electrons and was able to explain the anomalous behavior of the specific heat of metals in the Wiedemannâ€“Franz law.{{rp|101â€“103}} In 1912, The structure of crystalline solids was studied by Max von Laue and Paul Knipping, when they observed the X-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms.{{rp|48}}JOURNAL, Eckert, Michael, Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions, Acta Crystallographica A, 2011, 68, 1, 10.1107/S0108767311039985, 22186281,weblink 2012AcCrA..68...30E, 30â€“39, In 1928, Swiss physicist Felix Bloch provided a wave function solution to the SchrÃ¶dinger equation with a periodic potential, called the Bloch wave.BOOK, Han, Jung Hoon, Solid State Physics, 2010, Sung Kyun Kwan University,weblink dead,weblink" title="web.archive.org/web/20130520224858weblink">weblink 2013-05-20, 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.JOURNAL, Perdew, John P., Ruzsinszky, Adrienn, Fourteen Easy Lessons in Density Functional Theory, International Journal of Quantum Chemistry, 2010, 110, 2801â€“2807,weblink 13 May 2012, 10.1002/qua.22829, 15, The Thomasâ€“Fermi theory, developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a variational parameter. Later in the 1930s, Douglas Hartree, Vladimir Fock and John Slater developed the so-called Hartreeâ€“Fock wavefunction as an improvement over the Thomasâ€“Fermi model. The Hartreeâ€“Fock method accounted for exchange statistics of single particle electron wavefunctions. In general, it's very difficult to solve the Hartreeâ€“Fock equation. Only the free electron gas case can be solved exactly.BOOK, Neil W. Ashcroft, N. David Mermin, Solid state physics, 1976, Saunders College, 978-0-03-049346-1, {{rp|330â€“337}} Finally in 1964â€“65, Walter Kohn, Pierre Hohenberg and Lu Jeu Sham proposed the density functional theory which gave realistic descriptions for bulk and surface properties of metals. The density functional theory (DFT) has been widely used since the 1970s for band structure calculations of variety of solids.### Symmetry breaking

Some states of matter exhibit*symmetry breaking*, where the relevant laws of physics possess some form of symmetry that is broken. A common example is crystalline solids, which break continuous translational symmetry. Other examples include magnetized ferromagnets, which break rotational symmetry, and more exotic states such as the ground state of a BCS superconductor, that breaks U(1) phase rotational symmetry.WEB,weblink Spontaneous Symmetry Breaking in Particle Physics: a Case of Cross Fertilization, Nambu, Yoichiro, 8 December 2008, Nobelprize.org, JOURNAL, Greiter, Martin, cond-mat/0503400, Is electromagnetic gauge invariance spontaneously violated in superconductors?, 16 March 2005, 10.1016/j.aop.2005.03.008, 319, 2005, Annals of Physics, 217â€“249, 2005AnPhy.319..217G, Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons. For example, in crystalline solids, these correspond to phonons, which are quantized versions of lattice vibrations.JOURNAL, Leutwyler, H., Phonons as Goldstone bosons, Helv.phys.acta ), 70, 1997, 1997, hep-ph/9609466, 1996hep.ph....9466L, 275â€“286,

### Phase transition

Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as temperature. Classical phase transition occurs at finite temperature when the order of the system was destroyed. For example, when ice melts and becomes water, the ordered crystal structure is destroyed. In quantum phase transitions, the temperature is set to absolute zero, and the non-thermal control parameter, such as pressure or magnetic field, causes the phase transitions when order is destroyed by quantum fluctuations originating from the Heisenberg uncertainty principle. Here, the different quantum phases of the system refer to distinct ground states of the Hamiltonian 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.Two classes of phase transitions occur:*first-order transitions*and

*second-order*or

*continuous transitions*. For the latter, the two phases involved do not co-exist at the transition temperature, also called the critical point. Near the critical point, systems undergo critical behavior, wherein several of their properties such as correlation length, specific heat, and magnetic susceptibility diverge exponentially.JOURNAL, Vojta, Matthias, cond-mat/0309604, Quantum phase transitions, 2003, 10.1088/0034-4885/66/12/R01, 66, 12, Reports on Progress in Physics, 2069â€“2110, 2003RPPh...66.2069V, 10.1.1.305.3880, These critical phenomena present serious challenges to physicists because normal macroscopic 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.BOOK, Condensed-Matter Physics, Physics Through the 1990s, National Research Council, 1986,weblink 978-0-309-03577-4, {{rp|75ff}}The simplest theory that can describe continuous phase transitions is the Ginzburgâ€“Landau theory, which works in the so-called mean 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.BOOK, Malcolm F. Collins Professor of Physics McMaster University, Magnetic Critical Scattering, Oxford University Press, USA, 978-0-19-536440-8, 1989-03-02, {{rp|8â€“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.{{rp|11}}

## Experimental

Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of electric and magnetic fields, measuring response functions, transport properties and thermometry.BOOK, Richardson, Robert C., Experimental methods in Condensed Matter Physics at Low Temperatures, 1988, Addison-Wesley, 978-0-201-15002-5, Commonly used experimental methods include spectroscopy, with probes such as X-rays, infrared light and inelastic neutron scattering; study of thermal response, such as specific heat and measuring transport via thermal and heat conduction.File:Lysozym diffraction.png|thumb|upright|Image of X-ray diffraction pattern from a proteinprotein### Scattering

{{Further|Scattering}}Several condensed matter experiments involve scattering of an experimental probe, such as X-ray, optical photons, 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 1 electron volt (eV) and is used as a scattering probe to measure variations in material properties such as dielectric constant and refractive index. X-rays have energies of the order of 10 keV and hence are able to probe atomic length scales, and are used to measure variations in electron charge density.BOOK, Chaikin, P. M., Lubensky, T. C., Principles of condensed matter physics, 1995, Cambridge University Press, 978-0-521-43224-5, registration,weblink {{rp|33â€“34}}Neutrons can also probe atomic length scales and are used to study scattering off nuclei and electron spins and magnetization (as neutrons have spin but no charge). Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes.{{rp|33â€“34}}BOOK, Wentao Zhang, Photoemission Spectroscopy on High Temperature Superconductor: A Study of Bi2Sr2CaCu2O8 by Laser-Based Angle-Resolved Photoemission, 22 August 2012, Springer Science & Business Media, 978-3-642-32472-7, {{rp|39â€“43}} Similarly, positron annihilation can be used as an indirect measurement of local electron density.JOURNAL, Siegel, R. W., Positron Annihilation Spectroscopy, Annual Review of Materials Science, 1980, 10, 393â€“425, 10.1146/annurev.ms.10.080180.002141, 1980AnRMS..10..393S, Laser spectroscopy is an excellent tool for studying the microscopic properties of a medium, for example, to study forbidden transitions in media with nonlinear optical spectroscopy. {{rp|258â€“259}}### External magnetic fields

In experimental condensed matter physics, external magnetic fields act as thermodynamic variables that control the state, phase transitions and properties of material systems.WEB, Committee on Facilities for Condensed Matter Physics, Report of the IUPAP working group on Facilities for Condensed Matter Physics : High Magnetic Fields,weblink International Union of Pure and Applied Physics, 2004, The magnetic field is not simply a spectroscopic tool but is a thermodynamic variable which, along with temperature and pressure, controls the state, the phase transitions and the properties of materials., Nuclear magnetic resonance (NMR) is a method by which external magnetic fields are used to find resonance modes of individual electrons, thus giving information about the atomic, molecular, and bond structure of their neighborhood. NMR experiments can be made in magnetic fields with strengths up to 60 Tesla. Higher magnetic fields can improve the quality of NMR measurement data.{{rp|69}}BOOK, High Magnetic Fields, Nuclear Magnetic Resonance in Solids at very high magnetic fields, Moulton, W. G., Reyes, A. P., Herlach, Fritz, Science and Technology, World Scientific, 2006,weblink 978-981-277-488-0, {{rp|185}} Quantum oscillations is another experimental method where high magnetic fields are used to study material properties such as the geometry of the Fermi surface.JOURNAL, Doiron-Leyraud, Nicolas, Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor, Nature, 2007, 447, 565â€“568, 10.1038/nature05872, 0801.1281, 2007Natur.447..565D, 7144, 17538614, etal, High magnetic fields will be useful in experimentally testing of the various theoretical predictions such as the quantized magnetoelectric effect, image magnetic monopole, and the half-integer quantum Hall effect.BOOK, Committee to Assess the Current Status and Future Direction of High Magnetic Field Science in the United States; Board on Physics and Astronomy; Division on Engineering and Physical Sciences; National Research Council, High Magnetic Field Science and Its Application in the United States: Current Status and Future Directions,weblink 25 November 2013, National Academies Press, 978-0-309-28634-3, {{rp|57}}### Cold atomic gases

File:Bose Einstein condensate.png|thumb|left|The first Boseâ€“Einstein condensate observed in a gas of ultracold rubidiumrubidiumUltracold atom trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in atomic, molecular, and optical physics. The method involves using optical lasers to form an interference pattern, which acts as a*lattice*, in which ions or atoms can be placed at very low temperatures. Cold atoms in optical lattices are used as

*quantum simulators*, that is, they act as controllable systems that can model behavior of more complicated systems, such as frustrated magnets.JOURNAL, Buluta, Iulia, Nori, Franco, Quantum Simulators, Science, 2009, 326, 5949, 10.1126/science.1177838, 2009Sci...326..108B, 108â€“11, 19797653, In particular, they are used to engineer one-, two- and three-dimensional lattices for a Hubbard model with pre-specified parameters, and to study phase transitions for antiferromagnetic and spin liquid ordering.JOURNAL, Greiner, Markus, FÃ¶lling, Simon, Condensed-matter physics: Optical lattices, Nature, 2008, 453, 736â€“738, 10.1038/453736a, 2008Natur.453..736G, 7196, 18528388, JOURNAL, Jaksch, D., Zoller, P., The cold atom Hubbard toolbox, Annals of Physics, 2005, 315, 1, 52â€“79, 10.1016/j.aop.2004.09.010, cond-mat/0410614, 2005AnPhy.315...52J, 10.1.1.305.9031, In 1995, a gas of rubidium atoms cooled down to a temperature of 170 nK was used to experimentally realize the Boseâ€“Einstein condensate, a novel state of matter originally predicted by S. N. Bose and Albert Einstein, wherein a large number of atoms occupy one quantum state.NEWS, Glanz, James, 3 Researchers Based in U.S. Win Nobel Prize in Physics,weblink 23 May 2012, The New York Times, October 10, 2001,

## Applications

File:Fullerene Nanogears - GPN-2000-001535.jpg|thumb|right|Computer simulation of*nanogears*made of fullerenefullereneResearch in condensed matter physics has given rise to several device applications, such as the development of the semiconductor transistor, laser technology, and several phenomena studied in the context of nanotechnology.BOOK, Committee on CMMP 2010; Solid State Sciences Committee; Board on Physics and Astronomy; Division on Engineering and Physical Sciences, National Research Council, Condensed-Matter and Materials Physics: The Science of the World Around Us,weblink 21 December 2007, National Academies Press, 978-0-309-13409-5, {{rp|111ff}} Methods such as scanning-tunneling microscopy can be used to control processes at the nanometer scale, and have given rise to the study of nanofabrication.JOURNAL, Yeh, Nai-Chang, A Perspective of Frontiers in Modern Condensed Matter Physics, AAPPS Bulletin, 2008, 18, 2,weblink 19 June 2018, In quantum computation, information is represented by quantum bits, or qubits. The qubits may decohere 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, including Josephson junction qubits, spintronic qubits using the spin orientation of magnetic materials, or the topological non-Abelian anyons from fractional quantum Hall effect states.Condensed matter physics also has important uses for biophysics, for example, the experimental method of magnetic resonance imaging, which is widely used in medical diagnosis.

## See also

{{Div col}}- Soft matter
- Greenâ€“Kubo relations
- Green's function (many-body theory)
- Materials science
- Comparison of software for molecular mechanics modeling
- Transparent materials
- Orbital magnetization
- Symmetry in quantum mechanics
- Mesoscopic physics

## Notes

{{NoteFoot}}## References

{{Reflist}}## Further reading

- BOOK, Lecture Notes on Field Theory in Condensed Matter Physics, World Scientific, 2014, Mudry, Christopher, 978-981-4449-10-6, 10.1142/8697,
- JOURNAL, Khan, Abdul Qadeer, Abdul Qadeer Khan, Dimensional Anistrophy in Condensed Matter Physics, Seven National Symposium on Frontiers in Physics,weblink 21 November 1998, 7, 7, 7, 21 October 2012,
- P. M. Chaikin and T. C. Lubensky (2000).
*Principles of Condensed Matter Physics*, Cambridge University Press; 1st edition, {{ISBN|0-521-79450-1}}. - Alexander Altland and Ben Simons (2006).
*Condensed Matter Field Theory*, Cambridge University Press, {{ISBN|0-521-84508-4}}. - Michael P. Marder (2010).
*Condensed Matter Physics, second edition*, John Wiley and Sons, {{ISBN|0-470-61798-5}}. - Lillian Hoddeson, Ernest Braun, JÃ¼rgen Teichmann and Spencer Weart, eds. (1992).
*Out of the Crystal Maze: Chapters from the History of Solid State Physics*, Oxford University Press, {{ISBN|0-19-505329-X}}.

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