Condensed matter physics

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Condensed matter physics
States of matter
Phase phenomena
Electronic phases
Electronic phenomena
Magnetic phases
Quasiparticles
Soft matter
Scientists

Condensed matter physics is the field of

physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics 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 the American Physical Society.[3] These include solid state and soft matter physicists, who study quantum 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 with chemistry, materials science, engineering 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.[6]

A variety of topics in physics such as

specific heat.[8] Deputy Director of the Yale Quantum Institute A. Douglas Stone makes a similar priority case for Einstein in his work on the synthetic history of quantum mechanics.[9]

Etymology

According to physicist

Cavendish Laboratories, Cambridge from Solid state theory to Theory 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 the Springer-Verlag journal Physics 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 and Cold War politics of the time.[14]

References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic 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'".

History

Further information: Timeline of condensed matter physics

Classical physics

Johannes van der Waals with the helium
liquefactor at Leiden in 1908

One of the first studies of condensed states of matter was by

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.[17][note 1]

In 1823,

Johannes 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 and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively.[16]

specific 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 at

University of Leiden discovered superconductivity in mercury, 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]

Advent of quantum mechanics

Drude's classical model was augmented by

Walter Brattain and William Shockley developed the first semiconductor-based transistor, heralding a revolution in electronics.[6]

Bell labs

In 1879,

Landau quantization and laid the foundation for the theoretical explanation for the quantum Hall effect discovered half a century later.[29]: 458–460 [30]

Magnetism as a property of matter has been known in China since 4000 BC.

Néel on antiferromagnetism led to developing new magnetic materials with applications to magnetic storage devices.[31]
: 36–38, g48 

Modern many-body physics

high-temperature superconductor. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.[34]

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

Robert 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.[37]

The quantum Hall effect: Components of the Hall resistivity as a function of the external magnetic field[38]: fig. 14 

The study of phase transitions and the critical behavior of observables, termed critical phenomena, was a major field of interest in the 1960s.[39] 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.[39]

The quantum Hall effect was discovered by Klaus 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.

Daniel Tsui observed the fractional 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 a
variational method solution, named the Laughlin 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 by David J. Thouless and collaborators[44] was further expanded leading to the discovery of topological insulators.[45][46]

In 1986,

high temperature superconductor, La2-xBaxCuO4, which is superconducting at temperatures as high as 39 kelvin. [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 of strongly correlated materials
continues to be an active research topic.

In 2012, several groups released preprints which suggest that samarium hexaboride has the properties of a topological insulator[49] in accord with the earlier theoretical predictions.[50] Since samarium hexaboride is an established Kondo 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

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

gauge symmetries
.

Emergence

Main article: Emergence

Theoretical understanding of condensed matter physics is closely related to the notion of

collective excitations behave like photons and electrons, thereby describing electromagnetism as an emergent phenomenon.[52] Emergent properties can also occur at the interface between materials: one example is the lanthanum aluminate-strontium titanate interface, where two band-insulators are joined to create conductivity and superconductivity
.

Electronic theory of solids

Main article: Electronic band structure

The metallic state has historically been an important building block for studying properties of solids.

X-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms.[22]: 48 [54] In 1928, Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, known as Bloch'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.

exchange 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 and Lu Jeu Sham proposed the density 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]

Symmetry breaking

Main article: Symmetry breaking

Some states of matter exhibit symmetry breaking, where the relevant laws of physics possess some form of

U(1) phase rotational symmetry.[57][58]

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.[59]

Phase transition

Main article: 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, pressure, or molar 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.

In

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.[60]

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

specific heat, and magnetic susceptibility diverge exponentially.[60] 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.[61]
: 75ff 

The simplest theory that can describe continuous phase transitions is the

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.[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

Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of

conduction
.

Image of X-ray diffraction pattern from a protein crystal.

Scattering

Further information: Scattering

Several condensed matter experiments involve scattering of an experimental probe, such as

keV 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 

nonlinear optical spectroscopy.[61]
: 258–259 

External magnetic fields

In experimental condensed matter physics, external

magnetic 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 60 tesla. 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 the Fermi surface.[70] High magnetic fields will be useful in experimental testing of the various theoretical predictions such as the quantized magnetoelectric effect, image magnetic monopole, and the half-integer quantum Hall effect.[68]
: 57 

Magnetic resonance spectroscopy

The local structure, as well as the structure of the nearest neighbour atoms, can be investigated in condensed matter with magnetic resonance methods, such as electron paramagnetic resonance (EPR) and nuclear 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 the nuclei become the probe of these hyperfine 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 include NMR, nuclear quadrupole resonance (NQR), implanted radioactive probes as in the case of muon spin spectroscopy (SR), Mössbauer spectroscopy, NMR and perturbed 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.

Cold atomic gases

Main article: Optical lattice
The first Bose–Einstein condensate observed in a gas of ultracold rubidium atoms. The blue and white areas represent higher density.

spin liquid ordering.[72][73][43]

In 1995, a gas of

S. N. Bose and Albert Einstein, wherein a large number of atoms occupy one quantum state.[74]

Applications

Computer simulation of nanogears made of fullerene molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale.

Research in condensed matter physics

molecular car, molecular windmill and many more.[79]

In

spintronic qubits using the spin orientation of magnetic materials, or the topological non-Abelian anyons from fractional quantum Hall effect states.[78]

Condensed matter physics also has important uses for biomedicine, for example, the experimental method of magnetic resonance imaging, which is widely used in medical diagnosis.[78]

See also

Notes

  1. ^ 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 1935[18] that a state metallic hydrogen exists at sufficiently high pressures (over 25 GPa), but this has not yet been observed.

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Further reading

External links

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