condensed matter physics

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Condensed matter physics is the field of that deals with the macroscopic and microscopic physical properties of , especially the and which arise from forces between s. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the phase exhibited by certain materials at low , the ic and ic phases of on s of atoms, and the found in ic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the s of , , , and other to develop mathematical models. 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, and the Division of Condensed Matter Physics is the largest division at the . The field overlaps with , , and , and relates closely to and . The of condensed matter shares important concepts and methods with that of and . A variety of topics in physics such as , , , , etc., were treated as distinct areas until the 1940s, when they were grouped together as '. Around the 1960s, the study of physical properties of s was added to this list, forming the basis for the more comprehensive specialty of condensed matter physics. The was one of the first institutes to conduct a research program in condensed matter physics.

# Etymology

According to physicist , the use of the term "condensed matter" to designate a field of study was coined by him and , when they changed the name of their group at the , from ''Solid state theory'' to ''Theory of Condensed Matter'' in 1967, as they felt it better included their interest in liquids, , and so on. Although Anderson and Heine helped popularize the name "condensed matter", it had been used in Europe for some years, most prominently in the journal ''Physics of Condensed Matter'', launched in 1963. 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 politics of the time. References to "condensed" states can be traced to earlier sources. For example, in the introduction to his 1947 book ''Kinetic Theory of Liquids'', 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 condensed matter physics

## Classical physics

One of the first studies of condensed states of matter was by , in the first decades of the nineteenth century. Davy observed that of the forty s known at the time, twenty-six had lic properties such as , and high electrical and thermal conductivity. This indicated that the atoms in 's were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as and could be liquefied under the right conditions and would then behave as metals. In 1823, , then an assistant in Davy's lab, successfully liquefied and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and . Shortly after, in 1869, chemist studied the from a liquid to a gas and coined the term to describe the condition where a gas and a liquid were indistinguishable as phases, and physicist supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures. By 1908, and were successfully able to liquefy hydrogen and then newly discovered , respectively. in 1900 proposed the first theoretical model for a 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 . 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 and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures. In 1911, three years after helium was first liquefied, Onnes working at discovered in , when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value. The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades. , 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."

Drude's classical model was augmented by , , and other physicists. Pauli realized that the free electrons in metal must obey the . Using this idea, he developed the theory of in 1926. Shortly after, Sommerfeld incorporated the into the free electron model and made it better to explain the heat capacity. Two years later, Bloch used to describe the motion of an electron in a periodic lattice. The mathematics of crystal structures developed by , and others was used to classify crystals by their , and tables of crystal structures were the basis for the series ''International Tables of Crystallography'', first published in 1935. was first used in 1930 to predict the properties of new materials, and in 1947 , and developed the first -based , heralding a revolution in electronics. In 1879, working at the discovered a voltage developed across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current. This phenomenon arising due to the nature of charge carriers in the conductor came to be termed the , 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, in 1930 developed the theory of and laid the foundation for the theoretical explanation for the discovered half a century later. Magnetism as a property of matter has been known in China since 4000 BC. However, the first modern studies of magnetism only started with the development of by Faraday, and others in the nineteenth century, which included classifying materials as , and based on their response to magnetization. studied the dependence of magnetization on temperature and discovered the phase transition in ferromagnetic materials. In 1906, introduced the concept of s to explain the main properties of ferromagnets. The first attempt at a microscopic description of magnetism was by and through the that described magnetic materials as consisting of a periodic lattice of that collectively acquired magnetization. The Ising model was solved exactly to show that cannot occur in one dimension but is possible in higher-dimensional lattices. Further research such as by Bloch on s and on led to developing new magnetic materials with applications to devices.

## Modern many-body physics

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 and the . After , several ideas from quantum field theory were applied to condensed matter problems. These included recognition of modes of solids and the important notion of a quasiparticle. Russian physicist used the idea for the wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles. Landau also developed a for continuous phase transitions, which described ordered phases as . The theory also introduced the notion of an to distinguish between ordered phases. Eventually in 1956, , and developed the so-called of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by s in the lattice can give rise to a bound state called a . The study of phase transitions and the critical behavior of observables, termed , was a major field of interest in the 1960s. , and developed the ideas of s and . These ideas were unified by in 1972, under the formalism of the in the context of quantum field theory. The was discovered by , Dorda and Pepper in 1980 when they 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. In 1981, theorist proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance is proportional to a topological invariant, called , whose relevance for the band structure of solids was formulated by and collaborators. Shortly after, in 1982, and observed the where the conductance was now a rational multiple of the constant $e^2/h$. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a solution, named the . The study of topological properties of the fractional Hall effect remains an active field of research. Decades later, the aforementioned topological band theory advanced by and collaborators was further expanded leading to the discovery of s. In 1986, and discovered the first , a material which was superconducting at temperatures as high as 50 s. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role. A satisfactory theoretical description of high-temperature superconductors is still not known and the field of s continues to be an active research topic. In 2009, and researchers at discovered spontaneous electric fields when creating s of various gases. This has more recently expanded to form the research area of . In 2012 several groups released preprints which suggest that has the properties of a in accord with the earlier theoretical predictions. Since samarium hexaboride is an established , 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 , the and the . Theoretical models have also been developed to study the physics of s, such as the , s and the use of mathematical methods of and the . Modern theoretical studies involve the use of of electronic structure and mathematical tools to understand phenomena such as , s, and .

## Emergence

Theoretical understanding of condensed matter physics is closely related to the notion of , wherein complex assemblies of particles behave in ways dramatically different from their individual constituents. 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. Similarly, models of condensed matter systems have been studied where s behave like s and s, thereby describing as an emergent phenomenon. Emergent properties can also occur at the interface between materials: one example is the , where two band-insulators are joined to create conductivity and .

## 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 in 1900 with the , which explained electrical and thermal properties by describing a metal as an of then-newly discovered s. He was able to derive the empirical and get results in close agreement with the experiments. This classical model was then improved by who incorporated the of electrons and was able to explain the anomalous behavior of the of metals in the . In 1912, The structure of crystalline solids was studied by and Paul Knipping, when they observed the pattern of crystals, and concluded that crystals get their structure from periodic of atoms. In 1928, Swiss physicist provided a wave function solution to the with a potential, known as . 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. The , developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a . Later in the 1930s, , and developed the so-called as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for of single particle electron wavefunctions. In general, it's very difficult to solve the Hartree–Fock equation. Only the free electron gas case can be solved exactly. Finally in 1964–65, , and proposed the 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 that is broken. A common example is s, which break continuous . Other examples include magnetized , which break , and more exotic states such as the ground state of a , that breaks phase rotational symmetry. in states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone s. For example, in crystalline solids, these correspond to s, which are quantized versions of lattice vibrations.

## 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 . 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 s, the temperature is set to , and the non-thermal control parameter, such as pressure or magnetic field, causes the phase transitions when order is destroyed by s originating from the . Here, the different quantum phases of the system refer to distinct s of the . 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 . Near the critical point, systems undergo critical behavior, wherein several of their properties such as , , and diverge exponentially. These critical phenomena present serious challenges to physicists because normal 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. The simplest theory that can describe continuous phase transitions is the , which works in the so-called . 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. Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant. 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.

# 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 s, measuring s, and . Commonly used experimental methods include , with probes such as , and ; study of thermal response, such as and measuring transport via thermal and heat .

## Scattering

Several condensed matter experiments involve scattering of an experimental probe, such as , optical s, s, etc., on constituents of a material. The choice of scattering probe depends on the observation energy scale of interest. has energy on the scale of 1 (eV) and is used as a scattering probe to measure variations in material properties such as and . X-rays have energies of the order of 10 and hence are able to probe atomic length scales, and are used to measure variations in electron charge density. s can also probe atomic length scales and are used to study scattering off nuclei and electron and magnetization (as neutrons have spin but no charge). Coulomb and measurements can be made by using electron beams as scattering probes. Similarly, annihilation can be used as an indirect measurement of local electron density. is an excellent tool for studying the microscopic properties of a medium, for example, to study s in media with .

## External magnetic fields

In experimental condensed matter physics, external s act as s that control the state, phase transitions and properties of material systems. (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 . Higher magnetic fields can improve the quality of NMR measurement data. is another experimental method where high magnetic fields are used to study material properties such as the geometry of the . High magnetic fields will be useful in experimentally testing of the various theoretical predictions such as the quantized , image , and the half-integer .

## Nuclear spectroscopy

The , the structure of the nearest neighbour atoms, of condensed matter can be investigated with methods of , which are very sensitive to small changes. Using specific and radioactive , the nucleus becomes the probe that interacts with its surrounding electric and magnetic fields (). The methods are suitable to study defects, diffusion, phase change, magnetism. Common methods are e.g. , , or (PAC). Especially PAC is ideal for the study of phase changes at extreme temperature above 2000 °C due to no temperature dependence of the method.

## Cold atomic gases

trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in . The method involves using optical lasers to form an , 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 . In particular, they are used to engineer one-, two- and three-dimensional lattices for a with pre-specified parameters, and to study phase transitions for and ordering. In 1995, a gas of atoms cooled down to a temperature of 170 was used to experimentally realize the , a novel state of matter originally predicted by and , wherein a large number of atoms occupy one .

# Applications

Research in condensed matter physics has given rise to several device applications, such as the development of the , technology, and several phenomena studied in the context of . Methods such as can be used to control processes at the scale, and have given rise to the study of nanofabrication. In , information is represented by quantum bits, or s. The qubits may 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 qubits, qubits using the orientation of magnetic materials, or the topological non-Abelian s from states. Condensed matter physics also has important uses for , for example, the experimental method of , which is widely used in medical diagnosis.

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