Condensed Matter Physics 2

[Martha Vanschaick]

Thediversity 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 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 more comprehensive specialty of condensed matter physics.[7] The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics.[7] According to the founding director of the Max Planck Institute for Solid State Research, physics professor Manuel Cardona, it was Albert Einstein who created the modern field of condensed matter physics starting with his seminal 1905 article on the photoelectric effect and photoluminescence which opened the fields of photoelectron spectroscopy and photoluminescence spectroscopy, and later his 1907 article on the specific heat of solids which introduced, for the first time, the effect of lattice vibrations on the thermodynamic properties of crystals, in particular the 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]

According to physicist Philip Warren Anderson, the use of the term "condensed matter" to designate a field of study 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,[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'".

One 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.[16] 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.[17][note 1]

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]

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.[35] 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. Soviet 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.[35] 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.[36] Eventually in 1956, John Bardeen, Leon Cooper and 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 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]

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 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.[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 where 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.

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.[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 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 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.[60]

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.[63] 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.

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