Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the 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.
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
An electron and an electron hole that are attracted to each other by the Coulomb force can form a bound state called an exciton. It is an electrically neutral quasiparticle that exists mainly in condensed matter, including insulators, semiconductors, some metals, but also in certain atoms, molecules and liquids. The exciton is regarded as an elementary excitation that can transport energy without transporting net electric charge.
In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron are free to move within the crystal lattice and serve as charge carriers to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band to the conduction band, then current can flow. Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances having large band gaps are generally insulators, those with small band gaps are semiconductor, and conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.
In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also known as the avoided crossing principle. Polaritons describe the crossing of the dispersion of light with any interacting resonance. To this extent polaritons can also be thought of as the new normal modes of a given material or structure arising from the strong coupling of the bare modes, which are the photon and the dipolar oscillation. The polariton is a bosonic quasiparticle, and should not be confused with the polaron, which is an electron plus an attached phonon cloud.
Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes.
In theoretical physics, a roton is an elementary excitation, or quasiparticle, seen in superfluid helium-4 and Bose–Einstein condensates with long-range dipolar interactions or spin-orbit coupling. The dispersion relation of elementary excitations in this superfluid shows a linear increase from the origin, but exhibits first a maximum and then a minimum in energy as the momentum increases. Excitations with momenta in the linear region are called phonons; those with momenta close to the minimum are called rotons. Excitations with momenta near the maximum are called maxons.
In electromagnetism, Brillouin scattering, named after Léon Brillouin, refers to the interaction of light with the material waves in a medium. It is mediated by the refractive index dependence on the material properties of the medium; as described in optics, the index of refraction of a transparent material changes under deformation.
In condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely related phenomena that arise when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types is aperiodic if copies of these tiles can form only non-periodic tilings.
Paul Joseph Steinhardt is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences.
Dan Shechtman is the Philip Tobias Professor of Materials Science at the Technion – Israel Institute of Technology, an Associate of the US Department of Energy's Ames National Laboratory, and Professor of Materials Science at Iowa State University. On April 8, 1982, while on sabbatical at the U.S. National Bureau of Standards in Washington, D.C., Shechtman discovered the icosahedral phase, which opened the new field of quasiperiodic crystals.
Khatyrkite is a rare mineral which is mostly composed of copper and aluminium, but may contain up to about 15% of zinc or iron. Its chemical structure is described by an approximate formula (Cu,Zn)Al2 or (Cu,Fe)Al2. It was discovered in 1985 in a placer in association with another rare mineral cupalite. These two minerals have only been found at 62°39′11″N174°30′02″E in the area of the Iomrautvaam, a tributary of the Khatyrka river, in the Koryak Mountains, in Anadyrsky District, Chukotka, Russia. Analysis of one of the samples containing khatyrkite showed that the small rock was from a meteorite. A geological expedition has identified the exact place of the original discovery and found more specimens of the Khatyrka meteorite. The mineral's name derives from the Khatyrka zone where it was discovered. Its type specimen is preserved in the Mining Museum in Saint Petersburg, and parts of it can be found in other museums, such as Museo di Storia Naturale di Firenze.
An icosahedral twin is a nanostructure appearing in atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, with twenty interlinked tetrahedral crystals joined along triangular faces having three-fold symmetry. A related, more common structure has five units similarly arranged with twinning, which were known as "fivelings" in the 19th century, more recently as "decahedral multiply twinned particles", "pentagonal particles" or "star particles". A variety of different methods lead to the icosahedral form at size scales where surface energies are more important than those from the bulk.
Hyperuniform materials are characterized by an anomalous suppression of density fluctuations at large scales. More precisely, the vanishing of density fluctuations in the long-wave length limit distinguishes hyperuniform systems from typical gases, liquids, or amorphous solids. Examples of hyperuniformity include all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter.
Brent Fultz is an American physicist and materials scientist and one of the world's leading authorities on statistical mechanics, diffraction, and phase transitions in materials. Fultz is the Barbara and Stanley Rawn, Jr. Professor of Applied Physics and Materials Science at the California Institute of Technology. He is known for his research in materials physics and materials chemistry, and for establishing the importance of phonon entropy to the phase stability of materials. Additionally, Fultz oversaw the construction of the wide angular-range chopper spectrometer (ARCS) instrument at the Spallation Neutron Source and has made advances in phonon measuring techniques.
Sriram Rajagopal Ramaswamy is an Indian physicist. He is a professor at the Indian Institute of Science, Bangalore, and previously the director of the Tata Institute of Fundamental Research (TIFR) Centre for Interdisciplinary Sciences in Hyderabad.
Theo Willem Jan Marie Janssen, better known as Ted Janssen, was a Dutch physicist and Full Professor of Theoretical Physics at the Radboud University Nijmegen. Together with Pim de Wolff and Aloysio Janner, he was one of the founding fathers of N-dimensional superspace approach in crystal structure analysis for the description of quasi periodic crystals and modulated structures. For this work he received the Aminoff Prize of the Royal Swedish Academy of Sciences in 1988 and the Ewald Prize of the International Union of Crystallography in 2014. These achievements were merit of his unique talent, combining a deep knowledge of physics with a rigorous mathematical approach. Their theoretical description of the structure and symmetry of incommensurate crystals using higher dimensional superspace groups also included the quasicrystals that were discovered in 1982 by Dan Schechtman, who received the Nobel Prize in Chemistry in 2011. The Swedish Academy of Sciences explicitly mentioned their work at this occasion.
Dov I. Levine is an American-Israeli physicist, known for his research on quasicrystals, soft condensed matter physics, and statistical mechanics out of equilibrium.
Aperiodic crystals lack three-dimensional translational symmetry but still exhibit three-dimensional long-range order. In other words, they are periodic crystals in higher dimensions. They are classified into three different categories: incommensurate modulated structures, incommensurate composite structures, and quasicrystals.
Freedman, B., Lifshitz, R., Fleischer, J. et al. Phason dynamics in nonlinear photonic quasicrystals. Nature Mater 6, 776–781 (2007). https://doi.org/10.1038/nmat1981
