It also implied that the Hall conductance can be characterized in terms of a topological invariable called Chern number which was formulated by Thouless and collaborators. Laughlin, in , realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a variational method solution, named the Laughlin wavefunction. Thouless was further expanded leading to the discovery of topological insulators. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron—electron interactions play an important role.

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It also implied that the Hall conductance can be characterized in terms of a topological invariable called Chern number which was formulated by Thouless and collaborators. Laughlin, in , realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a variational method solution, named the Laughlin wavefunction.

Thouless was further expanded leading to the discovery of topological insulators. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron—electron interactions play an important role.

In , David Field and researchers at Aarhus University discovered spontaneous electric fields when creating prosaic films [ clarification needed ] of various gases. This has more recently expanded to form the research area of spontelectrics. Theoretical[ edit ] 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 Ginzburg—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. Main article: 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. Electronic theory of solids[ edit ] Main article: Electronic band structure The metallic state has historically been an important building block for studying properties of solids.

He was able to derive the empirical Wiedemann-Franz law and get results in close agreement with the experiments. The Hartree—Fock method accounted for exchange statistics of single particle electron wavefunctions. Only the free electron gas case can be solved exactly. The density functional theory DFT has been widely used since the s for band structure calculations of variety of solids. 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. For example, in crystalline solids, these correspond to phonons , which are quantized versions of lattice vibrations. 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.

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. 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. 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. Such probes include effects of electric and magnetic fields , measuring response functions , transport properties and thermometry. Image of X-ray diffraction pattern from a protein crystal.

Further information: Scattering Several condensed matter experiments involve scattering of an experimental probe, such as X-ray , optical photons , neutrons , etc. 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.

Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes. 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. Using specific and radioactive nuclei , the nucleus becomes the probe that interacts with its sourrounding electric and magnetic fields hyperfine interactions. The methods are suitable to study defects, diffusion, phase change, magnetism.

Common methods are e. Cold atomic gases[ edit ] 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. Ultracold 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.

Bose and Albert Einstein , wherein a large number of atoms occupy one quantum state. It is hoped that advances in nanoscience will lead to machines working on the molecular scale. Research in condensed matter physics [38] [67] has given rise to several device applications, such as the development of the semiconductor transistor , [3] laser technology, [53] and several phenomena studied in the context of nanotechnology.

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.

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