In condensed matter physics, a pseudogap describes a state where the

Fermi surface In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crys ...

of a material possesses a partial

energy gap In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is often known more abstractly as ...

, for example, a

band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ' ...

state where the Fermi surface is gapped only at certain points. The term pseudogap was coined by

Nevill Mott Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. ...

in 1968 to indicate a minimum in the density of states at the Fermi level, ''N''(''E''_F), resulting from

Coulomb repulsion Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...

between electrons in the same atom, a

band gap In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference ( ...

in a disordered material or a combination of these. In the modern context pseudogap is a term from the field of

high-temperature superconductivity High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previou ...

which refers to an energy range (normally near the Fermi level) which has very few states associated with it. This is very similar to a true 'gap', which is an energy range that contains no allowed states. Such gaps open up, for example, when electrons interact with the lattice. The pseudogap phenomenon is observed in a region of the phase diagram generic to cuprate high-temperature superconductors, existing in underdoped specimens at temperatures above the superconducting transition temperature. Only certain electrons 'see' this gap. The gap, which should be associated with an insulating state, only exists for electrons traveling parallel to the copper-oxygen bonds. Electrons traveling at 45° to this bond can move freely throughout the crystal. The

therefore consists of

Fermi arc In the field of unconventional superconductivity, a Fermi arc is a phenomenon visible in the pseudogap state of a superconductor. Seen in momentum space, part of the space exhibits a gap in the density of states, like in a superconductor. This ...

s forming pockets centered on the corner of the

Brillouin zone In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice ...

. In the pseudogap phase these arcs gradually disappear as the temperature is lowered until only four points on the diagonals of the Brillouin zone remain ungapped. On one hand, this could indicate a completely new electronic phase which consumes available states, leaving only a few to pair up and superconduct. On the other hand, the similarity between this partial gap and that in the superconducting state could indicate that the pseudogap results from preformed

Cooper pair In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...

s. Recently a pseudogap state has also been reported in strongly disordered conventional superconductors such as

TiN Tin is a chemical element with the symbol Sn (from la, stannum) and atomic number 50. Tin is a silvery-coloured metal. Tin is soft enough to be cut with little force and a bar of tin can be bent by hand with little effort. When bent, t ...

, NbN, or granular aluminum.

Experimental evidence

A pseudogap can be seen with several different experimental methods. One of the first observations was in NMR measurements of YBa₂Cu₃O_6+''x'' by H. Alloul ''et al.'' and by

specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...

measurements by Loram ''et al.'' The pseudogap is also apparent in

ARPES Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelec ...

(Angle Resolved Photoemission Spectroscopy) and STM (

Scanning tunneling microscope A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986 ...

) data, which can measure the

density of states In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states i ...

of the electrons in a material.

Mechanism

The origin of the pseudogap is controversial and still subject to debate in the condensed matter community. Two main interpretations are emerging: 1. The scenario of preformed pairs In this scenario, electrons form pairs at a temperature ''T*'' that can be much larger than the critical temperature ''T''_c where superconductivity appears. Values of ''T*'' of the order of 300 K have been measured in underdoped cuprates where ''T''_c is about 80 K. The superconductivity does not appear at ''T*'' because large phase fluctuations of the pairing field cannot order at this temperature. The pseudogap is then produced by incoherent fluctuations of the pairing field. The pseudogap is a normal state precursor of the superconducting gap due to local, dynamic pairing correlations. This point of view is supported by a quantitative approach of the attractive pairing model to specific heat experiments. 2. The scenario of a non-superconductivity-related pseudogap In this class of scenarios, many different possible origins have been put forward, such as the formation of electronic stripes,

antiferromagnetic In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...

ordering, or other exotic

order parameter In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

s competing with superconductivity.

References

{{reflist

External links

The pseudogap in high-temperature superconductors: an experimental survey (review article) (1999)

Phase fluctuations and pseudogap phenomena

The Mysterious Pseudogap in High Temperature Superconductivity, an Infrared View (2003)

The pseudogap: friend or foe of high Tc? (Review) (2005)

* ttps://arxiv.org/abs/1501.04154 Pseudogap from ARPES experiment: three gaps in cuprates and topological superconductivity (Review) (2015) Quantum phases High-temperature superconductors Correlated electrons