Pseudogap
Encyclopedia
The term 'pseudogap' was coined by Nevill Mott in 1968 to indicate a minimum in the density of states at the Fermi energy
, N(EF), resulting from Coulomb repulsion between electrons in the same atom, a bandgap in a disordered material or a combination of these. In the modern context pseudogap is a term from the field of high-temperature superconductivity
which refers to an energy range (normally near the Fermi energy
) which has very few states associated with it. This is very similar to a '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 is a zone of the Phase diagram generic to cuprate high-temperature superconductors, existing in underdoped specimens at temperatures above the superconducting transition temperature.
A pseudogap is only observed in hole-doped Cuprate superconductors. And the isotope effect is only emerged on the boundary of phases between superconducting and pseudogap state.
Interestingly, 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 degrees to this bond can move freely throughout the crystal. The Fermi surface
therefore consists of Fermi Arcs forming pockets centered on the corner of the Brillouin zone
. 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 super-conduct. 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 pairs.
Recently a pseudogap state has also been reported in strongly disordered conventional superconductors like TiN and NbN.
(Angle Resolved Photoemission Spectroscopy) and STM (Scanning tunneling microscope
) data, which can measure the density of states
of the electrons in a material.
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 Tc where superconductivity appears. T* of the order of 300K have been measured in underdoped cuprates where Tc is about 80K. 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 non coherent 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 confirmed by a quantitative approach of the attractive pairing model to specific heat experiments.
2. The scenario of a non superconducting related pseudogap
In this class of scenarios, many different origins have been put forward: like the formation of electronic stripes, anti-ferromagnetic ordering, exotic order parameter competing with superconductivity.
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
, N(EF), resulting from Coulomb repulsion between electrons in the same atom, a bandgap 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 superconductivity
High-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...
which refers to an energy range (normally near the Fermi energy
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
) which has very few states associated with it. This is very similar to a '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 is a zone of the Phase diagram generic to cuprate high-temperature superconductors, existing in underdoped specimens at temperatures above the superconducting transition temperature.
A pseudogap is only observed in hole-doped Cuprate superconductors. And the isotope effect is only emerged on the boundary of phases between superconducting and pseudogap state.
Interestingly, 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 degrees to this bond can move freely throughout the crystal. The Fermi surface
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
therefore consists of Fermi Arcs forming pockets centered on the corner of the Brillouin zone
Brillouin zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. The boundaries of this cell are given by planes related to points on the reciprocal lattice. It is found by the same method as for the Wigner–Seitz cell in the Bravais 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 super-conduct. 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 pairs.
Recently a pseudogap state has also been reported in strongly disordered conventional superconductors like TiN and NbN.
Origin
A pseudogap can be seen with several different experimental methods. One of the first observations was in specific heat measurements of YBa2Cu3O6+x by Loram et al. The pseudogap is also apparent in ARPESARPES
Angle-resolved photoemission spectroscopy , also known as ARUPS , is a direct experimental technique to observe the distribution of the electrons in the reciprocal space of solids...
(Angle Resolved Photoemission Spectroscopy) and STM (Scanning tunneling microscope
Scanning tunneling microscope
A scanning tunneling microscope is an instrument for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer , the Nobel Prize in Physics in 1986. For an STM, good resolution is considered to be 0.1 nm lateral resolution and...
) data, which can measure the density of states
Density of states
In solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...
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 Tc where superconductivity appears. T* of the order of 300K have been measured in underdoped cuprates where Tc is about 80K. 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 non coherent 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 confirmed by a quantitative approach of the attractive pairing model to specific heat experiments.
2. The scenario of a non superconducting related pseudogap
In this class of scenarios, many different origins have been put forward: like the formation of electronic stripes, anti-ferromagnetic ordering, exotic order parameter competing with superconductivity.