Unconventional superconductor
Encyclopedia
Unconventional superconductors are materials that display superconductivity
which does not conform to either the conventional BCS theory
or the Nikolay Bogolyubov
's theory or its extensions.
The first unconventional singlet d-wave superconductor, CeCu2Si2, a type of
heavy fermion
metal, was discovered in 1978 by Frank Steglich
. In the early eighties, many more unconventional, heavy fermion
superconductors were discovered, including UBe13, UPt3 and URu2Si2. In each of these materials, the anisotropic nature of the pairing is implicated by the power-law dependence of the nuclear magnetic resonance
(NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt3 was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.
The first unconventional triplet superconductor, organic material (TMTSF)2PF6, was discovered by Denis Jerome and Klaus Bechgaard
in 1979. Recent experimental works by Paul Chaikin
's and Michael Naughton's groups as well as theoretical analysis of their data by Andrei Lebed have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)2X (X=PF6, ClO4, etc.) organic materials.
High-temperature singlet d-wave superconductivity was discovered by J.G. Bednorz and K.A. Müller
in 1986, who discovered that the lanthanum
-based cuprate
perovskite
material LaBaCuO4 develops superconductivity at a critical temperature (Tc) of approximately 35 K
(-238 degrees Celsius
). This is well above the highest critical temperature known at the time (Tc = 23 K) and thus the new family of materials were called high-temperature superconductors. Bednorz and Müller received the Nobel prize
in Physics for this discovery in 1987. Since then, many other high-temperature superconductors have been synthesized. As early as 1987, superconductivity above 77 K, the boiling point of nitrogen
, was achieved. This is highly significant from the point of view of the technological applications of superconductivity
, because liquid nitrogen
is far less expensive than liquid helium
, which is required to cool conventional superconductors down to their critical temperature. The current record critical temperature is about Tc = 133 K (−140 °C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity.
On the other hand, in recent years other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as the strontium
-ruthenate oxide compounds, but that, like the high-temperature superconductors, are unconventional in other ways (for example, the origin of the attractive force leading to the formation of Cooper pair
s may be different from the one postulated in BCS theory
). In addition to this, superconductors that have unusually high values of Tc but that are not cuprate perovskites have been discovered. Some of them may be extreme examples of conventional superconductors (this is suspected of magnesium diboride
, MgB2, with Tc = 39 K). Others display more unconventional features.
In 2008 a new class (layered oxypnictide
superconductors), for example LaOFeAs, were discovered that do not include copper. An oxypnictide of samarium
seems to have a Tc of about 43 K which is higher than predicted by BCS theory
. Tests at up to 45 teslas
suggest the upper critical field of LaFeAsO0.89F0.11 may be around 64 teslas. Some other iron-based superconductor
s do not contain oxygen.
, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa2Ca2Cu3Ox), at 138 K and is held by a cuprate-perovskite material, possibly 164 K under high pressure.
After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity
, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.
One goal of all this research is room-temperature superconductivity.
-barium
-copper
-oxide
), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.
s are made by mixing oxide
s in stoichiometric quantities and then heating in a furnace at high temperatures in an oxygen-rich atmosphere.
. The mechanism that causes the electrons in these crystals to form pairs is not known.
Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modeling difficult.
measurements and, more recently, by angle-resolved photoemission
and measurements of the microwave penetration depth in a HTS crystal. NMR measurements probe the local magnetic field around an atom and hence reflect the susceptibility of the material. They have been of special interest for the HTS materials because many researchers have wondered whether spin correlations might play a role in the mechanism of the HTS.
NMR measurements of the resonance frequency on YBCO indicated that electrons in the copper oxide superconductors are paired in spin-singlet states. This indication came from the behavior of the Knight shift
, the frequency shift that occurs when the internal field is different from the applied field: In a normal metal, the magnetic moments of the conduction electrons in the neighborhood of the ion being probed align with the applied field and create a larger internal field. As these metals go superconducting, electrons with oppositely directed spins couple to form singlet states. In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane. While this observation by some group supported the d symmetry of the HTS, other groups could not observe it.
Also, by measuring the penetration depth, the symmetry of the HTS order parameter can be studied. The microwave penetration depth is determined by the superfluid density responsible for screening the external field. In the s wave BCS theory, because pairs can be thermally excited across the gap Δ, the change in superfluid density per unit change in temperature goes as exponential behavior, exp(-Δ/kBT). In that case, the penetration depth also varies exponentially with temperature T. If there are nodes in the energy gap as in the d symmetry HTS, electron pair can more easily be broken, the superfluid density should have a stronger temperature dependence, and the penetration depth is expected to increase as a power of T at low temperatures. If the symmetry is specially dx2-y2 then the penetration depth should vary linearly with T at low temperatures. Unfortunately, there was no consensus among researchers with these penetration depth experiments.
Photoemission spectroscopy
also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons. Because the technique is sensitive to the angle of the emitted electrons one can determine the spectrum for different wave vectors on the Fermi surface. However, within the resolution of the angle-resolved photoemission spectroscopy (ARPES
), researchers could not tell whether the gap goes to zero or just gets very small. Also, ARPES are sensitive only to the magnitude and not to the sign of the gap, so it could not tell if the gap goes negative at some point. This means that ARPES cannot determine whether the HTS order parameter has the d symmetry or not.
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
which does not conform to either the conventional BCS theory
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
or the Nikolay Bogolyubov
Nikolay Bogolyubov
Nikolay Nikolaevich Bogolyubov was a Russian and Ukrainian Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and to the theory of dynamical systems; a recipient of the Dirac Prize...
's theory or its extensions.
The first unconventional singlet d-wave superconductor, CeCu2Si2, a type of
heavy fermion
Heavy Fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons. Electrons, a kind of fermion, found in such materials are sometimes referred to as heavy electrons...
metal, was discovered in 1978 by Frank Steglich
Frank Steglich
Frank Steglich is a German physicist.He received the Gottfried Wilhelm Leibniz Prize by the Deutsche Forschungsgemeinschaft in 1986 and a number of other recognitions...
. In the early eighties, many more unconventional, heavy fermion
Heavy Fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons. Electrons, a kind of fermion, found in such materials are sometimes referred to as heavy electrons...
superconductors were discovered, including UBe13, UPt3 and URu2Si2. In each of these materials, the anisotropic nature of the pairing is implicated by the power-law dependence of the nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
(NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt3 was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.
The first unconventional triplet superconductor, organic material (TMTSF)2PF6, was discovered by Denis Jerome and Klaus Bechgaard
Klaus Bechgaard
Klaus Bechgaard is a Danish scientist and chemist, noted for being one of the first scientists in the world to synthesize a number of organic charge transfer complexes and demonstrate their superconductivity, threreof the name Bechgaard salt...
in 1979. Recent experimental works by Paul Chaikin
Paul Chaikin
Paul Chaikin is an American physicist. Professor Paul Chaikin earned his undergraduate degree from Caltech, where he studied under Richard Feynman, and his doctorate from the University of Pennsylvania. He co-wrote Principles of Condensed Matter Physics with T.C...
's and Michael Naughton's groups as well as theoretical analysis of their data by Andrei Lebed have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)2X (X=PF6, ClO4, etc.) organic materials.
High-temperature singlet d-wave superconductivity was discovered by J.G. Bednorz and K.A. Müller
Karl Alexander Müller
Karl Alexander Müller is a Swiss physicist and Nobel laureate. He received the Nobel Prize in Physics in 1987 with Johannes Georg Bednorz for their work in superconductivity in ceramic materials.-Biography:...
in 1986, who discovered that the lanthanum
Lanthanum
Lanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is the first element of the lanthanide series. It is found in some rare-earth minerals, usually in combination with cerium and...
-based cuprate
Cuprate
Cuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...
perovskite
Perovskite
A perovskite structure is any material with the same type of crystal structure as calcium titanium oxide , known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the face centers. Perovskites take their name from this compound, which was first discovered in the Ural mountains of...
material LaBaCuO4 develops superconductivity at a critical temperature (Tc) of approximately 35 K
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
(-238 degrees Celsius
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...
). This is well above the highest critical temperature known at the time (Tc = 23 K) and thus the new family of materials were called high-temperature superconductors. Bednorz and Müller received the Nobel prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...
in Physics for this discovery in 1987. Since then, many other high-temperature superconductors have been synthesized. As early as 1987, superconductivity above 77 K, the boiling point of nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
, was achieved. This is highly significant from the point of view of the technological applications of superconductivity
Technological applications of superconductivity
Some of the technological applications of superconductivity include:* the production of sensitive magnetometers based on SQUIDs* fast digital circuits ,...
, because liquid nitrogen
Liquid nitrogen
Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...
is far less expensive than liquid helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
, which is required to cool conventional superconductors down to their critical temperature. The current record critical temperature is about Tc = 133 K (−140 °C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity.
On the other hand, in recent years other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as the strontium
Strontium
Strontium is a chemical element with the symbol Sr and the atomic number 38. An alkaline earth metal, strontium is a soft silver-white or yellowish metallic element that is highly reactive chemically. The metal turns yellow when exposed to air. It occurs naturally in the minerals celestine and...
-ruthenate oxide compounds, but that, like the high-temperature superconductors, are unconventional in other ways (for example, the origin of the attractive force leading to the formation of Cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
s may be different from the one postulated in BCS theory
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
). In addition to this, superconductors that have unusually high values of Tc but that are not cuprate perovskites have been discovered. Some of them may be extreme examples of conventional superconductors (this is suspected of magnesium diboride
Magnesium diboride
Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...
, MgB2, with Tc = 39 K). Others display more unconventional features.
In 2008 a new class (layered oxypnictide
Oxypnictide
In chemistry, oxypnictides are a class of materials including oxygen, a pnictogen and one or more other elements...
superconductors), for example LaOFeAs, were discovered that do not include copper. An oxypnictide of samarium
Samarium
Samarium is a chemical element with the symbol Sm, atomic number 62 and atomic weight 150.36. It is a moderately hard silvery metal which readily oxidizes in air. Being a typical member of the lanthanide series, samarium usually assumes the oxidation state +3...
seems to have a Tc of about 43 K which is higher than predicted by BCS theory
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
. Tests at up to 45 teslas
Tesla (unit)
The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...
suggest the upper critical field of LaFeAsO0.89F0.11 may be around 64 teslas. Some other iron-based superconductor
Iron-based superconductor
Iron-based superconductors are chemical compounds with superconducting properties. In 2008, led by recently discovered iron pnictide compounds , they were in the first stages of experimentation and implementation...
s do not contain oxygen.
History and progress
- April 1986 - The term high-temperature superconductor was first used to designate the new family of cuprateCuprateCuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...
-perovskitePerovskiteA perovskite structure is any material with the same type of crystal structure as calcium titanium oxide , known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the face centers. Perovskites take their name from this compound, which was first discovered in the Ural mountains of...
ceramicCeramicA ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...
materials discovered by Johannes Georg BednorzJohannes Georg BednorzJohannes Georg Bednorz is a physicist at the IBM Zürich Research Laboratory. He is best known for his role in the discovery of high-temperature superconductivity, for which he shared the 1987 Nobel Prize in Physics.-Life and work:...
and Karl Alexander MüllerKarl Alexander MüllerKarl Alexander Müller is a Swiss physicist and Nobel laureate. He received the Nobel Prize in Physics in 1987 with Johannes Georg Bednorz for their work in superconductivity in ceramic materials.-Biography:...
, for which they won the Nobel Prize in PhysicsNobel Prize in PhysicsThe Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
the following year. Their discovery of the first high-temperature superconductor, LaLanthanumLanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is the first element of the lanthanide series. It is found in some rare-earth minerals, usually in combination with cerium and...
BaBariumBarium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in Group 2, a soft silvery metallic alkaline earth metal. Barium is never found in nature in its pure form due to its reactivity with air. Its oxide is historically known as baryta but it reacts with...
CuOCopper oxideCopper oxide is a compound from the two elements copper and oxygen.Copper oxide may refer to:*Copper oxide , a red powder;*Copper oxide , a black powder...
, with a transition temperature of 35 K, generated great excitement.
- LSCO (La2-xSrxCuO2) discovered the same year.
- January 1987 - YBCO was discovered to have a Tc of 90 K.
- 1988 - BSCCO discovered with Tc up to 107 K, and TBCCO (T=thallium) discovered to have Tc of 125 K.
, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa2Ca2Cu3Ox), at 138 K and is held by a cuprate-perovskite material, possibly 164 K under high pressure.
- Recently, other unconventional superconductors, not based on cuprate structure, have been discovered. Some have unusually high values of the critical temperature, Tc, and hence they are sometimes also called high-temperature superconductors.
After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.
One goal of all this research is room-temperature superconductivity.
Examples
Examples of high-Tc cuprate superconductors include La1.85Ba0.15CuO4, and YBCO (yttriumYttrium
Yttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and it has often been classified as a "rare earth element". Yttrium is almost always found combined with the lanthanides in rare earth minerals and is...
-barium
Barium
Barium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in Group 2, a soft silvery metallic alkaline earth metal. Barium is never found in nature in its pure form due to its reactivity with air. Its oxide is historically known as baryta but it reacts with...
-copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
-oxide
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.
Process
PerovskitePerovskite
A perovskite structure is any material with the same type of crystal structure as calcium titanium oxide , known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the face centers. Perovskites take their name from this compound, which was first discovered in the Ural mountains of...
s are made by mixing oxide
Oxide
An oxide is a chemical compound that contains at least one oxygen atom in its chemical formula. Metal oxides typically contain an anion of oxygen in the oxidation state of −2....
s in stoichiometric quantities and then heating in a furnace at high temperatures in an oxygen-rich atmosphere.
Ongoing research
The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physicsCondensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
. The mechanism that causes the electrons in these crystals to form pairs is not known.
Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modeling difficult.
Possible mechanism
The most controversial topic in condensed matter physics has been the mechanism for high-Tc superconductivity (HTS). There have been two representative theories on the HTS. Firstly, it has been suggested that the HTS emerges by antiferromagnetic spin fluctuation in a doped system. According to this theory, the pairing wave function of the HTS should have a dx2−y2 symmetry. Thus, whether the symmetry of the pairing wave function is the d symmetry or not is essential to demonstrate on the mechanism of the HTS in respect of the spin fluctuation. That is, if HTS order parameter (pairing wave function) does not have d symmetry, then a pairing mechanism related to spin fluctuation can be ruled out. Secondly, there was the interlayer coupling model, according to which a layered structure consisting of BCS-type (s symmetry) superconductor can enhance the superconductivity by itself. By introducing an additional tunneling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter in the HTS as well as the emergence of the HTS. Thus, in order to solve this unsettled problem, there have been numerous experiments such as photoelectron spectroscopy, NMR, specific heat measurement, etc. Unfortunately, the results were ambiguous, where some reports supported the d symmetry for the HTS but others supported the s symmetry. This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc.Previous studies on the symmetry of the HTS order parameter
The symmetry of the HTS order parameter has been studied in nuclear magnetic resonanceNuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
measurements and, more recently, by angle-resolved photoemission
ARPES
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...
and measurements of the microwave penetration depth in a HTS crystal. NMR measurements probe the local magnetic field around an atom and hence reflect the susceptibility of the material. They have been of special interest for the HTS materials because many researchers have wondered whether spin correlations might play a role in the mechanism of the HTS.
NMR measurements of the resonance frequency on YBCO indicated that electrons in the copper oxide superconductors are paired in spin-singlet states. This indication came from the behavior of the Knight shift
Knight shift
The Knight shift is a shift in the nuclear magnetic resonance frequency of a paramagneticsubstance first published in 1949 by the American physicist Walter David Knight.The Knight shift is due to the conduction electrons in metals...
, the frequency shift that occurs when the internal field is different from the applied field: In a normal metal, the magnetic moments of the conduction electrons in the neighborhood of the ion being probed align with the applied field and create a larger internal field. As these metals go superconducting, electrons with oppositely directed spins couple to form singlet states. In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane. While this observation by some group supported the d symmetry of the HTS, other groups could not observe it.
Also, by measuring the penetration depth, the symmetry of the HTS order parameter can be studied. The microwave penetration depth is determined by the superfluid density responsible for screening the external field. In the s wave BCS theory, because pairs can be thermally excited across the gap Δ, the change in superfluid density per unit change in temperature goes as exponential behavior, exp(-Δ/kBT). In that case, the penetration depth also varies exponentially with temperature T. If there are nodes in the energy gap as in the d symmetry HTS, electron pair can more easily be broken, the superfluid density should have a stronger temperature dependence, and the penetration depth is expected to increase as a power of T at low temperatures. If the symmetry is specially dx2-y2 then the penetration depth should vary linearly with T at low temperatures. Unfortunately, there was no consensus among researchers with these penetration depth experiments.
Photoemission spectroscopy
Photoemission spectroscopy
Photoemission spectroscopy , also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance...
also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons. Because the technique is sensitive to the angle of the emitted electrons one can determine the spectrum for different wave vectors on the Fermi surface. However, within the resolution of the angle-resolved photoemission spectroscopy (ARPES
ARPES
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...
), researchers could not tell whether the gap goes to zero or just gets very small. Also, ARPES are sensitive only to the magnitude and not to the sign of the gap, so it could not tell if the gap goes negative at some point. This means that ARPES cannot determine whether the HTS order parameter has the d symmetry or not.